§ 6. Tachogram Samples.

Changing the load from full to 0 gives an increase in the number of revolutions by 3%, but without any overshoot; the new number of revolutions is established after 1½ sec. Instantaneous application of full load gives an overshoot of 4%, and after a slight over-regulation the new speed is established after 5 sec.

Finally, in Figs. 55—56 are shown tachograms of the newest 2000 kW turbine-dynamo of the Sulzer works, with the new hydraulic governing system¹; the normal speed of the turbine is 1500. As we see, with an instantaneous decrease of load from ¾ to ¹⁄₁₀ and back, the greatest overshoot is 4.5%; the over-regulation observed is quite insignificant; the change in the established number of revolutions is 2.5%; the latter occurs after 4½ sec. under loading and after 6¼ sec. under unloading. The difference in the number of revolutions at full load and at no load is about 3.5%.

In conclusion, we shall present a quite special tachogram, Fig. 57, taken from a 5000 kW V. K. E. turbogenerator in 1913². This tachogram was obtained with the aid of a Siemens & Halske oscillograph, and is in fact a photographic record of the voltage of the exciter machine of the generator, which received excitation from a constant-voltage source—from an accumulator battery, just like the exciter machine itself.

Fig. 57.

In such a case the voltage of the machine varies directly in proportion to the angular speed of rotation.

As indicated in the diagram, when the load is reduced from 5000 kW to 0, the number of revolutions increases by only 3.32%, and after a short while

is set at \(\pm 3.2\%\). Small teeth—the influence of a finite number of coils in the machine winding—do not depend on the uniformity of rotation.

The indicated method undoubtedly deserves attention; unfortunately, the oscillograph is an excessively expensive and complicated instrument, and, moreover, too sensitive for transport.

Chapter II

Measurement of Work

7. The work of a turbine and its measurement.—In contrast to reciprocating machines, with regard to steam turbines one usually speaks only of useful or actual (effective) work.

Although in the theory of steam turbines one also speaks of the indicated work of a turbine, i.e., of the work performed by the steam without deducting mechanical losses, such as: ventilation resistances to the rotation of the turbine wheel or drum, friction in the bearings, the work of auxiliary devices such as oil pumps, etc., nevertheless, in view of the difficulty of measuring these losses, and partly also because in practice it is much more important to know the actually available power of the turbine, the indicated work is usually not determined in tests.

On the contrary, very often, in cases where the turbine is connected to a dynamo machine, interest is taken not in the work of the turbine itself, but in the work of the entire unit, and sometimes its power is even measured in electrical horsepower, i.e. in kW divided by 0.736.

However, this somewhat confusing designation is now almost no longer used. If the matter concerns the turbine itself, then its power is measured in h.p.; if it concerns the entire unit, then in kW. True, at the present time a serious proposal has appeared to replace the unit of work hitherto accepted, \(1\) h.p. \(= 75\) kgf·m/sec, by the kilowatt \(= 102\) kgf·m/sec, and to call it, at least initially, “large horsepower”².

However, until this proposal has been generally accepted, it is better to adhere to the former unit of work—\(1\) h.p.

In view of the fact that steam turbines connected in a single unit with a dynamo machine are the most widespread installation, the measurement of work in kW in this case has its justification; but for the turbine designer it is nevertheless of interest to calculate the work, separating out the loss in the dynamo machine in the form of its output, and also taking into account the work expended on the condenser, i.e. the consumption

energy for the air pump, if there is one, for the pumps for cooling water and for removal of condensate.

Thus, when expressing the work in kW, it should be explained that it includes only the actual, i.e. useful, energy which can be delivered to the network, or also the work expended on the refrigerator. Passing to the turbine itself, one must add to this latter quantity of work, relating to the unit, the losses in the dynamo-machine, i.e. divide by its efficiency.

When directly measuring the power of a turbine by means of brakes or dynamometers, the preceding questions fall away.

Finally, mention should also be made of a method sometimes used of calculating, for better comparability of the steam consumption of turbines with that of similar reciprocating engines, the steam consumption per 1 indicated h.p. In this case they simply multiplied the steam consumption per 1 effective h.p.-hour by 0.90 to 0.93³, i.e. they calculated, by analogy with reciprocating engines, the mechanical efficiency of the turbine as $\eta_m = 0.90$ or $0.93$. This method is, of course, incorrect and cannot be recommended, if only because in modern turbines $\eta_m$ reaches 0.97 and even 0.985. Equally inexpedient is the determination of the indicated power of a turbine in the form $N_i = N_e + N_r$⁴, where $N_r$ is the no-load work, since the quantity $N_r$ is far from constant and varies with the load and with the operating conditions of the turbine; the results of turbine testing must not be tied to accidental circumstances independent of it. For comparability, it is necessary, on the contrary, to express the work of reciprocating steam engines in effective h.p. instead of indicated h.p. And indeed, recently, perhaps partly under the influence of the increasing spread of steam turbines and internal-combustion engines, the designation of the power of reciprocating steam engines also in effective h.p., instead of the previously usual designation in indicated h.p., has been gaining ever wider acceptance.

As regards the methods of measuring the work of turbines, as is already clear from the preceding, they fall into two groups, essentially differing from each other: if the turbine is connected with a dynamo-machine, then its work is determined by means of electrical measurements—current strength and voltage; in all other cases the work is measured either by means of brakes, with destruction of the work, as, for example, in small turbines, or by means of dynamometers, without its destruction, as, for example, in large marine turbines.

8. Measurement and absorption of electrical energy.—In measuring electrical energy, two cases must be distinguished: direct current and alternating current.

Chapter II. Measurement of Work.

In the first case it is sufficient to measure only the current strength \(i\) in amperes and its voltage \(e\) in volts. Their product, \(i \cdot e\), divided by 1000, gives the developed work in kilowatts. In view of the voltage drop when the current passes through the wires, it is not immaterial where it is measured; it is more correct to measure the voltage at the very terminals of the dynamo machine, although often the voltage drop to the distribution board is so small that it may be neglected.

Readings on the voltmeter and ammeter are taken simultaneously every 5 minutes, and sometimes, with a very constant load, every 10 minutes.

In the case of a constant load, its mean value may, for simplicity, be computed as the product of the arithmetical means of the corresponding readings.

With a fluctuating load it is more correct to find its mean value as the arithmetical mean of the products of the corresponding individual readings; although it should be noted that the error from the simplified calculation by the first method is small, rarely exceeding 1%.

In the case of alternating current, the product \(i \cdot e\) must be multiplied by \(\cos \varphi\), where \(\varphi\) is the angle of phase displacement. Its exact determination is accompanied by difficulties, and therefore it is preferred to measure the energy developed by alternating-current machines by means of special instruments—wattmeters—which give the load directly in kilowatts. Wattmeter readings are also taken every 5 minutes.

In Fig. 58 is shown a sample connection diagram for such a test: \(d\) is an alternating-current generator, to whose terminals three networks are connected—first, the main one, into which are connected the ammeter \(a\), the wattmeter \(w\), and the load resistance \(b\), in which the electrical energy is destroyed; then an auxiliary network, into which is connected the special auxiliary resistance \(r\) for the wattmeter, without induction, of several tens of thousands of ohms; finally, a third, very short network for connecting the electrostatic voltmeter \(v\).

Fig. 58.

With such a scheme one must not forget to add to the wattmeter readings the loss of energy developed by the machine and going through the branch

with an auxiliary resistance \(r\). If \(e\) is the voltage of the dynamo, i.e. that measured by means of the voltmeter \(v\), in volts, and \(r\) is the magnitude of the resistance of the rheostat \(r\) in ohms, then the loss of energy in kW is

\[ L = 0.001 e^{2}/r. \tag{1} \]

This correction is usually small, so that for various loads it may be considered constant, being calculated only for the mean normal voltage.

In order to pass to the power of the turbine, the electrical energy developed by the dynamo machine and expressed in kW must be divided by \(0.736\), in order to pass to horsepower, and then divided further by the efficiency \(\eta_{\mathrm{e}}\) of the dynamo machine.

The magnitude \(\eta_{\mathrm{e}}\) is often supplied by the factory that built the dynamo machine; determining it experimentally requires special instruments and instructions and does not fall within the scope of our discussion, but constitutes a separate department of electrical measurements.

Here it should merely be indicated that, when connecting the dynamo machine and all the measuring instruments to it, one must adhere strictly to the very same circuit that was used in determining the value of the efficiency. Thus, the ammeter must be connected in such a way that it also measures the current expended on excitation. In the case of excitation by an external current, for example in alternating-current machines, the energy expended on excitation must be measured separately and subtracted from the developed power before dividing by \(\eta_{\mathrm{e}}\), which is usually determined including the losses for excitation.

Load resistances. After measuring the electrical energy, it must be led away somewhere. Most often it has to be destroyed, by converting it, for example, into heat. Sometimes the energy can be delivered to a network or used for charging a storage battery; however, even in this case part of the current still has to be destroyed, in order to have a means of setting the required magnitude of the load and maintaining it constant for the duration of the given test.

By the words “destroy electrical energy” we mean converting it into some other form of energy and leading it away without use, most often into thermal or chemical energy (decomposition of water). This conversion is carried out by means of special resistances, called, according to their purpose, load resistances.

By construction, load resistances may be divided into resistances made of incandescent lamps, metallic resistances, and water resistances.

Resistances made of incandescent lamps are very convenient, but it is difficult to assemble them for any considerable current strength, since too large a number of lamps is required; and even if there is a stock of old bulbs, their connections and sockets are too expensive.

Chapter II. Measurement of Work. § 8.

A carbon 16-candlepower lamp at 110 volts consumes about 0.5 amp.; at 220 volts, about 0.25 amp. The lamps are connected in parallel. High voltages in the primary circuit also make it difficult to construct a resistance from lamps: at 440 volts it is still possible to connect, in series, two lamps of 220 volts each, but still higher voltages force one to abandon such a resistance.

Finally, at the present time, with the ever-increasing spread of economical metallic lamps, which usually burn until the filament breaks, there will soon no longer be large stocks at stations of replaced carbon lamps that have darkened but have not yet burned out.

Metallic resistances are usually made of iron wire, more rarely of manganin or constantan wire, because of their high cost.

In constructing a metallic resistance, two quantities must be calculated: the magnitude of the resistance \(r\) in ohms and the surface area \(F\) in \(\text{m}^2\) for the radiation of heat.

The magnitude \(r\) is found as the quotient obtained by dividing the voltage \(e\), in volts, by the current strength \(i\), in amperes,

\[ r = e / i. \tag{2} \]

The determination of the dimensions of the wire from the resistance \(r\) thus found is carried out with the aid of the equation

\[ r = c . l / f, \tag{3} \]

where \(l\) is the length of the wire in m., \(f\) the cross-sectional area in \(\text{mm}^2\), and \(c\) the specific resistance.

Taking into account the circular cross-section of the wire with diameter \(d\) mm. and the parallel connection of \(n\) rows of wire, each consisting of a length \(l\) m., equation (3) can be transformed into

\[ r = 1.27 c . l / d^2 . n, \tag{4} \]

For iron \(c = 0.10 \div 0.14\); for manganin and constantan \(c = 0.40 \div .50\).

In view of such constancy and definiteness of \(c\), equation (4) may be written simply, for iron, as

\[ r = 0.15 . l / n . d^2, \tag{5} \]

and for manganin and constantan as

\[ r = 0.55 l / n . d^2. \tag{6} \]

On the basis of observations, for the radiation of heat without excessive heating of the wire, about \(0.14\ \text{m}^2\) per 1 kW is needed, i.e.

\[ F = 0.00014 e . i; \tag{7} \]

incidentally, with good ventilation the area may be considerably smaller; conversely, when ventilation is difficult, it must be larger.

§ 8. Load Resistances.

Substituting for \(F\) its expression in terms of the dimensions of the wire and remembering that \(F\) is expressed in \(\text{m}^2\), \(l\) in m, and \(d\) in mm, we obtain

\[ n . l . d \geq 9{,}045\, e . i . \tag{8} \]

With the aid of equations (4), respectively (5) or (6), and equation (8), one can, by specifying one of the quantities, for example \(d\), find the other two—\(n\) and \(l\).

With proper assembly, the wires may safely be allowed to heat to a dark-red glow.

To reduce the dimensions of the whole apparatus, the wire may be wound into spirals with a diameter \(D\) 10–20 times greater than \(d\). During assembly the spirals must be stretched so that the turns are not too close to one another. For thin wire the pitch should be not less than \(3d\); for thick wire it is better to make it up to \(5d\), even up to \(10d\). Assembly is conveniently carried out by suspending the spirals from a horizontal gas pipe fixed under the ceiling and wrapped in asbestos cardboard.

The setting of the required load and its subsequent maintenance at a constant value, despite the decrease of resistance as the wire heats up—that is, so to speak, the regulation of the load—may be carried out, according to equation (3), in two ways: either by changing \(l\) or by changing \(f\), i.e. according to equation (4), by changing the number \(n\).

For more considerable loads it is necessary to use the second method, connecting the spirals in parallel and providing switches for individual spirals or groups of them, which also makes it possible to change the load rapidly when testing the regulation of the unit.

For more accurate regulation of the load, part of the resistance is made by connecting spirals in series and bringing the connections from individual sections to buttons, over which a sliding contact can move, as in starting resistances. If necessary, for this purpose one may also directly take a ready-made, sufficiently large starting resistance from an electric motor.

Water resistances are more convenient than the preceding ones, especially when testing high-power machines, for which they are easier and cheaper to make. They consist of sheets of roofing iron forming electrodes and immersed in water. To increase the electrical conductivity of the water, whereby a steadier load is obtained, a little sulfuric acid is sometimes added to the water. The drawback of such acidification is the evolution of rather suffocating vapors. If the load resistance is located near the machine, and still more so inside the machine building, for example in its basement, then instead of acid it is better to add to the water a little, up to 1%, common salt or calcined soda; a weak soda solution may readily be brought to boiling. With direct current above 500 volts (with flowing water, from 220 volts) and with alternating current from 1000 volts, plain fresh water may be used directly.

As the water heats up, its resistance falls, and the load increases. In order to prevent boiling of the water and unpleasant steam formation, as well as changes in the load, it is useful to make the water in the resistance flowing, i.e., so that cold water continuously enters from below little by little and more heated water flows away near the upper layers. At high voltages, above 1000 volts, it must be remembered that the water usually comes out with an electric charge, which it does not immediately lose; therefore appropriate measures must be taken to protect from danger persons who may come into contact with it.

As regards regulation of the load when setting it at the beginning of the test, and also for maintaining its constancy while the water is being heated, for this purpose it is most convenient to change the wetted surface of the electrodes and to use one of the following methods: either change the depth of immersion of the plate electrodes, raising them on blocks in order to reduce the load and immersing them to increase it, or, with stationary electrodes, conversely, lower or raise the water level in the reservoir. Especially for increasing the load, when the water is not changed but is only added as it boils away, another method may also be used—to add soda or common salt; even a small increase in the strength of the solution noticeably increases the conductivity, i.e., the load.

In conclusion it may be mentioned that water, especially well water, often contains mineral salts in quantities that noticeably increase its electrical conductivity. Thus, the author once had to work with ferruginous water whose electrical conductivity was several hundred times greater than that of pure water. Having noticed this, the electrodes, two iron sheets, were placed very far apart, more than 100 cm; nevertheless, when they were immersed in this water, such a strong current was immediately obtained that it was as though a short circuit had occurred. Such water must not be used to fill the resistance, but it is very convenient to use it when other, pure water is available: by admitting a larger or smaller jet of strongly conducting water (with a resistance using flowing water), one can regulate the magnitude of the load very conveniently and precisely, much more conveniently and smoothly than by adding soda or salt.

The dimensions of the electrodes may be determined according to the following data: for 1 ampere of current it is necessary to have a surface \(s = 5 \div 15\ \mathrm{cm.^2}\) of the positive electrode and the same amount of the negative electrode, with a distance between the electrodes of about \(80 \div 100\ \mathrm{mm.}\) and with current voltages up to 1000 volts, taking the specific resistance of the water as \(2000\ \mathrm{ohm/cm.^3}\); when the voltage is increased above 1000 volts, the distance between the electrodes should be increased by approximately \(40 \div 50\ \mathrm{mm.}\) for each 1000 volts.

At voltages up to 220 volts it is better to take a large electrode surface, \(s = 20\) and even \(25\ \mathrm{cm.^2/amp.}\), and a distance between them of about 100 mm.

8. Calculation of Load Resistances.

A more exact choice of the magnitude \(s\) depends on the magnitude of the heating of the water and is indicated below, Table 1.

With a more considerable electrode surface it is convenient to divide it into several sheets, placing them in parallel, and to connect each sheet in turn now to one pole, now to the other. In this case, in all the sheets except the two outer ones, both surfaces will operate, and the surface of the intermediate sheets must be entered into the calculation doubled.

Since the electrical energy in a water resistance is converted chiefly into heat, in order to remove it one must, besides the current strength, take into account also the amount of work in kW. Thus, the quantity of water in the tank should be about 100 liters for each 100 kW. Further, the quantity of flowing water depends on what heating of the water it is desired to allow; namely, for 100 kW, the water consumption \(q\), in liters/sec., must be, for the removal of the corresponding heat,

\[ q = 240 / \Delta t, \tag{9} \]

where \(\Delta t\) is the permissible number of °C of temperature rise of the water; \(\Delta t\) is taken from \(30^\circ\) to \(90^\circ\). The magnitude \(q\), and indirectly therefore also \(\Delta t\), also determines the least permissible value of the electrode surface \(s\) per 1 amp. of current. The following Table 1 gives a practically established indication for this dependence.

Table 1.

	30	50	70	90
Temperature rise \(\Delta t^\circ\)C	30	50	70	90
Electrode surface \(s\), cm\(^2\)/amp.	2.8	4.8	8.2	16

Instead of arranging the sheets in rows, they are sometimes rolled up in pairs in the form of concentric cylinders. With such an arrangement of the sheets it is more convenient to devise an appliance for raising and lowering them without skewing; but it requires a greater number of them, since only one side of each is utilized. In order not to impede the motion of the water with such an arrangement of the sheets, holes should be made in them, and rather many of them; the diameter of the holes may be taken as 12–20 mm, the distance between them along the circumference of the cylinder and between the rows as 35–50 mm.

It is sufficient to take sheets 0.5–1.0 mm thick. For permanent use in laboratories and testing stations they are sometimes taken up to 3 mm thick and painted with oil paint. In these cases the tanks are also made riveted of iron and, to avoid corrosion, are well painted with red lead in several coats. At present tanks are also made of reinforced concrete.

At acceptance tests one usually uses ordinary wooden tubs or else wooden boxes of sufficient tightness. A small leakage of water does no harm, since the water must in any case be changed gradually.

When using wooden vessels at high voltages, above 1000 volts, it must be borne in mind that fire (a voltaic arc) may appear from the iron parts, threatening to spoil the vessel and in any event being a source of needless trouble in extinguishing it. It is therefore necessary to take a vessel made of a single piece of wood—a barrel with wooden hoops, or a box fastened with wooden clamps and wedges, without nails.

If the load is regulated by raising and lowering sheets, then they are fastened together by a common wooden frame, or by an iron one on insulators; if by changing the water level, corresponding cocks must be provided in the reservoirs for draining off the water.

If there is a river or pond nearby, the electrodes may be immersed directly in them; but, so that agitation of the water, changing the wetted surface, does not affect the load, the electrodes must be immersed completely in the water, while a more exact regulation of the load is to be effected by means of part of the sheets immersed in a barrel. When using a pond, the electrodes may be made by nailing iron sheets to wooden beams and lowering them directly to the bottom. To prevent them from floating up, stones or bricks must be tied to them.

For carrying out tests with various loads and instantaneous changes of load, it is useful, in addition to varying the wetted surface, to divide the whole resistance into several groups, the wires to which have their own separate switches. Properly, 3 groups are sufficient: one of \(1/2\) load and two of \(1/4\) load each.

Mention may also be made of a resistance construction that is a combination of metal and water resistance and is very convenient, especially for laboratories, because of its compactness: this is a resistance made of manganin or even iron wire wound in a screw line on round sticks, which are placed in a vessel with running water.

The calculation is made as for an ordinary metallic resistance, but in equation (8) the coefficient \(0.045\) may be replaced by \(0.004\); or, instead of calculating the cooling by equation (8), one may simply determine the cross-sectional area of the wires connected in parallel from the permissible maximum current density.

For iron, by specifying the diameter \(d\), the number of wires \(n\) may be found from the current strength \(i\) and from the condition of permissible current density\(^ {16}\)

\[ 36\, n \cdot d^{3.5} = i, \tag{10} \]

\(^ {16}\) Hütte, 21. Aufl., 1911, II, S. 918.

and for manganin and constantan,

\[ 24\, n . d^{3.5} \ge i. \tag{11} \]

The consumption of cooling water is, of course, calculated from the same equation (9) as above.

9. Brakes with Blocks.

If a steam turbine is not connected to a dynamo, then in order to test it under load, and to determine the influence of the conditions of its operation, in most cases it has to be loaded artificially, by means of so-called brakes.

According to their design, brakes may be divided into two essentially different groups: the simpler brakes with the friction of solid bodies, which are modifications and improvements of the ordinary Prony brake, and the so-called hydraulic, or water, brakes. In essence, however, both are devices in which mechanical work is converted by friction into heat, which is discharged uselessly to the outside, most often by means of running water.

Simple brakes are used only for small turbines; for large ones they become too bulky and heavy.

In Figs. 59 and 60 the simplest brake is shown for a 30-horsepower Laval turbine, whose working shaft, after gearing,

Fig. 59.          Fig. 60.

makes 2000 rev./min. So that the blocks do not wear away too quickly, they may be made of hard wood, for example oak. The load is changed by increasing or decreasing the pressure of the blocks; for this purpose the nut \(a\) is turned in the appropriate manner by the handwheels, until the moment of friction at the circumference of the pulley balances the moment of the load \(G\) with arm \(l\). In view of the fact that the moment of friction is continually changing, now increasing and now decreasing, it is useful, in order to maintain equilibrium, to have, in addition to the constant moment \(Gl\), also a correspondingly varying moment. Such is the moment of the tension \(g\) of the spring dynamometer on the arm \(l_2\). In total, the moment of friction is balanced by the difference of the moments,

\[ M = (Gl - gl_2). \]

Equilibrium is maintained owing to the fact that, when the friction increases, the brake is carried along in the direction of rotation of the machine, the tension \(g\) decreases, and \(M\) increases; when the friction decreases, the reverse occurs.

Chapter II. Measurement of Work. § 9.

The cast-iron movable counterweight \(p\) serves to balance the brake with respect to the axis of the shaft. In order to obtain more easily the required pressure of the shoes, stiff spiral springs \(f,f\) are placed under the nuts.

The work of the turbine is converted by friction into heat, which is carried away by the cooling water. In the present design the cooling water is poured directly onto the pulley. To avoid splashing water indoors, the entire brake is enclosed in a sheet-metal casing; the water is poured in a continuous small stream into the funnel \(c\), flows down into the trough \(e\), and from it is discharged through the gutter or pipe \(i\) into the sewer. Enough water is admitted so that it runs off after being heated to \(40 \div 50^\circ\).

The work developed by the turbine, in horsepower, is calculated from the expression

\[ N_e=\frac{2\pi n}{60\cdot 75}\left(Gl-gl_2\right) =0{,}001396\cdot n\left(Gl-gl_2\right). \tag{12} \]

The number of revolutions \(n\) is measured as indicated above; the arms \(l\) and \(l_2\) are measured beforehand with the greatest possible accuracy, and the reading \(g\) is taken as the arithmetic mean of all readings made during the whole test every 5 minutes.

It remains to say something about balancing the proper weight of the brake by means of the counterweight \(p\). For this purpose the load \(G\) and the dynamometer \(g\) are detached from the brake, the nuts \(a,b\) are loosened enough so that a triangular prism, a piece of a file, or, better, a sharper triangular piece of iron can be placed under the upper shoe. The triangular prism is, of course, placed exactly over the axis of the shaft and so that the upper face lightly touches the place of the shoe; then both sides of the brake are balanced by moving the counterweight \(p\), which is then secured in the required position by means of a clamping bolt.

When designing a new brake for other \(N_e\) and \(n\), one must choose the arm \(l\) and, neglecting the quantity \(g l_2\), find from equation (12) the load \(G\), by means of which, having the diameter of the pulley \(d\), or else choose it, for example, from the condition that the circumferential speed \(u\) on it should not be more than \(25\ \mathrm{m/sec}\), i.e.

\[ \frac{\pi D n}{60}<25, \tag{13} \]

then it is no longer difficult, from the strength conditions, to determine both the cross-section of the lever \(l\) and that of the tightening bolts. It remains only to choose the width \(b\) of the wooden shoes.

According to Bach\(^{17}\) it may be found from the condition

\[ b\cdot d\cdot w \geq 75N_e, \tag{14} \]

where the coefficient \(w\) may be taken from \(0.5\) to \(5\), depending on the method of cooling, air or water, and on the pressure per \(1\ \mathrm{cm}^2\) of surface—

\(^{17}\) Hütte, 1911, II, p. 326.

§ 9. Calculation of a Brake with Shoes

of the pulley. With water cooling, high speed, and low pressure, as in steam turbines, one may take \(w = 5\). At the same time, for the sake of the brake’s stability, it is useful to observe the purely practical rule—not to make \(b\) less than 1.5 diameters of the shaft on which the brake pulley is mounted.

According to recently published detailed experiments by H. Schwetje \(^{18}\), for smooth operation of the brake the pressure \(p\), kg/cm\(^2\), between the shoes and the pulley should be taken from the condition

\[ p \leq a/u, \tag{15} \]

where the peripheral speed \(u\) should not be taken less than 3 m/sec, and \(a\) is an empirical coefficient depending on the nature of the wood; for \(u \geq 5\) m/sec, for hard wood—beech and oak—one may take \(a = 150\), for soft wood—poplar—\(a = 100\); for lignum vitae one may take, for \(u \leq 15\) m/sec, simply \(p \leq 25\) kg/cm\(^2\).

As for the coefficient of friction \(\mu\) of the shoes on a cast-iron pulley, when lubricated with oil it varies within the limits \(0.05 \div 0.12\) for hard wood (beech, oak, lignum vitae), rising to \(0.12 \div 0.16\) for soft woods (birch, poplar).

Having specified the corresponding value of \(\mu\), one may find the force \(S\) for which the cross-section of the more highly stressed tie bolt must be calculated,

\[ S = 4\mu \cdot G \cdot l/D, \tag{16} \]

where \(G\) is the previously mentioned brake load in kg on the arm \(l\) in m, and \(D\) is the diameter of the pulley, also in m. It is evident that shoes made of soft wood give a lighter construction of the whole brake, for which reason they should be preferred despite their more rapid wear.

In Fig. 61, p. 46, there is shown a photograph of a brake of a more convenient construction, likewise for a Laval turbine, but of 10 h.p. at \(n = 2400\) rev/min. Its chief difference from the preceding construction as regards cooling is the use of a special pulley with flanges for water cooling—and the extraordinary lightness of the entire device, with the absence of harmful pressure on the bearings of the working shaft under small loads. The symmetry of the construction gives the brake greater strength and balance with respect to the axis of the shaft. It is evident that, with the indicated arrangement of the load \(G\) and the dynamometer \(d\), the arms \(l = l_2\), and equation (12) simplifies, taking the form

\[ N_e = k \cdot n (G - g), \tag{17} \]

where the constant \(k = 0.001396\,l\).

No further explanation of Fig. 61 is needed; one may only add that, to reduce the wear of wooden shoes, it is useful to make them not from boards, but from end-grain oak or

\(^{18}\) H. Schwetje. Beiträge zur Kenntniss der Reibungsverhältnisse zwischen Holz und Eisen, insbesondere bei Bremseinrichtungen für Leistungsmessungen. Berlin, 1912.

birch blocks. For smooth operation the pulley must be lubricated, and rather abundantly. The simplest thing is to install a drip oiler.

The diameter of the tube \(c\), which carries away the water scooped up by the scoop, may be calculated from the quantity of cooling water, assuming a velocity of \(0.3\)—\(0.5\) m/sec. The flow rate \(q\) will be found from the corresponding quantity of heat removed, in liters/sec per 1 indicated horsepower,

\[ q = 0.182 / \Delta t, \tag{18} \]

where \(\Delta t\) is the number of degrees C by which the water temperature rises, which may be taken from \(30^\circ\) to \(40^\circ\).

Fig. 61.

For braking very small turbines, of \(1 \div 10\) hp, as well as for small loads of somewhat larger turbines, and, finally, for alternate braking of machines with pulleys of different diameters, the device shown in Figs. 62 and 63\(^ {18}\) is very practical. This is the so-called band brake, in which a band made of a leather or woven belt, with wooden blocks attached to it to prevent its wearing out, is put by its ends over hooks \(e,e\). The wooden lever \(i\), to which a load is suspended, or the floor on which a support resting on the platform of decimal scales is placed, lies on an iron platform \(a\), provided with four rollers \(b,b\); eyebolts \(c,c\), which move freely in the lever \(i\) and

\(^ {18}\) Z. V. d. I. 1911, p. 1181.

tightening the platform \(a\) toward it by means of the springs \(d,d\). In the lever \(i\) an iron or bronze bushing \(f\) is fitted, serving as a nut for the spindle \(g\); by turning the latter by the flywheel \(h\), the band is tightened to the desired degree.

The brake pulley must be water-cooled, as in Fig. 61. Its surface, for smooth operation, must be lubricated, preferably continuously, by means of an oil can.

Figs. 62 and 63.

When suspending the weight from the lever \(i\), one must, of course, attach to it also a spring dynamometer, which takes up the inevitable oscillations, and whose mean reading is simply subtracted from the magnitude of the load; provided, of course, that the point of application of the weight and of the dynamometer is the same, as in Fig. 61. In addition, to the magnitude of the load must also be added the entire weight of the unbalanced end of the lever \(i\), found by direct weighing on decimal scales with the above-mentioned placement of a triangular prism under the brake.

The brake described makes it possible to apply and measure the very smallest load, if the band is released or almost released and the end of the lever \(i\) is balanced at least in part.

The dotted portions of the circumference under the rollers show the applicability of one and the same brake to pulleys of very different diameters, for which it is only necessary to change the length of the band.

10. Water brakes.—For fairly considerable power, it is expedient to replace the friction of solid bodies by the friction of a fluid, internal friction as well as friction against solid bodies.

In Figs. 64 and 65 is shown a water brake designed by Prof. Stumpf⁵: on the end of the extended turbine shaft \(A\)

Chapter II. Measurement of Work. § 10.

fastened, by means of a steel sleeve, to two iron disks \(D,D\); a cast-iron casing enclosing them hangs on the fixed axle \(B\), about which it can rotate freely; the axle \(B\) is fixed in the stand \(I\); in order to increase the friction between the two halves of the casing, the intermediate disk \(H\) is clamped. A lever \(L\), made of box iron, is attached to the casing, and to its end is fastened a strut \(S\), ending in a knife-edge resting on the platform of decimal scales; the lever \(L\) must stand strictly horizontal, which is checked with a level. Water enters through a flexible pipe, the flange of which is bolted to flange \(C\), and exits through a similar pipe bolted to flange \(E\).

Drawings 64 and 65.

The disks \(D,D\) and \(H\) are made of 10-millimeter iron and are provided with a row of holes, partly in order to increase the resistance to rotation and partly in order to equalize the axial pressures; for the latter purpose the opening \(F\) communicates, by means of gas pipes not shown in Drawings 64 and 65, with a similar opening on the other side of the casing. It was intended to use the opening \(G\) for observing the motion of the water, but, owing to the excessively strong splashing of the water, it had to be closed.

To change the load, it is necessary to change the quantity of water in the casing; for this purpose one may proceed in two ways: either to reduce to a greater or lesser degree the discharge of water at \(E\), or to change the quantity of water supplied at \(C\). In addition, in order to obtain the same load at different numbers of revolutions, the brake was provided with interchangeable disks \(D,D\), of diameters 800, 900, and 1000 mm.

The brake was used for numbers of revolutions from 1000 to 4000 per minute, giving, as desired, a load from 200 to 2000 h.p.

The power of the machine when loaded by this brake is computed from the expression

\[ N_e=\frac{2\pi \cdot L \cdot P \cdot n}{60.75}=0.00279\,P.n, \tag{19} \]

§ 10.

Water Brakes

where, for the given brake, the arm \(L = 2000\) mm = 2 m, \(P\) is the pressure in kg of the knife on the platform of the decimal scales, and \(n\) is the number of revolutions per minute.

The sensitivity of the brake is expressed approximately by \(\pm 0.33\) kg, which gives, for the smallest pressure of 46 kg at \(N_e\) of about 200 h.p., an error of only \(\pm 0.7\%\); at a greater load the error becomes still smaller.

If axle \(B\) is provided with ball bearings, then the sensitivity of the brake increases several more times, although this will scarcely even be required.

For calculating the dimensions and the number of disks when designing another brake of this type, one may rely on the following equation, which gives the relation between the power \(N_e\), the diameter of the disks \(D\), their number \(i\), and the number \(n\) of revolutions per minute,

\[ N_e = i \cdot C \cdot D^a \cdot n^b, \tag{20} \]

where, for the brake described, the following were found: the constant \(C = 2.127 \cdot 10^{-17}\), \(a = 5.366\), \(b = 2.66\). Although, with the internal outline of the casing, its capacity, etc., the quantities \(C\), \(a\), and \(b\) must vary, they will not do so to such an extent that equation (20) could not be used, bearing in mind the above-mentioned methods of regulating the power. The water consumption may be calculated by the equation (18) indicated above, allowing \(\Delta t\) from \(40^\circ\) to \(60^\circ\)C.

In operation the brake is very good, obedient, quiet, and easily regulated. Its only drawback consists in the fact that its established state, i.e., the corresponding constant temperature of the water in it, is not reached quickly.

It is further advisable to provide the casing with supports on both sides, as will be seen in the following design. With one-sided suspension the sensitivity of the brake is less, and it sometimes goes into a strong oscillatory motion.

In Figs. 66 and 67 an even more powerful brake of the same type is shown, for 3000 h.p. at only 600 rev./min.²⁰) In addition to increasing the diameter to 2000 mm, we see another 6 disks rotating in separate chambers. The thickness of the iron disks is 20 mm; in order to avoid axial shocks they are aligned as carefully as possible with respect to flatness and perpendicularity to the axis of rotation; the disks have no holes. The cast-iron casing rests on two supports with ball bearings. The distance between the walls of the casing and the disks, both from the sides and around the circumference, is 50 mm.

The shaft, to which the disks are fastened, passes freely through openings in the casing, which are closed by rings of thin sheet metal to prevent splashing of the water, and rotates in two bearings. It is connected with the turbine by means of a rigid coupling. Water is supplied—

²⁰) Z. V. d. I. 1906, p. 1313.

V. Malyšev.—Testing of Steam Turbines.

Chapter II. Measurement of Work. § 10.

...passes through the regulating valves into two funnels arranged at the side, passes along the double bottoms of the casing into channels located between two adjacent chambers and leading it to the shaft, and, through the openings \(c,c\), enters both chambers and is then thrown back toward the circumference by centrifugal force. The water is discharged from each chamber separately through valves in open streams; its temperature may be brought up to \(70\div 80^\circ\text{C}\), but not higher, since steam formation impairs the smooth operation of the brake.

Fig. 66.

The torque transmitted to the casing of the apparatus can be measured either by means of decimal scales, or by means of spring or hydraulic dynamometers with the manometer \(A\) in Fig. 67. As a check, one may calculate the heat carried away by the water, measuring the water consumption and the average rise of its temperature, and determine the number \(N_e\) of effective horsepower, remembering that the work of 1 effective horsepower in 1 hour is equal to 632.3 heat units. Usually \(N_e\), found from the quantity of heat carried away by the water, is somewhat less than that found by means of the scales, owing to the unavoidable loss by the casing of a certain part of the heat through radiation.

§ 10. The Brakes of Stumpf and Olden.

To regulate the magnitude of the absorbed work, it is necessary, as in the preceding brake, to vary the opening of the two inlet or outlet water valves with which each chamber is provided at the bottom.

Openings I—VII were made for connecting manometers, the readings of which, at one and the same number of revolutions, depend on the quantity of water contained in the brake, i.e., on the magnitude of the load. At \(n = 602\) rev./min. and \(N_e = 3040\) h.p., the pressures increase almost according to the law of a straight line from \(p_{\mathrm{VII}} = 0.2\) to \(p_{\mathrm{I}} = 2.2\) atm. gauge.

Drawing 67.

To increase the limiting load of the turbine, it is perhaps possible to provide the disks with openings; but then the possibility is not excluded that certain difficulties may arise owing to irregularities in the unfinished cast-iron walls of the casing. This, however, can be helped by lining them with smooth sheet metal or by making them of sheet iron.

For accurate and reliable regulation of the load and elimination of any axial pressure, one may recommend the arrangement of Olden’s brake according to the scheme in Drawings 68 and 69: the immovable partitions have sufficiently large openings \(a\) at the cylindrical surface itself, owing to which the pressures and free levels in all chambers are establi—

are made strictly identical. For coarse stepwise regulation of the load, corresponding ones of the valves \(e\) are opened, whereby the corresponding water level is established. For finer regulation it is possible, by slightly closing this valve, to increase the water content and to set its level between this valve and the next one nearest to the shaft.

Drawing 68 and 69.

With stepwise regulation by completely opening the valves, and with their flow cross-section sufficient in comparison with the cross-section of the inlet valve, fluctuations of the water pressure before the latter do not affect the load of the brake. When regulating simultaneously by throttling the inlet, it is necessary that the water pressure before the inlet valve be sufficiently constant. To reduce the unavoidable fluctuations of pressure before the inlet, it is useful to throttle the water with the inlet valve; and in order that the supply of water should not be excessively small, and, consequently, that the latter should not heat up too much, it is useful to admit the water through 2–3 valves opened only slightly.

For braking turbines that are not especially large, one may conveniently use Ehermann’s spring device, drawings 70 and 71⁶).

The brake itself consists, similarly to the preceding designs, of a cast-iron casing \(a\), freely turning on two supports \(b,b\), with 4–6 iron disks about 500 mm in diameter rotating inside it. On the inner cylindrical surface of the casing there are blades which can be turned from outside. By changing the angle of rotation of the blades, the load can be regulated within considerable limits.

The torque transmitted to the brake casing is taken up by means of a lever formed from two converging iron strips \(c,c\), fastened at one end by bolts to the casing, and at the other fastened together by the same bolts, with an iron spacer placed between them, to which the lower end of the screw spring \(d\) is attached. The upper end of the spring \(d\) is moved by means of the screw \(e\), screwed by a handwheel into a nut formed in the crosspiece \(g\). Locknuts serve to secure the screw \(e\)

with the instrument vibrating during operation. The crossbar \(g\) is fastened to uprights made of two pieces of channel iron. To the end of the lever \(c,c\), by means of a lever transmission, is connected the pointer \(h\), which indicates, on an enlarged scale, the deviations of the lever from its mean position and thereby ensures its accurate setting in this position. The extension of the spring is indicated by a scale along which the pointer \(h\) moves; this pointer is attached to one of the two channel-section uprights. This scale is obtained by graduation through the direct suspension of loads \(p\) from the end of the lever with an arm \(l = 857\) mm, which is also introduced into the calculation when determining the work of the turbine.

Drawings 70 and 71.

During the test of the turbine, having tightened the spring to the desired amount according to the scale, the load is regulated by turning the above-mentioned blades, or by the water consumption, so that the pointer shows the mean position of the lever.

At \(n = 3000\) rev./min., with such a brake one can obtain a load of up to 350 h.p. In operation it is convenient, although somewhat less accurate than when the end of the lever acts on a platform of decimal scales. Namely, with a scale length of about 150 mm \(= 100\) kg, the accuracy of setting the spring indicator may be taken as about 0.5 mm, which at \(n = 3000\)

corresponds to about 1.2 h.p. With loads above 120 h.p. this is equivalent to an error of \(\pm 1\%\), and at \(N_e = 240\) and above, even only \(\pm 0.5\%\); but at smaller loads it gives a fairly appreciable error.

For braking machines of great power, especially those rotating with a moderate number of revolutions, such as, for example, modern marine turbines, which themselves make from 600 to 1200 r.p.m., while the speed of the propeller shaft after the gearing that reduces the number of revolutions is only 120 to 300 r.p.m., the water brakes described, with smooth disks, become too bulky. In these cases it is useful to provide both the rotating and the stationary parts of the brake with devices that increase the resistance to rotation, more precisely, to the motion of the water.

One of the oldest designs, first proposed as early as 1877, then repeatedly modified and now brought to a considerable degree of perfection, is the Froude brake.

The idea of its construction may be explained from Drawings 72 and 73: the side walls of the casing, Drawing 72, bolted together from three castings, form, together with the wheel rotating inside it, which is bolted together from two castings, two annular spaces of elliptical cross-section; the walls of the casing and of the wheel are provided with flat ribs inclined at \(45^\circ\) to the plane of rotation and toward it, as is seen from Drawing 73, which represents part of a cylindrical section in developed form. The resulting pockets \(d,d\) serve to increase the resistance to the displacement of the water. Water enters under a small head through a flexible pipe into the casing, into the annular space \(a\); from there, through a series of openings not shown in Drawing 72, into the cavity \(b\) of the wheel, then through the passages \(c,c\), bored through the thickness of the ribs, into the centers of the pockets \(d,d\). Under the action of centrifugal force the water enters the annular cavity \(e\), from which it flows downward after passing through a special regulating cock. The magnitude of the load depends on the quantity of water contained in the apparatus,

§ 10. Froude Water Brake.

For the brake to operate smoothly, the air accumulating in the pockets must be removed; this is done by means of channels \(f,f\), drilled in the ribs of the casing, annular channels \(g,g\), and outlet \(h\) with a small cock, opened as required.

In Figs. 74 and 75 the external view of such a brake is shown; \(a\) is the water inlet, \(b\) the outlet, \(c\) the outlet regulating cock, \(d\) the funnel into which the spent water flows, \(e\) the safety valve;

Figs. 74 and 75.

\(f,f\) are the coupling halves for connection to the shaft of the machine under test; \(g\) are weights consisting of a row of cast-iron disks and acting on the arm \(l = 3500\) mm; \(h\) is a movable weight for finer adjustment of the load; \(i\) is the counterweight balancing the brake’s own weight; \(k\) is an oil dashpot with a spring connection for smoother operation.

To increase sensitivity, the casing rests on rollers \(m,m\), whose axles, in turn, rotate in ball bearings; \(n\) is a flexible pipe.

In the brake shown in Figs. 74 and 75, both the wheel and the casing are made of steel, which makes it possible to subject it to work up to 5080 h.p. at 350 rpm.

In Fig. 76, p. 56, the curve of the greatest power of this brake at various speeds is presented. At point \(a\) the curve has a break, and above it the torque remains constant.

In less large brakes the casing is also made of cast iron, and the wheel of the same steel or of bronze. Regulation is carried out either by inserting tin disks between the wheel and the casing, reducing the resistance to rotation of the wheel, or by reducing the quantity of water in the brake.

The cost of Froude brakes is not especially high, from 2 to 4 rubles per h.p., reckoned by the greatest power at the highest number of revolutions for the corresponding type, but their dimensions are rather bulky, as is seen from Figs. 74 and 75.

Sometimes a centrifugal water pump may be used as a brake, forcing the water to circulate from the discharge ...

of the discharge back into the suction side, and to place between them only a regulating valve. Of course, in order to maintain the established temperature of the water, part of it has to be continuously let out and replaced with cold water.

Fig. 76.

The design of the Rateau brake, Figs. 77 and 78⁷, is a modification and improvement of the preceding instrument. The wheel \(a\) of the centrifugal pump is keyed onto the shaft, onto the end \(b\) of which is fitted a semi-elastic coupling for direct connection with the steam turbine. The casing is supported on two ball bearings \(c,c\); friction in the glands \(d,d\) does not affect the accuracy of the instrument’s readings, since it enters into the measured torque. The cylindrical slides \(e,e\), turned from the outside by means of worm gears and handwheels \(f,f\), regulate the circulation of the water, which from the wheel \(a\) enters the annular diffuser \(g\), and from it, through two symmetrical annular channels \(h,h\), passes again into the suction guide apparatus of the pump. Fresh cold water is supplied by means of the auxiliary centrifugal pump \(i\) and through the regulating cocks \(j,j\), while the heated water flows upward, together with air, through the openings \(k,k\) and the regulating cocks, not shown in Fig. 77. Incidentally, fresh water from the pump can also enter along the hollow shaft of the instrument.

Measurement of the torque is carried out by means of the lever \(l\), a hardened knife-edge on the end of which presses on the right arm of the balance beam

$m$; onto the left arm, on the hook $h$, weights are suspended, which, owing to this arrangement, are made 5 times lighter; the engagement of the rocker $m$, when it is positioned as in Fig. 78, with the projection on the casing near the left end of the rocker prevents a dangerous overturning, possible during direct hanging in the event of a sudden surplus of turbine power; $g$ is a spring dynamometer for imparting stability to the apparatus, equalizing and taking account of small fluctuations of the load, and $p$ is a small oil cataract. In the calculations it is, of course, necessary to subtract from the magnitude of the acting loads the weight of the unbalanced arm $l$, determining it by direct weighing on scales.

Figs. 77 and 78.

The indicated brake absorbs work $N_e = 800$ hp at $n = 3800$ to $4000$ rev./min.

The brake operates quite calmly and keeps the load so constant that Rateau determines, by means of it, from the heat carried away, ...

the water, the mechanical equivalent of heat \(E\), and obtained for it, on the average, a value not differing from the accepted \(E = 427\).

In Fig. 79 is shown, at \(1/25\) natural size, a Râteau system brake, built by the Brest Works in Nantes for testing turbines of 10,000 h.p. at 650 r.p.m.,⁸ a counter-mine-carrier Furieux and

Fig. 79.

Foi. Since there was not enough steam in the workshops for testing these turbines, it was necessary to carry out the tests after installing the turbines on the ships. The brake shaft was connected to the turbine shaft, the propeller shaft and auxiliary engine having been removed. Since the dimensions of the room were limited, the brake had to be very compact, and the moment measurement had to be taken upward, to the deck, Fig. 80. The outside diameter of the brake is only 1.5 m; the wheel diameter is 1200 mm; the length of the lever transmitting the torque to the scales is only 1800 mm. In order to reduce the weight \(p_1\), which balances this torque, in addition to the upper lever \(c\) with a ratio of arms \(1:10\), an intermediate lever \(b\) with a ratio of arms \(2:25\) was also included, so that as a result the weight \(p_1\), neglecting the tension of the dynamometer \(p_2\), is only \(1/125\) of the tensile force of the tie-rod \(a\).

The wheel of this brake is unsymmetrical—the water enters it from only one side; this gives an axial force that replaces the axial component from the propeller and balances the axial pressure of the steam turbine. To reduce and regulate this axial force, the rear annular part of the wheel, bounded by cylindrical ribs, can be supplied, through a special pipe with valves, with the full or partial pressure in the discharge chamber of the brake. The wheel

§ 10. Râteau Water Brakes

was made, as in the preceding brake, of bronze, although it could also have been cast from steel.

The load is regulated in the same way as in the preceding design. In Fig. 81 are shown the results of testing a turbine of 8000 hp at 650 rpm. The dotted curves delimit the range of application of this brake; the left-hand curve corresponds to the greatest—

the loads with the fully open cylindrical gate valve \(e\); the right-hand curve—the minimum loads with the gate valve \(e\) closed. Fig. 81 shows that the range of application of the brake embraces very different loads and numbers of revolutions, and that, within especially wide limits, up to tenfold, the load can be varied at one and the same number of revolutions.

The curves drawn with solid lines give the values of the loads obtained at different numbers of revolutions of the turbine at the corresponding constant initial steam pressures; the figures in kg/qcm entered in Fig. 81 indicate the absolute steam pressures before the last stage of the turbine, and it should be noted that in marine turbines steam can be admitted into different stages in order to attain the most economical consumption at a given speed of the vessel. These curves have a parabolic form, as is required by theory.

In conclusion, it may be mentioned that, when working with this brake at large loads, the steam consumption proved to be higher than that which can be calculated theoretically, and much higher—by as much as 8–10%—whereas in land turbines the contrary is usually observed. This unexpected phenomenon must be explained by the large quantity of moisture entrained by the steam when marine boilers are forced, which increases the apparent steam consumption measured by the condensate led away from the surface condenser.

Finally, Figs. 82–84 show a brake absorbing 6000 h.p. at 300 rev./min.,⁹ built by the American firm Westinghouse & Co. in Pittsburgh. The distinctive feature of this brake is that its parts, which convert mechanical work into heat, are made

Figs. 82 and 83.

after the pattern of the blades of reaction steam turbines. It should be noted that this brake was built by the works after the model of brakes used by it for testing steam turbines of lower power.

§ 10. Westinghouse Water Brake.

The small number of revolutions of the brake is explained by the fact that it was connected not directly to the steam turbine, which made 1500 rev./min., but to the propeller shaft after a special gear transmission, introduced to improve the efficiency of the propeller. The brake was built specially to determine the mechanical efficiency of the indicated transmission, which proved to be 98.5%, and, in its turn, proved to be very sensitive and accurate.

The brake consists of a cast-iron drum \(a\), wedged on the shaft, with 10 rows of turbine blades fastened on its surface. As may be seen from the cylindrical developed section, Fig. 84,

Fig. 84.

in order to balance the axial pressure, the blades in the two halves of the drum are inclined in different directions; the axial width of the blades is 22 mm, their height (length) 125 mm. Instead of guide apparatus, between the rows of blades there are flat strips \(b,b\), of section \(25 \times 8\) mm; the strips opposite the middle of the drum are made three times wider. Cast-iron rings \(c,c\), provided with 24 radial ribs \(d,d\) each, are screwed to the ends of the drum. Similar ribs \(e,e\) are also cast into the channels of the casing. The casing is made of two halves, bolted together along the horizontal plane of division, after the manner of steam turbines. The casing is suspended on the shaft by means of bearings \(f,f\), lubricated with oil supplied by a special pump under a pressure of about 0.7 kg/cm².

Water is supplied to the brake through branch pipes \(g,g\), entering them through flexible tubes; it is then thrown toward the middle plane of the drum, emerges through openings \(n\), Fig. 84, onto its outer surface, divides into two streams and passes along the rows of blades in both directions, toward the edges of the drum, then through the channels with ribs \(e,e\) again enters the inside of the drum and repeats its circuit.

The hot water is gradually removed through branch pipes \(h,h\), and part of it escapes in the form of steam through branch pipes \(i,i\).

In order that the pressure on the decimal scales should not be too great, notwithstanding the comparatively small length of the casing lever,

pressure is expediently transmitted to the scales by means of an intermediate lever \(k\), Figs. 83 and 85, consisting of an I-beam, resting at one end on a steel prism lying on decimal scales, and at the other on a prism lying on a fixed support. The lever from the brake casing rests on the lever \(k\), of course also by means of a prism. The ratio of the arms \(l:(l_1+l)\) may be taken as 1:4 or 1:5.

Fig. 85.

In Fig. 85, \(s\) is a gear transmission reducing the number of revolutions of the turbine \(t\), equal to 1500 per minute, to 300 rev./min. of the brake \(r\).

In conclusion it may be noted that this design is one of the most compact. Thus, for example, the outside diameter of the wheel, including the blades, is only 1870 mm, and its width 850 mm, and this for 6000 h.p. at only 300 rev./min., whereas the brake according to Fig. 66, with approximately the same dimensions at \(n=300\) rev., can give a load of not more than 400 b.h.p.

11. Torsion indicators. General remarks.—Torsion dynamometers, or, as they are now usually called, torsion indicators, are based on measuring the angle of twist of a shaft transmitting a more or less constant torque.

This method of measuring work was proposed and first applied in the middle of the last century by Hirn.

Simple in concept, it nevertheless presents considerable practical difficulties, which may be considered to have been eliminated only during the last 7–10 years, and then fully only for uniform rotation, as, for example, in steam turbines or electric motors.

This method is based on the fact that, between the angle of twist and the torque, for all grades of iron and steel, there exists a strict proportionality. If \(\varphi\) is the angle of twist in angular units, \(M\) the torque in kg·cm, then for a given shaft

\[ \varphi = k \cdot M, \tag{21} \]

where the constant is

\[ k = L / G \cdot \theta, \tag{22} \]

\(L\) is the length of the shaft in cm on which the angle of twist is measured, \(G\) is the modulus of shearing elasticity in kg/cm\(^2\) of the shaft material, \(\theta\) is the polar mo-

§ 11. Torsion Indicators.

the moment of inertia, in cm\(^4\), of the cross-section of the shaft, assumed to be completely cylindrical.

Knowing \(M\), it is not difficult to find the corresponding work \(N_e\), etc., for which it is necessary only to know also the number of revolutions \(n\), and then

\[ N_e = M \frac{2\pi \cdot n}{60.75} = 0.001396\, M \cdot n . \tag{23} \]

The angle of torsion \(\varphi\), or, what is the same thing, the magnitude of the arc of torsion at a certain radius \(R\), is measured during the test; the quantities \(L\) and \(\Theta\) for the given shaft may be regarded as known, so that, in order to determine the torque \(M\), it is necessary only to know also the modulus of rigidity \(G\).

The quantity \(G\) can be found quite accurately by experiment with the aid of test shafts, or, still better, in the case of shafts that are not very thick, on the actual shaft itself.

For the materials at present used for shafts the quantity \(G\) varies very little. Thus, according to Frahm’s communication of 1902\(^ {25}\), 9 test shafts of Siemens-Martin steel from three different works gave, with very small deviations of the individual figures, the value \(G = 828000\) kg/cm\(^2\). The diameter of the shafts was 60 mm, the breaking load 40–47 kg/mm\(^2\) at an elongation of more than 20%. Two other shafts of the same material, but with a diameter of 175 mm, a breaking load of 44 to 50 kg/mm\(^2\), and an elongation of more than 20%, gave \(G = 820200\) kg/cm\(^2\) and \(G = 838900\) kg/cm\(^2\), on the average 829600 kg/cm\(^2\). The more considerable deviation from the mean value, amounting nevertheless to only about 1.1%, is explained by the fact that both shafts were made from different parts of one and the same ingot, which, as is known, have different structures.

Further, 4 shafts of crucible steel, tested in 1904 by Föttinger\(^ {26}\), gave on the average \(G = 828800\) kg/cm\(^2\), with the greatest deviation of the individual figures being 0.45%; the diameter of these shafts was 160 mm; the shafts were made from different ingots.

Finally, 12 shafts with diameter \(D = 250\) mm, with an internal bore, and 4 shafts with \(D = 273\) mm, also hollow (unfortunately, the diameters of the internal bore are not indicated), of Siemens-Martin steel, manufactured and tested at English works, gave, according to B. Tomkinson\(^ {27}\), on the average \(G = 847100\) kg/cm\(^2\), the deviations from the mean value being within \(\pm 1.4\%\). The \(G\) of these English shafts is only 2–3% greater than the \(G\) of the German shafts indicated above, which may partly be explained by the fact that the shafts were hollow; besides, the measurement of the internal diameter is associated with particularly great accuracy.

\(^ {25}\) Z. V. d. I. 1902, S. 801.
\(^ {26}\) Forsch. H. 25, 1905, S. 53.
\(^ {27}\) Trans. Inst. Nav. Arch., 1910, vol. LII, p. 184.

To give an idea of the quantities \(\varphi\) subject to measurement, the following example may be cited: the shaft of a marine turbine developing, at \(n=600\) rpm, \(N_e=5000\) h.p., has a diameter of 220 mm. Over a length \(L=10\) m the angle of twist is \(\varphi=0.0242\), or \(1^\circ13'12''\). If the twist is measured by the length of the arc on the circumference of the shaft, this corresponds to \(s=2.66\) mm.

Accurate measurement of such small quantities constitutes one of the principal difficulties in using this method.

Without dwelling on the older methods of measurement, although some of them have yielded quite satisfactory results, let us turn to modern methods and instruments.

First of all, it is useful to divide all existing methods into basic groups, of which three may be counted: purely mechanical, optical, and electrical.

12. Mechanical indicators.—Drawing 86 shows the general view of Kolli’s apparatus¹⁰; Drawing 87, p. 65, shows the measuring device itself on a larger scale.

Drawing 86.

Two toothed wheels are mounted on the main shaft; by means of Gall’s chains \(g\) and \(h\), and two corresponding gears, they set in rotation the auxiliary shafts \(a\) and \(b\), which are connected to the indicating instrument \(i\) by means of a two-thread rectangular screw and a coupling \(c\). One end of the coupling forms a nut, while the other is connected to shaft \(b\) by a long key, along which it can move freely; the coupling \(c\) can move the clamp \(d\), on the top of which is a toothed rack meshing with the gear \(e\), on whose axis the pointer \(f\) is mounted.

When the turbine shaft rotates without load, the coupling \(c\), and with it the pointer \(f\), are in the middle position. When the shaft transmits a certain twisting moment, it twists and, through the chain transmissions \(g\) and \(h\), turns shaft \(b\) relative to shaft \(a\), as a result of which the coupling \(c\) moves to the right or to the left, depending on the direction of rotation of the turbine shaft, and turns the pointer \(f\) to one side or the other. The scale over which the pointer \(f\) moves is divided into degrees and indicates, on an enlarged scale, the angle of twist of the turbine shaft, and consequently, by equation (23) in conjunction with equations (21) and (22), the corresponding work \(N_e\).

§ 12. Kolli Indicator

Increasing the scale of the dial is achieved in three ways: by the gear ratios in the chain transmissions \(g, h\), by the pitch of the screw in the coupling \(c\), and by the toothed gearing \(e\).

One and the same instrument can be used for various shafts, merely by regraduating the scale, or, more precisely, by establishing the value of its divisions as a function of the shaft diameter and of its length \(L\) between the chain transmissions.

Fig. 87.

Kolli’s instrument is convenient in those cases where the turbine shaft is accessible only at certain portions, since the axis of the rollers \(a\) and \(b\) may lie at an arbitrary distance from it. Another advantage of it is the direct determination of the desired work; a certain disadvantage is the absence of a record.

Indicators of torsion by Föttinger are constructed according to an entirely different scheme; he worked extensively on their design and created several types of them, depending on their purpose and on the requirements imposed.

In Fig. 88 one of Föttinger’s indicators is shown semischematically¹⁰: on the turbine shaft two disks are fastened, \(a\)—directly on the shaft, and \(b\)—on the end of an iron tube \(c\), fastened at its other end to the shaft and concentrically enclosing it without touching it. The angle of twist of the shaft over the length \(L\) is transmitted in the form of—

carrying the rotation of disks \(a\) and \(b\); by means of the lever mechanism \(defg\) this displacement is transmitted, on an enlarged scale, to the sleeve \(h\), which can move along the shaft. On the sleeve \(h\) there is a groove in which a split ring is fitted; the latter receives only a translational motion to the right and to the left and transmits it to the pointer \(i\), with a fixed axis of oscillation below. In the actual instrument, a rotation of disk \(b\) relative to disk \(a\) by 2 mm, reckoned along the circumference of the disks, gives a deflection of the end of pointer \(i\) by 80 mm. Such a considerable magnification makes it possible to take a comparatively small shaft length \(L\), which is very important when testing marine turbines, in which it is difficult to have the propeller shaft free over any considerable length.

Drawing 88.

The simple scheme indicated, in the actual instrument, requires a whole series of structural details, which may be seen from Drawings 89–95, representing an instrument built for tests with a boat that had an engine of \(6 \times 2\) h.p. at \(n = 300\) and up to \(n = 3000\) rev./min. These drawings are clear without further explanation.

By the same type, Fettinger built torsion indicators for marine turbine installations of 6000 and 10000 h.p. When such an indicator was compared, during operation of a turbine of 3000 h.p., with the readings of the water brake according to Drawing 67, the mean difference of their readings from 48 reports amounted to 0.04%, and the greatest to about 0.29%, which shows the remarkable accuracy of the instrument.

Fettinger’s torsion indicator is readily furnished with a recording device, Drawing 96, p. 68: pointer \(g\) is provided with a pencil, which faces the shaft and traces on paper attached to drum \(n\); the latter moves along guide \(o\), but does not itself participate in the rotation. Knowing on the diagram the position of the zero line, i.e. the mean position of the lever with the pencil, and the scale of the record,

§ 12. Fettinger Indicator.

![Technical drawings of the Fettinger indicator, including several views of the shaft-mounted mechanism and gauge arrangement.]

Drawing 89—90.

![Technical drawings of additional parts and assemblies of the Fettinger indicator.]

Drawing 91—95.

it is not difficult, from the magnitude of the ordinates, to determine the work transmitted by the shaft.

As regards obtaining the diagrams, it must be noted that a certain difficulty is presented by the considerable speed of motion of the pencil. A graphite pencil on writing paper is applicable for speeds up to \(1.0 \div 1.2\) m/sec. A stylus of hard brass gives a satisfactory diagram on dense indicator (lead-coated) paper at speeds up to \(3.0 \div 4.0\) m/sec.; it is important only that the point of the pencil be inclined to the paper. In large turbines the shaft diameter is so considerable that the speed of the sheet on the diagram drum reaches \(6 \div 10\) m/sec. In these cases it is necessary to reduce the speed of motion of the pencil over the paper.

Drawing 96.

In Drawing 97 there is shown an example of a scheme of the corresponding construction, in idea resembling the back gear of a lathe: the relative velocity between the pencil point and the paper is reduced by the fact that the diagram drum \(p\) rotates in the same direction as the shaft with the pencil, but only somewhat more slowly or more rapidly. This is attained by means of the gear wheels \(q, r, s\), and \(t\); wheel \(q\) is keyed to the turbine shaft, while \(t\) forms one piece with the diagram drum \(p\); gears \(r\) and \(s\) are keyed to the intermediate shaft \(o\). The gear ratios \(q\,r\) and \(s\,t\) are selected so that the drum \(p\) mo—

Drawing 97.

§ 12. Self-Recording Torsion Indicators.

make 10 revolutions for 11, 12, or 13 revolutions of the turbine shaft; then the relative speed of the pencil’s motion over the diagram drum will be reduced by \(10 : (11-10)=10\), respectively \(10 : (12-10)=5\), respectively \(10 : (13-10)=3\frac{1}{3}\) times.

In the constructive execution of such an arrangement it must be remembered that, in order to put on and remove the diagram paper, it must be possible to stop the drum and move it aside. This can be achieved by means of a friction clutch between the roller \(o\) and one of the wheels \(r\) or \(s\).

There are also other methods for reducing the speed of the pencil, but we shall not dwell on them, since for determining the power of turbines the record is not of essential importance and is unlikely to be often used.

Diagrams are necessary when measuring the fluctuating torque obtained in reciprocating engines; turbines give so uniform a torque that there is usually no need for diagrams. It is true that the blades of a propeller may give a somewhat fluctuating torque; on the other hand, in turbine tests such diagrams are sometimes desirable as a document.

In view of the constancy of the torque of turbines during their tests, there is also no reason not to use an integrating torsion indicator, which is a combination of the Föttinger indicator with a roller planimeter.

In conclusion, we shall describe the following two distinctive designs of torsion indicators.

The torsion indicator of Denny-Edgecombe, Fig. 98¹¹, p. 70, is fairly widespread; it consists of a cast-iron pipe \(a\), split along the axial plane, fastened at one end to the turbine shaft, and at the other end having a flange stretched out in the form of two handles \(b\) and \(c\). To one handle, \(b\), is attached a gear mechanism meshing with a toothed sector located on the cast-iron handle \(d\), rigidly fastened to the shaft. Handles \(c\) and \(e\) serve only to balance handles \(b\) and \(d\).

When handle \(b\) is turned relative to \(d\), the gear mechanism turns, to an increased degree, a light aluminum drum \(f\), which thereby moves, by means of an endless flexible wire and corresponding rollers, a light aluminum slide \(g\), freely moving along the axis of the shaft.

On pipe \(a\) and on slide \(g\) there are carefully machined flanges, against which bear the support roller \(h\), which establishes the position of the indicating mechanism, and the roller \(i\), pressed against the flange of the slide by means of the small weight \(k\) thrown over a pulley.

The roller \(i\) is fastened to the slide by a flexible wire, which passes around a light pulley \(l\) and turns it together with the pointer \(m\) attached to it. The scale is graduated in the same way as in the Kolley apparatus described above.

When readings are not being taken, by moving the roller \(i\) aside one can, as it were, lock the indicating instrument and close the box in which it is housed. The latter, of course, is firmly fastened to the floor or to the wall of the room.

Drawing 98.

The firm that builds the Denny-Edgcombe indicator will, if desired, also furnish it with a self-recording attachment.

Finally, mention may also be made of the Gari-Kemmings torsion indicator, which was used in the spring of 1912 in tests of the newest battleship of the U.S.A., “Florida,” with Parsons turbines¹²: a measuring tube, about 4.3 m long, is passed over the bored-through propeller shaft; one end of the tube is fastened to the shaft by means of three steel pins projecting from it, pressed against the walls of the shaft by a wedge driven into the tube; at the other end of the tube there is a lever protruding through a slot milled in the shaft flange; when the shaft is twisted, this lever deflects another lever, situated at the height of the flange and provided with pencils at both ends. If a sheet of paper is placed against the casing, from which these pencils project only slightly, two lines are obtained on it, the distance between them serving as a measure of the torsion of the shaft. From the form of these lines one can also judge the changes in the magnitude of the twisting moment during one revolution of the shaft.

13. Optical Indicators

These instruments, in their construction, are among the simplest, and when an enlarging device is added, among the most accurate—at least in the testing of turbines.

One of the first optical methods for measuring the angle of twist was the combination of the tube already known to us, embracing the shaft, with disks of rather considerable radius at the free end of the tube and close to the shaft; in the disks there are slots forming a small angle with the direction of the radius and inclined in different directions. The slots intersect approximately at the middle of the radius and form a small window through which a light source located behind the disks is visible. During rapid rotation the luminous window will appear as a bright circle on a dark background. When one disk is turned relative to the other, the diameter of this circle will increase or decrease, depending on the magnitude of the transmitted moment and the direction of rotation. By measuring the diameter of the luminous circle and knowing the law of its variation as a function of the twisting moment, the magnitude of the moment can be determined.

The shortcomings of this method are the difficulty of accurately measuring the diameter of the luminous circle and insufficient sensitivity for measuring small changes in the angle of twist.

A modification of this method is the Bevis-Gibson torsion indicator, one of the first to find practical application in determining the power of marine turbines.

Its operation may be explained from Figs. 99 and 100¹³: on the turbine shaft, at a distance \(l\) from one another, two disks \(a\) and \(b\) are fastened, with small holes near the circumference; moreover, in the absence of torsion these holes lie on a straight line parallel to the shaft axis; in front of disk \(a\) stands a fixed lamp with a strong electric bulb and with an aperture opposite the hole in the disk; in front of disk \(b\) stands the finder \(d\)—a sighting tube with a diaphragm in front of the objective; when the shaft is not twisted, all four apertures—in the lamp \(c\), in both disks \(a\) and \(b\), and in the diaphragm of the finder \(d\)—are on one straight line, and during rotation of the shaft, once for each revolution, a ray of light I—I will be visible in the eyepiece \(d\); owing to the fact that the retina of the eye retains the impression for \(1/10\)–\(1/5\) sec., beginning from 300 rpm and above, the light will be seen without flickering.

Figs. 99 and 100.

Chapter II. Measurement of Work. § 13.

When the shaft transmits a certain torque, the disk turns relative to \(a\), and the ray of light, having received the direction I—II or I—III, depending on the direction of rotation of the shaft, does not fall into the finder \(d\); but if the latter is moved to the side so that all 4 holes again lie on one straight line, even though not lying in the same plane with the axis of the shaft, the light will again become visible.

Having measured in degrees the amount by which the finder had to be moved, and knowing the distance \(l\), it is not difficult to determine the angle of twist of the shaft, and from it the twisting moment and the transmitted work. In practice the work of the machine is determined from the reading of the finder and the measured number of revolutions, in the form of the ordinate on a diagram prepared in advance. A specimen of such a diagram is given in Fig. 101 for a shaft 185 mm in diameter and a distance \(l = 5677\) mm.

[Fig. 101. Diagram with axes and scales: “rpm,” “angle of twist in °,” and “horsepower.”]

Fig. 102 shows a photographic view of the finder: \(d\) is the sight tube, \(e\) is a magnifying glass through which the reading is taken on scale \(f\), divided into degrees and hundredths of a degree; \(e\) moves together with \(d\) by means of a micrometer screw. With the usual distance from the shaft axis to the scale of about 350 mm, \(1^\circ\) corresponds to an arc of about 6 mm, and a reading of \(0.01^\circ\) to about 0.06 mm; such a reading is not difficult to make with sufficient accuracy by means of a vernier and a magnifying glass.

At a distance \(l = 6 \div 15\) m, taking the angle of twist of the shaft at full turbine load over this length as \(1.0 \div 2.0^\circ\) and the accuracy of setting the finder as \(0.01^\circ\), equal to the accuracy of the turbine reading, we obtain the possib—

§ 13. Optical Indicators

...an error in the reading and, consequently, also in the determination of the work of ±0.5–1.0%.

The accuracy of setting the finder depends, of course, on the size of the apertures at \(a\), \(b\), \(c\), and \(d\); in a carefully made instrument the apertures are made so small that moving the tube by \(0.01^\circ\) to one side or the other from the position of clearly visible light already causes it to disappear. It goes without saying that the luminous intensity of the lamp must be considerably increased for this purpose.

The instrument described is one of the most reliable and simple. Its chief drawback is the necessity of having a free shaft length of 12–15 m, and not less than 6 m.

Fig. 102.

In Figs. 103 and 104, p. 74, a diagram is shown of the Davis-Gibson dynamometer of the so-called radial design¹⁴, in which, by using two tubes and a radial direction of the beam, the required shaft length is reduced and it becomes possible to set up the instrument in a very cramped space; the beam of light is directed upward onto the deck. The operation of the instrument is self-evident without lengthy explanations: the disks with apertures are replaced by concentric drums with apertures on the cylindrical surface. The lamp receives current by means of sliding contacts. The finder is of the same construction as in the preceding instrument, but with apertures in the diaphragm of only 0.5 mm. Handling the instrument also does not differ in any way from that described above.

The distance between the shaft sections to which the tubes are attached may be taken as only 1000 mm, even down to 700 mm, but for the sake of accuracy of readings it is desirable to have the diameter of the outer drum as large as possible. The accuracy of readings with this instrument has been brought to

to ±0.001°, which corresponds, for example, with a measured shaft length of only 900 mm, giving a total deviation of the pointer of about 0.2°, to an accuracy of ±0.5%, i.e., no less than that of the preceding instrument.

Drawings 103 and 104.

The Amsler-Laffon torsion dynamometers are also distinguished by the extreme simplicity of their design. Drawing 105 schematically shows the instrument for a large marine turbine¹⁵: the angle of rotation of the free end of a pipe, fastened at its other end to the shaft, relative to the rim or flange on the latter is measured by means of divisions marked on the shaft and a vernier marked on the end of the pipe.

Drawing 105.

§ 13. Optical Indicators.

The question of how to read the indications of the scale during rotation is resolved in the following manner: opposite the scale there are two metal rods \(a, a\), between which a spark jumps, from the current supplied by a galvanic battery \(b\); the current is closed for one instant at each revolution of the shaft by means of the contacts \(c, c\) placed on the latter, precisely at the time when the scale is opposite the rods \(a, a\). Owing to the instantaneous passage of the spark illuminating the scale, the latter appears to stand motionless, and it is easy to take the required reading; at the same time, beginning from approximately 300 rev./min. and higher, even the flickering of the illumination is not noticeable.

For measuring less considerable work the factory builds separate dynamometers on the same principle, but of a somewhat simplified construction¹⁴. In Fig. 106 there is shown, approximately at \(1/12\) natural size, a dynamometer

Figs. 106 and 107.

for a small steam turbine, transmitting a torque of up to 25 kg·m, i.e. up to 100 h.p. at 3000 rev./min.; the torque is transmitted by a steel rod \(C\), the square ends of which are fastened by means of sockets in the flanges \(A\) and \(B\). One of the flanges is connected to the turbine, and the other to the dynamo or centrifugal pump. To flange \(A\) is connected, by means of the cast-iron bushing \(D\), the disk \(M\); to flange \(B\), by means of the tube \(E\), the disk \(N\); in order to avoid vibration of the tube \(E\), it is connected with \(D\) by means of two ball bearings. In the disks \(M\) and \(N\) slots are made, covered with transparent celluloid plates; on one there is marked a scale, and on the other a vernier, Fig. 107. In order to read from them the angle of rotation of one disk relative to the other, the designer made use of the idea of a stroboscope: on the tube \(E\) a third disk \(O\) is fixed, with a small window, and behind the disk \(M\) an electric lamp \(P\) is placed. During rapid rotation, into the eye of the observer located in front of disk \(O\), at each revolution, there will fall a ray of light, and with it also the image of the transparent celluloid scales in \(M\) and \(N\), which will—

must appear motionless and sufficiently illuminated to read their readings.

To the readings of this dynamometer, which gives the useful work, there should be added, at least for small transmitted torques and high numbers of revolutions, the loss of work in the dynamometer itself, the principal part of which consists of the work of friction of disk \(M\) against the air; the work of disks \(N\) and \(O\) is included in the instrument readings by itself.

According to Stodola’s experiments, the work of friction against the air, \(N_r\) h.p., may be calculated from the expression

\[ N_r = 0.00000458\,D^5 n^3 \gamma, \tag{24} \]

where \(D\) is the disk diameter in m., \(n\) is the number of rev./min., \(\gamma\) is the specific weight of the medium in kg/m\(^3\); for air one may take \(\gamma = 1.188\) kg/m\(^3\).

For the dynamometer shown in Fig. 106, at \(n = 3000\), \(N_r = 0.12\) h.p., a quantity which should not be neglected.

By changing rod \(C\) and taking it of various thicknesses, one can obtain the required sensitivity depending on the greater or smaller torque. The scale of the dial for the various rods is best determined by direct experiments, as will be indicated below, when the checking of torsion indicators in general is discussed.

So that, in the event of an accidental increase in load, rod \(C\) is not subjected to excessively strong torsion producing permanent deformation, the end of tube \(E\) and the bushings in flange \(A\) are provided with stop projections, by means of which the excess part of the twisting moment is taken up by tube \(E\).

Dynamometers of this type work well. Their chief drawback is a somewhat low accuracy of reading—or, rather, a scale that is too coarse, owing to the absence of any magnifying device necessary for better detecting small angles of rotation of one disk relative to the other—and a rather considerable length.

Among other instruments we shall describe the Hopkins and Fram torsion indicators, which are essentially combinations of optical with mechanical devices.

The main part of the Hopkins-Spring indicator\(^ {36}\), explaining its idea, is shown schematically in Figs. 108 and 109: as in many of the instruments described above, a tube is attached to the turbine shaft, embracing the shaft and ending in flange \(A\); nearby is a flange \(B\) attached to the shaft itself; to the latter is attached a small mirror \(m\), which can rotate about an axis \(o\) directed toward the axis of the shaft; behind the mirror is attached a small lever ending in a ball; the latter is located between two teeth \(d,d\), attached to flange \(A\).

\(^ {36}\) Trans. Inst. Nav. Arch., 1910, vol. LII, p. 184; Eng. 1908, p. 614; Buchetti, Nouveau guide pour l’essai des moteurs, 4-me édition, p. 152.

§ 13. Optical indicators.

So long as the shaft transmits no work and, consequently, is not twisted, the mirror \(m\) stands in a plane passing through the axis of the shaft. When the shaft is twisted, flange \(A\) turns relative to \(B\) and turns the mirror \(m\), upon which a ray of light from the lamp \(a\) falls. If \(e\text{-}o\), Fig. 109, is the normal to the plane of the mirror in the deflected position, then the reflected ray will fall on the scale \(a\text{—}b\) at point \(b\); by measuring the distance \(a\text{—}b=u\) and knowing the distance \(l\) from the lamp to the mirror, it is not difficult to find the magnitude \(r\) of the rotation of the flanges, and, knowing the distance from the shaft axis to the center of the ball, also the corresponding angle \(\varphi\).

The constructive design of the Hopkinson-Spring indicator for shafts from 200 to 300 mm in diameter is shown in Figs. 110 and 111, p. 78, approximately at \(1/12\) natural size. In view of the thin walls of the cast-iron pipe \(a\) and of the collar \(b\), to prevent vibration of the instrument there are two pairs of projections \(c,c\), pressed against one another by the spring \(d\) and serving as guides when the end \(a\) is turned relative to \(b\). The mirror instrument itself is arranged somewhat differently than in the above diagram: on both sides of a metal frame, capable of turning about the axis \(e\), Fig. 112, small mirrors \(m,m\) are fastened; when the end \(a\) is displaced relative to \(b\), the flexible steel plate \(g\), attached at one end to the boss \(h\) screwed to \(a\), and at the other to the lever \(f\), which forms a continuation of the frame with the mirrors, turns the latter relative to the axis \(e\). The nut \(n\) serves for setting the ray to the zero of the scale, while the accurately measured pitch of the thread \(n\) also makes it possible to determine the magnitude of the relative displacement of \(a\) and \(b\). The use of two mirrors gives a double reading: from one mirror the ray from the lamp \(i\) falls on the glass scale \(k\text{—}k\) when moving away from the scale; in Fig. 111 it is displaced along the width of the scale on its left side, while from the second mirror the ray falls on the scale on the right side after the shaft has turned through an angle of \(180^\circ\) with a small [[unclear: continuation at page bottom]], Fig. 111. In some instruments, to

Chapter II. Measurement of Work. § 13.

the flange \(b\) is covered by a fixed mirror, which during operation will indicate the 0 of the scale, provided, of course, that the ray from the rotating mirror, in the absence of torsion of the shaft, falls on the same place of the scale. The distance of the scale \(k—k\) and the lamp \(i\), and, correspondingly, the angle of rotation of the mirror from the turbine shaft, are shown in Figs. 110 and 111 not to scale. In practice, in order to increase the accuracy of the instrument readings, this distance is taken considerably larger—6–10 m.

Fig. 110—112.

Hopkinson’s instruments possess great sensitivity and accuracy. When the shaft vibrates, the ray, as it were, wanders over the scale by 4–5% of its greatest length, but nevertheless it is not difficult to find the mean, true reading. The only drawback is the cessation of readings if oil gets on the mirror, or if it becomes fogged by steam. If the scale and the light source are placed above the instrument, then no difficulty will be encountered in fitting it even on small vessels; on large vessels they may freely be placed at the side.

§ 13. Optical indicators.

Fram’s torsion indicator, Figs. 113 and 114¹⁶, is based on the same idea as the Hopkinson–Thring instrument, and was constructed simultaneously with it, but entirely independently. It also consists of a cast-iron tube with flange \(A\), fastened at its other end to the shaft, and of a flange \(B\), wedged onto the shaft, shown in Figs. 113 and 114 as half-drilled.

Figs. 113 and 114.

A light plate \(c\) with a small mirror \(m\) fits into the slot of the support \(a\), attached to flange \(A\); the other end of the plate \(c\) rests on the adjusting screw \(b\), attached to flange \(B\); a flat spring \(h\), bent in an arc and fastened at the rear to \(a\), and at its other end to the middle of plate \(c\), constantly keeps it pressed against its supports \(a\) and \(b\), while at the same time allowing it to incline with respect to the axis of the shaft. For greater sensitivity, plate \(c\) bears on \(a\) and \(b\) by means of two prisms attached to its rear surface.

When the turbine shaft experiences no torsion, the plane of the mirror is parallel to the axis of the shaft. When the shaft transmits work, flange \(A\) turns relative to \(B\), and the small mirror \(m\) inclines toward the axis of the shaft.

The measurement itself of the angle of inclination, making it possible to find the angle of torsion of the shaft, is carried out as follows: at a distance \(l\)

...from the axis of the shaft, parallel to it, there is a scale with divisions in mm, along which moves a pointer \(i\), attached to a lantern \(f\) with an incandescent lamp located inside it; in front of the lantern there is a narrow slit, which casts a beam onto the mirror \(m\); the lantern is moved along the scale by means of the rack-and-pinion gear \(d,d\). On the line normal to the plane of the mirror in its position of rest there is a telescope \(e\) with cross-hairs. When the mirror turns under the action of the twisting of the shaft, the lantern is moved until the flashing of the beam becomes visible in the telescope. Knowing the distance through which the lantern has been moved from 0, and the distance \(l\), it is not difficult to calculate the required angle of twist.

To set to 0, the telescope \(e\) can be displaced somewhat parallel to the axis of the shaft, owing to the oval holes in the stand. In addition, the telescope \(e\) can be rotated about an axis perpendicular to its optical axis, by means of the sector \(o\).

Notwithstanding the uniform rotation of the turbine, the shaft of the propeller under test experiences an alternating twisting moment, changing once per revolution under the action of the propeller blades; therefore the deflections of the beam will also be different at different instants. Although the magnitude of the oscillations of the deflection is small, it is better to make two readings—the greatest and the smallest deflection of the beam. For this purpose two mirrors are installed: one, \(m\), opposite a blade, and the other, \(m_2\), midway between two adjacent blades; with a three-bladed propeller the angle between the mirrors will be \(60^\circ\), as in Fig. 113, with a four-bladed propeller \(45^\circ\), etc. The two deflections are measured and the mean value is taken.

When setting up the instrument, it is necessary carefully to check the parallelism of the scale to the axis of the shaft and the position of the 0 of the scale, and also the coincidence of the threads in the eyepiece with its focus.

In conclusion we shall briefly describe the newest Japanese torsion indicator of K. Suehiro (Suyehiro)\(^{25}\), which is an ingenious combination of a whole series of the instruments described, but at the same time is based on an entirely independent idea. The operation of the instrument is explained by Figs. 115–118: to the shaft is attached a sleeve \(A\) with two symmetrical arms \(L_1\); at a distance \(l\) from it a tube \(B\) is attached to the shaft, the other end of which can turn freely in a groove in \(A\); to \(L_1\) is attached a scale \(S\), facing the shaft and having the form shown in Fig. 118, with divisions of \(1/4\) mm and a sharp edge, and a flat mirror \(M\), facing the telescope \(T\); \(M\) is separated from the axis of the shaft by exactly half as much as \(S\); in consequence of this the virtual image of the scale \(S\) will lie on the axis of the shaft and, with small dimensions of \(M\) and rapid rotation of the shaft, will be visible in \(T\) and appear stationary. To the tube \(B\) are attached two symmetrical arms \(L_2\), to the end of one of which a concave mirror \(m\) is attached so that—

\(^{25}\) Engng. 1913, XCVI, p. 459.

that the virtual image in it of the edge \(S\) also falls on the axis of the shaft; in this arrangement \(M\) and \(m\) are positioned so that in \(M\) only the divisions of the scale \(S\) are reflected—the right-hand part of Fig. 118—while in \(m\) only the “index edge,” the sharp boundary between the white and black regions, is reflected—the left-hand third of Fig. 118. When the shaft is twisted, \(m\) is displaced relative to \(M\), and in the tube \(T\) it is seen that the “index edge” has moved relative to the divisions of the scale. Knowing the scale of pressures, the distance \(S\) from the axis of the shaft, the length \(l\) of the shaft between the places of fastening \(A\) and \(B\), the moment of inertia of the shaft and its material, one can easily calculate the transmitted torque. The curvature of the little mirror \(m\) also serves to increase the apparent displacement of the “index edge” relative to the divisions of the scale.

Figs. 115–118.

To illuminate the scale \(S\), when the torque is constant, and when the readings are observed through a single tube, one electric lamp with a reflector beside the tube \(T\) is sufficient. When measuring a variable torque, it is better to equip the instrument with an electric lamp rotating together with the shaft and placed exactly opposite the scale.

According to the inventor of the instrument, its accuracy—or, more precisely, the error of its readings—is less than \(\pm 2\%\) for a length \(l\) of about 1530 mm.

The Saikeiro indicator was installed in parallel with another torsion indicator during the trials of the “Anio-Maru,” the first Japanese turbine vessel with geared transmissions between the shafts of the turbine and the propellers. The indicator worked so satisfactorily that its readings were taken as the basis for the award.

14. Electrical indicators.—An attempt was made to use electric current in the very first designs of torsion indicators. The resulting instruments, however, were partly insufficiently accurate and partly inconvenient in that they gave a reading only for some one angle of rotation (position) of the propeller shaft.

Being less accurate than optical methods, and in part also than mechanical methods, they have nevertheless now become fairly widespread in practice, and for that reason we have decided to dwell on them, selecting, however, only the newest and more improved among them.

The reason why they are willingly used in practice lies in the convenience of their installation: on two places of the shaft, at the required distance \(l\) from one another, two contacts are installed; no intermediate portion of the shaft is required for the readings; the length \(l\) of the shaft may be closed off; blind bulkheads may stand between the contacts—for measurement of the torsion angle this is immaterial.

One of the most widespread electrical torsion indicators is the Denny-Johnson instrument¹⁷.

Its arrangement is shown in Figs. 119 and 120: two bronze disks \(a\) and \(b\) are fastened on the turbine shaft at a distance \(l\) from one another. Permanent magnets \(e\) and \(f\), arranged radially, are attached to the disks; the projecting ends of the magnets are sharpened in the form of a wedge, so as to give a narrow but strong magnetic field. Beneath the disks, on small bronze supports provided with adjusting screws, are placed the armatures \(c\) and \(d\), made of soft iron, the upper surface of which is concentric with the shaft. Inside the armatures there is a certain number of identical coils separated from one another, in which a current is induced as the magnets pass.

On a distributing board situated at an arbitrary distance from the shaft are arranged the rotary switches \(c\) and \(d\). In armature \(c\) there are 6 main and 3 auxiliary coils, connected to the contact studs of switch \(c\). In armature \(d\) there are 13 main and 2 auxiliary coils, which are connected to the contact studs of switch \(d\).

Variable resistances \(r_1\) and \(r_2\) are included in both conductor systems \(c\) and \(d\) for regulating the current intensity.

§ 14. Denny–Johnson Electrical Indicator.

The switch \(k\) serves to switch the measuring instruments in the case of simultaneous testing of several turbines, for example on twin- and triple-screw vessels.

The telephone acoustic device \(t\) completes the installation.

The wiring diagram is shown, for clarity, in Fig. 121.

Figs. 119–121.

The action of the device is as follows: when the shaft is not subject to torsion, magnet \(e\) is located over the first coil of armature \(c\), while magnet \(f\) is already over the last coil of armature \(d\); with the planes, drawn through the axis of the shaft and the axes of the magnets, parallel to armatures \(c\) and \(d\), they form an angle \(\alpha\). The currents induced in these extreme zero coils have equal strength but opposite direction and therefore cancel one another; the telephone instrument emits no sound when the sliding contact \(d\) is positioned on the zero button.

If a certain torque is transmitted to the shaft, the angle \(\alpha\) will decrease owing to the twisting of the shaft; the zero coil of one of the armatures will be excited later than the zero coil of the other armature, the currents do not cancel, and the telephone instrument comes into action. Then the sliding contact \(d\) is turned, switching to one of the following coils, until the telephone becomes silent, which will indicate mutual cancellation of the current. From the number of buttons to which contact \(d\) is shifted, the angle of twist of the shaft is determined, knowing the distance along the arc between adjacent coils of armature \(d\); this distance is about 0.51 mm, which value, or rather its half, determines the degree

accuracy of measurement. The scales of switches $c$ and $d$ are usually graduated directly in linear magnitudes of change in the arc.

The distance between the disks is taken from 7 to 11 m, and even more. In view of the stepped character of the scale (the arrangement of the coils), it is possible that the noise in the telephone does not disappear completely at any position of the sliding contact $d$; then one finds the position of the contact at which the noise reaches its smallest value.

Switch $c$ is brought into action if the angle of twist of the shaft increases so much that switching to the last button (coil) $d$ is insufficient to eliminate or weaken the noise in the telephone. The distance between the armature coils $c$ is 10 times greater than the distance between the armature coils $d$, so that coarse magnitudes of twist are set by switch $c$, and the exact ones always by switch $d$. The complete indication is, of course, equal to the sum of the readings on the scales $c$ and $d$.

Other electrical torsion indicators use an external current from cells or from the general mains. Their basic ideas differ.

Thus, Gardner’s indicator consists of two disks made in the form of current interrupters: on the outer surface of the disks there alternate arcs, of equal length, of conducting and nonconducting material. Contacts in the form of brushes touch the disks and the shaft between the disks. A battery of cells and an ammeter are included in the circuit; its pointer stands at 0 if the shaft is not subjected to torsion, and is deflected the farther, the greater the angle of twist of the shaft.

Apparently the indicator of Barr and Stroud has the same operating scheme, but there is as yet no more detailed information about it in the literature.

The design of Rambal’s indicator is simpler and more reliable.

In Fig. 122 the scheme of this instrument is shown: on the turbine shaft $a$ are fixed two disks $b$ and $b_1$, into which steel contacts in the form of wedges $c$ and $c_1$ are set; spring-mounted contacts $d$ and $d_1$ touch them, of which $d$ is stationary, while $d_1$ can move along the guide $g$, concentric with the axis of the shaft. The contacts $d$ and $d_1$ slightly touch the contacts $c$ and $c_1$ at each revolution of the shaft; they are insulated and connected to one another by copper conductors $e, e$.

Fig. 122.

§ 14. Rambal’s Indicator

When the contacts \(c\) and \(c_1\) touch the contacts \(d\) and \(d_1\) at exactly one and the same instant, a current from the battery passes through the disks \(b\) and \(b_1\) and the shaft \(a\), and deflects the pointer of the galvanometer \(i\).

When the shaft is unloaded, the contacts \(c\) and \(c_1\) lie in one axial plane; when the shaft \(a\) is twisted, however, contact \(c_1\) will lag behind contact \(c\) by the magnitude of the angle of twist \(\alpha\); the closing of the current will cease; then \(d_1\) is moved until the current again begins to close. The magnitude of the displacement of contact \(d_1\) gives the magnitude of the angle of twist \(\alpha\).

In practice the galvanometer is replaced by a telephone receiver, which permits the position of best contact between the contacts to be established more accurately. The battery \(p\) consists of dry cells.

Disk \(b_1\) is mounted on the shaft in the engine room, near the turbine; disk \(b\), with the fixed contact, is mounted on the shaft as close as possible to the stern, in order to obtain as great a distance \(l\) as possible between the disks and, consequently, as large an angle of twist \(\alpha\) as possible, i.e. the greatest possible accuracy in determining the torque.

Drawing 123–125.

Drawings 123–125 show the construction of disks \(b\) and \(b_1\), which are cast as light as possible from cast iron; to avoid accidents, their spokes are covered with sheet metal screwed on from both sides. The disks are made bored to facilitate mounting on the shaft,

Their large diameter ensures accuracy in measuring the angle of twist.

In Fig. 123 the construction of the movable contact \(d_1\) is shown, and in Fig. 126 it is depicted in perspective view on a larger scale: the screw \(s\) serves to lower the wedge \(d_1\), made of hardened steel, and to obtain the required light contact between it and \(c_1\); the handle \(h\) serves to raise the contact \(d_1\) when measurements are not being made. The head \(r\) serves to move the contact \(d_1\) by means of the toothed wheel \(z\), which rolls along a toothed rack forming part

Fig. 126.

of an arc of a circle, which must be strictly concentric with the shaft, as must also the guide slide \(n_1\). The screw, which is fastened to the body of the toothed rack and passes through the slot \(g\), serves for setting, at least approximately, the zero of the scale. The whole apparatus is screwed, by means of the frame \(n\), to some fixed support; care must be taken that the indicated concentricity is maintained as accurately as possible.

The fixed contact \(d\) is arranged likewise on a spring, with an adjusting screw \(s\) and a switch \(h\), but without the device for displacement.

The scale is divided directly into degrees; for accuracy of readings a vernier is provided.

The simplicity of attachment and operation, the sufficient accuracy, and the comparatively low cost of the whole device have given it fairly wide use.

Although rarely, self-recording torsion indicators are nevertheless also used; in view of this we shall describe one of the newest—the instrument of Friedrich Lux¹⁸.

The basic idea of it is presented in Fig. 127: at each revolution of shaft \(a\), the contact of \(b_1\) with the fixed contact \(b_2\) closes—

§ 14. Lux Indicators.

... passes current from battery \(f\) in the primary circuit, which includes the primary winding \(p\), the shaft itself, and the sliding contact \(c\); by this an inductive current is excited in the circuit with the secondary winding \(s\) of the same coil, as a result of which a spark jumps between the point \(e\), fastened to the shaft \(a\), and the fixed ring \(d\) with divisions. So long as shaft \(a\) is not undergoing torsion, the spark jumps when \(e\) is opposite 0 on the scale. When the shaft transmits a certain twisting moment, the spark jumps at another point of the scale \(d\), and the angle between this point and 0 of the scale will be the angle of twist of the shaft over the length \(l\) between

Fig. 127 and 128.                                                                                             Fig. 129.

sections \(a_1\) and \(a_2\). To facilitate readings, and also to account for possible fluctuations of the twisting moment, several contacts \(b\) are attached in section \(a_1\), at equal distances from one another, and in section \(a_2\), correspondingly, several points \(e\). To increase the accuracy of the reading, especially at small angles of twist, the point \(e\) may be replaced by a knife with its blade parallel to the axis of shaft \(a\), and the circular scale by a spiral; in this case, at different twisting moments, the plane in which the spark jumps, if viewed from the side, is displaced along the axis of the shaft, and this displacement from the position of the spark plane at \(M=0\).

Chapter II. Measurement of Work.
§ 14.

is a measure of the torsion. The pitch of the spiral, which for clarity of the record must, of course, be very large, determines the scale of the “scale.”

Fig. 128 shows the diagram of a self-recording instrument: the current is likewise closed, as in the preceding diagram, by the contact of \(b_1\) and \(b_2\), but the battery \(f\) is divided into two, \(f_1\), \(f_2\), and the ring \(d\) is divided into two half-rings \(d_1\) and \(d_2\), insulated from one another. The primary current will go from \(f_1\) or \(f_2\), depending on whether the pointer \(c\) slides over \(d_1\) or \(d_2\); in these cases the current passes through the primary winding \(p\) in opposite directions; in view of this, in the secondary winding \(s\) a current will likewise be excited alternately in one direction and then in the other, and the automatic electromagnetic switch (relay) \(h\)-NVS will alternately connect into the network with the electric motor \(k\) either the battery \(f_3\) or \(f_4\). Depending on which of the batteries, \(f_3\) or \(f_4\), is connected, the armature \(k\) and its shaft \(i\), made in the form of a long worm, rotate in one direction or the other. The worm \(i\) is coupled to the worm sector \(m\), fastened to the split ring \(d_1, d_2\). When the shaft \(a\) does not transmit torque, the pointer \(c\) at the instant of contact of \(b_1\) and \(b_2\) is opposite the upper insulator separating \(d_1\) from \(d_2\), and the whole system remains without current—without motion. When the shaft \(a\), under the influence of the transmitted torque, twists, the pointer \(c\) at the instant of contact of \(b_1\) and \(b_2\) will be on \(d_1\) or \(d_2\), will close the current of battery \(f_1\) or \(f_2\), the relay will come into action, and the motor \(k\) will turn the sector \(m\) through such an angle \(\alpha\) that, at the instant of contact of \(b_1\) and \(b_2\), the pointer \(c\) stands opposite the insulator. The angle \(\alpha\) is the required angle of torsion of the shaft \(a\) over the length \(l\), and can be read by an indicator, by one means or another connected with the worm \(i\), and not shown in Fig. 128. The rotation of the worm \(i\) is recorded on the drum \(o\), with a vertical axis of rotation, by means of the worm wheel \(n\) and a cord thrown over several pulleys; the drum \(o\) receives rotation from a clock mechanism. At the point \(g\) the secondary circuit \(s\)-\(h\) is broken; when current passes, a spark jumps across at \(g\); this is done so that only the stronger current, excited when the primary current is broken, enters relay \(h\), while the weaker one—when the primary winding is closed—does not enter relay \(h\), being unable to overcome the resistance when passing across the break \(g\).

The self-recording torsion indicator described can be converted into a work counter, shown schematically in Fig. 129; two toothed racks, \(r_1\) and \(r_2\), slide up and down along the stand \(t\); \(r_1\) is displaced, by means of its wheel, by some mechanism in proportion to the magnitude of the angle of torsion of the shaft; \(r_2\) receives motion from the electric motor \(u\) by means of the chain transmission \(q\) and the corresponding toothed wheels. A wheel \(w_1\), seated on \(r\), is coupled with \(r\) ...

voluntarily on the same axle with the wheel \(u_2\) and connected with it by a ratchet mechanism; when \(r_2\) is raised, the wheel \(u_1\) rotates freely counterclockwise; when \(r_2\) is lowered, the wheel \(u_1\), through the ratchet, turns the wheel \(w_2\), which is engaged with the wheel of the summing counting mechanism \(u_2\). The motion of \(r_2\) is limited above by the contact spring \(v_1\), screwed to the bottom of the rack \(r_1\), and below by the contact spring \(v_2\), attached to the fixed support. Thus the length of the path traversed by \(r_2\) is proportional to the angle of twist of the shaft transmitting the torque.

The main conductors from the contacts on the shaft, whose angle of twist is being measured, are shown below in Fig. 129—\(x_1\) and \(x_2\). The primary circuit is closed once at each revolution of the shaft; at the same time the battery \(f_5\) is switched in, and the current from it enters the winding of the electromagnet \(y_2\); then the right arm of the rocking rod \(z\) is attracted, and by contact \(z_2\) the battery \(f_7\) is switched in, the current from which sets \(u\) in rotation and causes \(r_2\) to rise until it touches \(v_1\); by this the circuit in which the electromagnet \(y_1\) is located is closed, the rod \(z\) swings back in the opposite direction, the battery \(f_6\) is switched in, while \(f_7\) is switched out, and \(u\) begins to rotate in the opposite direction, and \(r_2\) to descend, until it presses \(v_2\) and thereby interrupts the current, as a result of which \(u\) will stop. Such a double stroke of \(r_2\) is repeated at every closure of the main circuit, i.e., at every revolution of the turbine shaft. Thus the counting mechanism will count off each time a quantity proportional to the angle of twist of the shaft, i.e., to the transmitted torque, and the sum of the readings will represent the product of the torque by the number of revolutions. If the modulus of elasticity of the shaft material, as well as its dimensions, are known, it is not difficult to calculate the conversion factor by means of which the readings of the instrument over an exactly known interval of time will express the work in h.p.-hr.

In conclusion, let us describe Johnson’s newest torsion indicator, which is a combination of a mechanical method of transmitting the angle of twist with its electrical measurement¹⁹, by means of switching in a Wheatstone bridge.

In Figs. 130 and 131, p. 90, the scheme of its construction is shown: a cast-iron tube \(b\) with a ring \(c\) is fastened to the shaft \(a\); opposite the latter, a ring \(d\) is fastened to the shaft; on the ring \(d\), between two projections, a wire \(e\) is stretched, lying in the plane of rotation perpendicular to the contact \(f\) sliding along it and fastened to the ring \(c\). The ends of the wire \(e\), made of a platinum-iridium alloy, distinguished by great hardness and high electrical resistance, are attached to two contact rings \(g\) and \(h\); the contact \(f\) is also connected with the contact ring \(i\) and further with a galvanometer.

When the shaft is not loaded, contact \(f\) is located exactly in the middle of wire \(e\) and divides its resistance in half; when the shaft is twisted, contact \(f\) slides toward one or the other end of \(e\), dividing its resistance into unequal parts.

Drawing 130 and 131.

In Drawing 132 the electrical circuit of this instrument is shown: current from a small battery \(k\), giving 4 volts, passes through the regulating resistance \(r\), the contact ring \(g\), into the resistance wire \(e\); here the current branches: part of it goes back into the battery directly through the contact ring \(h\) and the switch \(s\), while another part goes through contact \(f\), ring \(i\), into the galvanometer \(v\), and then again enters the battery \(k\).

Drawing 132.

Drawing 133 and 134.

Depending on the position of \(f\) on \(e\), the voltage of the current branched to the voltmeter will change and will serve as a measure of the angle of twist.

§ 14. Johnson’s Indicator.

The scale of the galvanometer \(v\) is divided into ohms, and its full length corresponds to the full magnitude of the resistance \(e\), or even directly to inches or mm of displacement of the end \(c\) relative to \(d\). When the shaft is not loaded, the pointer of the galvanometer must stand at the middle of the scale, at its 0; deviations of the pointer to the right or to the left depend on the direction of rotation of the shaft. In view of the difficulty of setting \(f\), with the unloaded shaft, exactly at the middle of \(e\), the scale of the galvanometer \(v\) is made movable, in order to facilitate setting to 0.

Before taking a reading, the switch \(m\) is placed on contact 1; by this means the resistance \(e\) is excluded from the circuit with the galvanometer \(v\); the adjusting resistance \(r\) is then set so that the pointer \(v\) takes the extreme position, the end of the scale; then one may be sure that the full length of the scale corresponds to the full length of the resistance \(e\). After this the switch \(m\) is placed on contact 2 and the reading is taken.

The knife switch \(t\) and the wires \(x\) and \(y\) serve for charging the battery \(k\).

The purpose of the opposed rings \(c_1\) and \(d_1\) is to serve as counterweights, so as not to disturb the uniformity of rotation of the shaft by the addition of the rings \(c\) and \(d\); for the same purpose they are also provided with counterweights \(q,q\).

Usually the dimensions of the tube and rings are chosen so that the length \(e\) is a little greater than 5 mm, i.e. the greatest displacement of the contact \(f\) from the middle is about 2.5 mm at the greatest load of the shaft. The swing of the pointer \(v\) is then 75 mm in each direction.

This torsion indicator requires a free length of shaft of not less than 1.5 or even 2 m. With a shorter length, the changes in the arms of the resistance \(e\) become too small, and the readings of the instrument are inaccurate. In order to use the instrument in these cases as well, it is necessary to add to it a transmission mechanism, Fig. 134: the contact \(f\) is made in the form of an unequal-armed lever rotating about the axis \(o\), fastened to the ring \(d\); the projection on the ring \(c\) enters the opening \(n\) of the lower end of the lever. The swing of the upper end of the lever is thus 10–12 times greater than the relative displacement of the ends of the rings \(c\) and \(d\). \(u\) is a plate of insulating material, on which are fastened the resistance \(e\), the sliding contact \(f\), and the corresponding connections of the insulated wires.

In Fig. 133 another arrangement of the transmission mechanism is shown, now abandoned because of dead travel: to the lever-contact \(f\) is attached a gear, rotated by a toothed sector \(j\), fastened to the insulator \(u\) on the ring \(d\). The contact rings \(g\), \(h\), \(i\) are shown in Figs. 133 and 134, of course, only for clarity of the diagram.

In Fig. 135 a photographic view is presented of three Johnson indicators for a three-screw vessel; with indicators 1 and 3 are also shown brackets with pins sliding over the contact rings.

Chapter II. Measurement Operations. § 14

Fig. 135.

Fig. 136.

§ 15. Calibration of Torsion Indicators

The corresponding distribution board is shown in Fig. 136. A particular advantage of this instrument is the extremely small required length \(l\) of the shaft, owing to which its readings are not affected by accidental deformations of the shaft under the unavoidable deformations of the ship’s hull.

15. Calibration and checking of torsion indicators.—For the correct determination of the twisting moment, it is very important to know precisely the modulus of torsional elasticity \(G\) of the material of the shaft on which the torsion indicator is installed.

The best way is to determine \(G\) experimentally, specifically on that piece of shaft on which the indicator will stand during the determination of the turbine output.

In Figs. 137 and 138 is shown the device used by Fettinger\(^{42}\) for determining the value of \(G\): the shaft being tested is fastened at one end, by means of a flange, to a fixed cast-iron support \(a\); the other end rests on an identical stand in the ball bearing \(b\), shown separately above, Fig. 137. To the free flange is screwed an iron I-beam \(c\), supported by the rod \(d\) in the form of a jack, which can be lengthened or shortened by turning the screw in it; the rod \(d\) must stand strictly vertical and rests on a platform of decimal scales \(e\).

Figs. 137 and 138.

\(^{42}\) Eng., 1908, CVI, p. 614.

Near the ends of the shaft, at the required distance $l$ from one another, two small mirrors $f$ and $g$ are attached; in them are reflected the divisions of stationary plumb scales $h, h$.

The shaft is twisted by screwing in the rod $d$, and after the torque has been balanced by the corresponding load on the scales $e$, readings are taken from the mirrors $f$ and $g$ with the aid of the sighting tubes $i$ and $k$. The difference of the readings gives the required angle of twist $\alpha$.

The modulus of elasticity $G$ is found for several moments, first with an increasing angle of twist and then with a decreasing one. In view of the incomplete homogeneity of the shaft material, it is useful to determine the value of $G$ also when twisting the shaft in the opposite direction, after moving the scales to position $e_2$. When working with a torsion indicator, the value of $G$ should be taken as the mean of all values found under the different test conditions.

During operation on a vessel, the propeller shaft is subjected, in addition to twisting, also to compression under the action of the axial component from the screw, which imparts motion to the vessel. The compressive stress may in some cases reach 20% of the torsional stress. By means of direct experiments it has been established that the additional compressive stress may increase the twist by up to 1% in a solid shaft and by up to 3–4% in a drilled shaft.

Finally, the modulus of elasticity $G$ is found to be somewhat different depending on whether the twisting force acts calmly, as in the calibration method indicated above, or whether the shaft vibrates, as during operation of the propeller shaft.

In view of these considerations, Gibson performs the calibration of the shaft in the following manner, Figs. 139–141: the shaft $a$ is fixed immovably at one end by means of a flange and bolts, and near the other end there is a bearing $b$, to which the levers $c,c$ are attached. On this same end of the shaft a hydraulic press $d$ with an iron

Figs. 139–141.

is applied immovably by means of a flange and bolts, and near the other end there is a bearing $b$, and to it are attached the levers $c,c$. On this same end of the shaft there presses a hydraulic press $d$ with an iron

§ 15. Checking the Zero of the Scale

by tie-rods \(c, e\); a ball thrust bearing is inserted between the shaft and the press; \(f\) is the handle of the press pump, and \(m\) its pressure gauge.

The twisting of the shaft is produced by means of screw iron tie-rods \(g\) and \(h\), which grip the ends of the lever \(c\) with the aid of calibrated spring dynamometers \(i\) and \(k\). To both ends of the shaft, at a distance \(l\) from one another, pointers \(n\) and \(o\) are attached; the difference of their readings on the scales \(p\) and \(q\) makes it possible to find the corresponding angle of twist.

With a pointer length of 1500 mm, \(1^\circ\) corresponds to an arc length of 26.16 mm, and the angle of twist can be measured even without a vernier with an accuracy of up to \(0.01^\circ\), which is quite sufficient in practice.

In order to bring the conditions of testing the shaft still closer to the working conditions on the vessel, Gibson advises tapping the shaft during the readings with wooden mallets.

If the torsion indicator occupies a length \(l\) of the shaft exceeding the length of the individual piece of shaft from which the propeller shaft is assembled, then, since it is difficult to take into account the influence of the intermediate flanges, and sometimes also of the bearings, it is better to calibrate at once the entire required length \(l\).

Finally, when testing newly built vessels with new propeller shafts, one should not forget that the material of the latter sometimes acquires additional stresses during machining; after the shaft has worked for some time on the vessel these stresses become equalized and cause some change in the modulus of elasticity \(G\). In view of this, it is recommended to calibrate the shaft both before testing the engines and, for control, after the test.

Checking the zero of the scale. When the indicator is attached to the shaft, it is necessary to find the zero of the scale, i.e. the position of the indicating instrument of the indicator for an unloaded shaft. In view of the fact that the shaft retains a certain torsion even at rest owing to friction in the bearings and in the stern tube, determination of the zero of the scale requires a certain degree of caution.

Sometimes the zero of the scale is taken simply to be that position of the pointer when the shaft is rotating at the very slowest speed.

Sometimes the initial position of the pointer is found in the following way: the engine is started at full speed, then the steam valve is immediately shut off and they wait until the vessel comes completely to a stop; the shaft will then be very close to a state of complete absence of torsion. In fact, at the moment when the engine ceases working, the end of the shaft with the screw propeller must be the driven one and must lag behind the end of the shaft at the turbine; but with the subsequent motion of the vessel under the influence of the momentum acquired by it, the shaft will begin to rotate under the action of the propeller screw, i.e. the direction of action of the forces will become reversed.

However, the most correct and reliable procedure is as follows: the shaft is rotated very slowly, first in one direction, and the position of the indicator pointer on the scale is marked; then the shaft is rotated just as slowly in the other direction, and the new position of the pointer is marked, which will be displaced from the previous one by several millimeters. The true zero of the scale lies midway between the two positions of the pointer thus found.

It is understood that, before determining the zero of the scale, the entire instrument must be inspected with particular care and the slightest lost motion in the joints and in the other transmissions eliminated.

General testing of torsion indicators. The most reliable check of torsion indicators is the comparison of their readings with the readings of a brake, best of all a water brake. Comparisons of this kind have been made and have confirmed the correctness of the readings of torsion indicators, provided, of course, that their construction is correct and that they are handled properly²⁰.

Torsion indicators may then be checked by placing two instruments simultaneously on one and the same shaft and comparing their readings. Thus, in testing the turbine steamship Lusitania of the Hamburg–American Line, the readings of the indicators—Fram’s optical indicator and Denny-Johnson’s electric indicator—were compared²¹; in tests of the steamships Themistocles and Cairn, the readings of the Bevis-Gibson optical indicator were compared with those of the Denny-Johnson electric indicator²¹. In tests of the English battleship Inflexible, Hopkins’s optical indicator and Denny-Johnson’s electric indicator were used simultaneously²². In all these tests, the readings of instruments of different types agreed quite satisfactorily.

Nevertheless, when using torsion indicators it must be remembered that these are extremely delicate instruments, which give correct readings only when handled with complete skill and care. In this connection, of course, only very carefully made instruments should be used, and preference should be given to the simpler designs.

16. Self-recording load indicator.—In concluding the chapter on the measurement of work, we shall mention Bettcher’s instrument, which, while not measuring the magnitude of the work itself, makes it possible to judge the relative magnitude of the load.

The instrument is based on the fact²³ that the position of the governor, and also of the part transmitting the action of the governor to the regulating organ of the machine, depends on the magnitude of the load. One extreme position of the part mentioned corresponds to the greatest load; the other—to idle running—

§ 16. The Boettcher Load Indicator

at idle. However simple the basic idea, its constructive implementation encountered difficulties, chiefly in eliminating the effect, inherent in the mechanism of the instrument, of oscillations of the aforementioned parts about the corresponding mean position, these oscillations being the result of the machine’s reaction upon the governor. The problem was solved by using a heavy pendulum in connection with suitable springs.

The heavy pendulum, \(c,c\), Fig. 140, is suspended so that it is in indifferent equilibrium; two stretched springs \(b,b\) connect the pendulum with the lever \(a\), which is connected by the rod \(i\) with the governor coupling or with another corresponding part; the springs \(b,b\) are taken of such dimensions, and their tension is so adjusted, that they take up completely the entire weight of the pendulum; in this way friction in its axis of swing is eliminated; the deflections of \(c\) are recorded by the lever \(d\), with a pencil at the end, on the diagram drum \(e\), which, under the action of the clockwork mechanism contained inside it, makes one revolution in 12 or 24 hours; the cover \(g\), together with the glass casing \(f\), protects the pencil and the diagram from accidental external damage.

Fig. 140.

In order to eliminate possible phenomena of resonance between the lever \(a\) and the weights \(c,c\), which distort the readings of the instrument, the lower points of attachment of the springs \(b,b\) may be shifted relative to the axis of swing \(c,c\).

In Fig. 141 a sample diagram is given, obtained with the aid of this instrument attached to a steam turbine coupled to a dynamo machine: line \(I—I\) corresponds to the turbine running idle, line \(II—II\) to the greatest load; at 9:34 a.m. an electric motor driving a compressor was switched on, period \(a\); from 10:55 a.m. to 11:25 a.m., period \(b\), the turbine was stopped; at 12:29 p.m. the compressor was switched on again, period \(c\); at 12:53 p.m.

the lighting was switched on, period \(d\). On average, the turbine operated with a load slightly less than \(1/2\).

Fig. 141.

The instrument described may be very useful for everyday observation of the operation of a station.

Moreover, in turbine tests, chiefly in acceptances, when the invariability of the load is an indispensable condition, the diagram obtained with its help may be useful as a document eliminating any dispute in this respect.

Chapter III

Measurement of Temperatures²³

17. Mercury thermometers.—Although at the present time there exist more accurate and more convenient instruments for measuring temperatures, such as thermoelements and instruments with electrical resistance, nevertheless glass mercury thermometers, owing to their simplicity and cheapness, are the most widely used.

These thermometers are best taken without a case, the so-called laboratory type, and, moreover, of the rod type, since thermometers with a scale enclosed in a second glass tube or jacket are more fragile.

The disadvantage of rod thermometers is that the paint on the divisions and numerals easily comes off; but since these are applied with hydrofluoric acid and are recessed, they can easily be renewed by coating the scale with paint made from lampblack or Dutch black mixed with drying oil, and wiping it with stiff paper; the paint will remain in the recesses. True, such paint is still less durable than the original, but its renewal is very simple.

So that thermometers should not break so easily from careless handling, it is better to take shortened thermometers; for low temperatures, directly with a scale from \(0^\circ\) to \(50^\circ\) C.; for temperatures above \(100^\circ\), part of the scale, approximately from \(+5^\circ\) to \(+95^\circ\), is replaced by a widening; for temperatures from \(200^\circ\) to \(400^\circ\), a second such widening is made after \(100^\circ\).

§ 17. Mercury Thermometers

It is desirable to preserve the divisions near \(0^\circ\) and \(+100^\circ\) so that the thermometer can subsequently be checked.

As regards the type of glass, for low temperatures, up to \(+100\div150^\circ\), one may use inexpensive thermometers made of so-called normal thermometric, or Jena, glass, or of glass of grade 16III; for higher temperatures thermometers should be taken of the best borosilicate glass, grade 59III. Incidentally, thermometers made of this glass are only slightly more expensive than the preceding ones, and therefore for more accurate tests it may be recommended that all thermometers be taken of glass 59III²⁴.

For temperatures up to \(+300^\circ\), and in extreme cases \(+330^\circ\), ordinary thermometers with an evacuated capillary tube may still be used. At \(+357^\circ\) mercury boils; therefore, for temperatures beginning from \(+300^\circ\) and higher, thermometers must be used in which the space above the mercury is filled with nitrogen or carbon dioxide under a pressure of \(10\div25\) atm. Since the presence of gas above the mercury adversely affects the accuracy of readings at low temperatures, such thermometers should be used only for temperatures above \(300^\circ\text{C}\).

Often thermometers installed by the factory are already present on the steam pipe. These are usually so-called factory thermometers, provided with a metal casing to protect them from mechanical damage. The lower part of the casing, screwed into the pipe, is made either with slots, which is better, or closed and filled, for heat transfer, with oil, mercury, or fine metal filings for temperatures above \(300^\circ\). Such a thermometer usually has a scale with divisions every \(2^\circ\).

In Fig. 142 such a thermometer is shown for temperatures from \(160\div400^\circ\text{C}\). The length \(l\), inserted into the pipe, is taken at about one half of the pipe diameter, but, for the sake of accuracy of readings, not less than 80 mm.

Although such factory thermometers are less accurate than good rod-type, so-called laboratory thermometers, sufficiently correct readings can nevertheless be obtained with their aid if they are properly checked. In checking, which is most simply done by comparison with a normal thermometer, it must be borne in mind that factory thermometers are graduated with a protruding mercury column, so that the corresponding corrections need not be introduced. This is one of their advantages. Another advantage is the greater sensitivity of the readings if the lower fitting is made with slots.

Chapter III. Measurement of Temperatures. § 17.

Handling thermometers. In order to increase the accuracy of the readings and the sensitivity of the instrument, i.e., to reduce as far as possible the inevitable lag of the readings when the temperature fluctuates, it is desirable that the bulb with the mercury be in direct contact with the medium whose temperature is being measured.

At the same time, to avoid a change in temperature due to heat exchange with the surrounding medium, the measurements should be made as close as possible to the place whose temperature is to be known.

A glass thermometer may be introduced into a pipe, or into a vessel containing steam or water, in several ways; when the pressure inside the pipe or vessel is small, one may simply drill an opening in the wall and insert into it a slightly conical rubber stopper with a small hole, into which the thermometer is tightly pushed. For better fastening of the thermometer, which is necessary at more considerable pressures, from 2 to 5 atm., it is useful to tap the opening in the wall slightly, and to grease the thermometer lightly with mineral oil before pushing it into the rubber stopper. After several days the stopper adheres so firmly to the glass that it cannot be removed except by tearing it apart. Finally, the stopper may also be tied to the pipe with wire.

If the measurement of temperature is intended to be made not only during a brief test but also subsequently—for example, in the cooling water leaving a surface condenser—then it is better to arrange a clamp in the form of a stuffing box, Fig. 143: into the pipe there is soldered or tightly screwed a piece of iron or brass tubing a, with a thread on its thickened outer end; by means of the compression nut b pressure is applied to the rubber ring c, thereby obtaining the required tightness. The force of friction prevents the thermometer from being forced out of the pipe by the water pressure; in addition, the rubber may be glued to the thermometer, as above, after lubricating it with oil. When the thermometer is taken out, a tin disk is placed in the nut b.

Fig. 143.

Fig. 144.

At pressures above 4–5 atm. one has to abandon direct insertion and use a fitting of the type shown in Fig. 144. The fitting is made of a copper tube and also either

§ 17. Handling Thermometers.

is soldered into the wall or screwed into it on a gasket. For better heat transfer, oil is poured into the fitting, or, better still, mercury; but in that case it must, of course, be made of iron.

When using oil in measuring high temperatures, one must bear in mind that oil sometimes contains constituents that boil at a temperature lower than that specified for the given oil; in view of this it happens that the thermometer indicates considerably below the true temperature until the aforementioned constituents boil away, and then it immediately rises.

It is therefore more reliable to fill the fitting with mercury up to \(340^\circ\), and above that with tin or another low-melting metallic alloy. In doing this, one need only remember to remove the thermometer before the temperature falls to the solidification temperature of the corresponding metal, since otherwise the alloy, solidifying, will crush the mercury bulb.

Among the low-melting metals that must be used instead of mercury, if the fitting is not machined iron, the following may be indicated: \(15\%\) by weight of tin, \(25\%\) lead, and \(60\%\) bismuth—melting point \(+125^\circ\); \(70\%\) tin and \(30\%\) lead \(+190^\circ\); tin \(+232^\circ\). It is dangerous to use pure lead, whose melting point is \(326^\circ\), since the steam temperature may accidentally fall below \(326^\circ\), and the thermometer will be ruined.

Into a vertical pipe the fitting is inserted obliquely, at an angle of \(30 \div 45^\circ\).

The disadvantage of using a fitting consists in the fact that part of the heat passes through the fitting to the pipe and is radiated from the latter, so that even at not very high temperatures the thermometer bulb has a temperature somewhat lower than that of the medium moving through the pipe. The resulting error can, however, be reduced, practically even eliminated, by wrapping the pipe around the fitting and also covering the top of the fitting itself with a heat-impermeable material.

Break in the mercury column. The capillary tube of the thermometer usually ends at the top in an expansion into which mercury enters if the thermometer has accidentally been heated above its limiting temperature; without this expansion the mercury, on excessive rise, would rupture the glass. When using a thermometer, it is necessary to see that no mercury remains in the expansion; otherwise the thermometer readings will be lower than the true temperature. If the mercury is not quite clean, part of the column may separate even without heating, from shaking, for example, during shipment of the instrument.

To join the mercury column, one may lightly tap the lower end of the thermometer against a wooden table, or, taking it in the right hand, strike it forcefully and sharply against the left, or make use of centrifugal force: taking the thermometer by its upper end, swing it rapidly with an outstretched arm.

Chapter III. Measurement of Temperatures. § 17.

In winter it is very easy and reliable to connect the column, cool the thermometer enough for all the mercury to collect in the bulb, while, of course, the thermometer should be lightly tapped or shaken. The same result can be achieved with the aid of some cooling mixture.

Corrections. In more precise investigations, when it is desirable to determine the temperature with an accuracy of up to \(0.1^\circ\), the readings even of the best, fully serviceable thermometer require several corrections.

1. A correction for the emergent column of mercury. Normally, the graduation of laboratory thermometers is carried out in such a way that all the mercury is exposed to the action of the corresponding temperature. Therefore, if during use of the thermometer part of the capillary tube with mercury protrudes outward, then this part of the mercury column will have a different temperature, and consequently its length will be different than if it were all immersed in the given medium. As a result, the thermometer reading will be incorrect, and it is necessary to introduce a certain correction, often called the “stem correction.”

This correction can be calculated from the expression

\[ \nu = n (t' - t_c)\alpha, \tag{25} \]

where \(t'\) is the temperature indicated by the thermometer, \(t_c\) is the mean temperature of the emergent mercury column, \(n\) is the number of degrees by which the column protrudes, and \(\alpha\) is the apparent coefficient of expansion of mercury, taking into account the expansion of the glass tube. Depending on the composition of the glass, this quantity ranges from \(\alpha = 0.00027\) for ordinary Jena glass down to \(\alpha = 0.000155\) for the best glass 59III.

For the temperature \(t_c\), one may with sufficient accuracy take directly the temperature of the surrounding air, measured by a thermometer whose bulb hangs at the middle of the height of the emergent column. Since, owing to the good heat conduction of mercury, the mean temperature of the emergent column is higher than the external temperature, especially when the column is short, it is more correct to take for \(\alpha\) a somewhat reduced value. With sufficient accuracy one may take, for inexpensive thermometers, \(\alpha = 0.0002\), and for thermometers made of glass 59III, \(\alpha = 0.00014\).

The significance of this correction may be judged from the following example: the temperature of strongly superheated steam is measured with a thermometer made of glass 59III; the thermometer indicates \(t' = 337^\circ\); it is inserted into the fitting up to the division \(+40^\circ\); a thermometer hanging nearby indicates \(t_c = +25^\circ\). Then, by formula (25), and, as indicated above, taking \(\alpha = 0.00014\), we have

\[ \nu = (337 - 40)(337 - 25)\,0.00014 = 13^\circ; \]

the temperature is \(337^\circ\) or \(350^\circ\)—a large difference.

§ 17. Corrections to Thermometer Readings.

Another example: the steam pressure is 10.5 atm. by the pressure gauge; at the boiler it was only slightly superheated; it is necessary to find out whether the superheat has been preserved or not. In view of the expected low temperature, a thermometer with a scale up to \(+200^\circ\), made of Jena glass with \(\alpha = 0.0002\), is taken; the reading gives \(t' = 185^\circ\), i.e. the temperature of saturated steam at an absolute pressure of 11.5 atm. It would seem necessary even to determine the moisture content of the steam. But if one notes that the thermometer is inserted up to the division \(+30^\circ\), and that the air temperature near it is \(t_c = 28^\circ\), we obtain the correction

\[ \nu = (185 - 30)(185 - 28)\,0.0002 = 4.9^\circ; \]

besides the fact that between \(185^\circ\) and \(190^\circ\) there is a rather considerable difference, this proves that the steam is still superheated, though only slightly, and the need to determine its moisture content is removed.

However, the correction \(\nu\) is necessary not only in measuring high temperatures, but may also be significant for comparatively low temperatures. Thus, for example, in measuring the temperature of condensate the correction may amount to \(0.1 \div 0.2^\circ\), i.e. it may still affect the value of the tenths digit in precise measurements.

Nevertheless, in cases where it is necessary to know not the absolute temperature, but only the difference between two temperatures, and moreover ones that do not differ greatly from one another, the error may practically be reduced to zero without introducing a correction, if the thermometers are inserted so that the mercury columns in both project by approximately the same number of degrees.

1. Correction for the influence of pressure. A vessel with mercury experiences pressure from inside from the mercury column and from outside—atmospheric pressure or the pressure of the medium into which it is immersed. The effects of these pressures are mutually opposite, but both tend to change the capacity of the vessel with mercury and thereby shift the whole scale.

If the thermometer was graduated at a barometric pressure of 760 mm, then at another external pressure \(h\), expressed likewise in mm Hg, a correction must be introduced:

\[ \mu = (760 - h)\,\beta, \tag{26} \]

where \(\beta\) is a coefficient depending on the kind of glass and determined experimentally. Numerically, \(\beta\) varies from 0.0001 to 0.0002; for thermometers made of glass 59III \(\beta = 0.000152\), and for 16III and ordinary Jena glass it is closer to 0.0002.

The fluctuation of the height of the barometer in our measurements may safely be neglected, but when a thermometer is introduced directly, without a socket, the pressure of the water or steam in the pipe may noticeably affect the thermometer reading. Thus, for example, if the cooling water entering the condenser has a gauge pressure of 3 atm., then the correction for a thermometer made of glass 16III is

\[ \mu = (760 - 4 \times 735.5)\,0.0002 = -0.41^\circ. \]

As we see, the correction cannot be neglected if the temperature is measured with an accuracy of up to \(0.1^\circ\).

However, even when measuring the temperature in the condenser or of the condensate itself, if the measurement is made correctly, i.e. directly at the condenser, before the pump, the correction can affect the tenths digit. For example, at a pressure in the condenser of \(0.05\) kg/cm² abs., i.e. about 37 mm Hg, the magnitude of the correction is

\[ \mu = (760 - 37)\cdot 0.0002 = +0.14^\circ. \]

1. correction for the displacement of 0° and, consequently, of the entire scale under the influence of thermal after-effect. However good and accurate an instrument may be, with the passage of time the influence of thermal after-effect is inevitable. The corresponding correction can most simply be found empirically—by verification.

The verification of a thermometer may be carried out either by determining the position of \(0^\circ\) by immersing the thermometer in melting ice, or by comparing its readings with an accurate standard instrument furnished with a certificate of the German Physico-Technical Imperial Institute (P.-T. I.). The latter method has the further advantage that, besides finding the true position of \(0^\circ\), by successive comparison of the working thermometer with the accurate one, corrections are simultaneously obtained for a series of temperatures, depending on the imperfect cylindricity of the capillary tube. The comparison is made by immersing both thermometers in water and stirring it well. By making the comparison with water of different temperatures, a table of corrections is compiled for the entire scale of the thermometer, which is then used subsequently.

In more accurate tests it is useful to determine \(0^\circ\) as often as possible, not less often than every 2–3 months. Repeated comparison of the whole scale is, of course, unnecessary; when the position of \(0^\circ\) changes it is only necessary to enter the corresponding changes in the indicated table of corrections.

Fig. 145.

The verification of \(0^\circ\) is performed very conveniently in the apparatus shown in Fig. 145: \(a\) is a brass or zinc cylindrical vessel 100–120 mm in diameter, closed at the top, with a conical bottom in which there is an opening and a tube \(b\) for draining the water that forms, since otherwise, when water accumulates, its temperature rises as a result of absorption of heat from the surrounding air. However, only the excess water need be drained, so that the mercury bulbs do not come into contact with air but remain below the water level; for this purpose a rubber tube is slipped over the branch pipe \(b\) and provided with a clamp.

§17. Verification of Mercury Thermometers.

For accurate verification at \(0^\circ\), the ice must be taken perfectly pure, i.e., obtained from distilled water. For better contact of the ice with the thermometer, the apparatus should be filled with pieces of ice as small as possible, or, better still, with ice scraped with a knife. The thermometer should be kept in the ice for 10–15 minutes and removed only after its readings have become fully established.

Verification at \(100^\circ\) is carried out in an apparatus of the type shown in Fig. 146: on a tripod stands a brass boiler \(a\), onto the neck of which is fitted a cylinder \(b\) of zinc or tinned sheet iron with double walls; a cover \(g\) is placed on top, into the nozzle-openings of which are inserted corks, through which the instruments being verified are passed; the openings \(e\) and nozzle \(d\) connect the internal cavity with the outside atmosphere; \(f\) is a glass water manometer communicating with the internal steam space; by this manometer the flame of the burner heating boiler \(a\) is regulated so that vaporization is not too intense and the steam pressure is equal to the atmospheric, barometric pressure \(B\).

When using the apparatus, it is necessary to see that the sensitive part of the instrument being verified—the mercury bulb, the junction of the thermoelement, or the platinum spiral—is by no means immersed in the water, since the temperature of the latter is not equal to the temperature of the steam, determined from the barometric pressure \(B\). On the other hand, the sensitive part should not be raised unnecessarily high above the water level.

For checking, it is useful also, in this apparatus, to keep in it an accurate normal thermometer.

It must not be forgotten that the temperature of water vapor is equal to \(100^\circ\text{C}\) only at a barometric pressure \(B = 760\) mm. At a higher pressure the temperature is higher; at a lower pressure, lower. With sufficient accuracy it may be considered that for each 1 mm Hg of pressure the temperature changes by \(\pm 0.037^\circ\). With precision instruments and measurements, and with a considerable deviation of the barometric pressure from normal, this correction must by no means be neglected.

Verification of a thermometer at higher temperatures is carried out most simply by comparison with an accurate instrument in an oil bath, well stirred by a stirrer or at least simply by a paddle.

Chapter III. Measurement of Temperatures

§ 18. Thermoelements. General remarks.

The thermoelectric method of measuring temperatures is based on the fact that if two rods of different metals are joined—soldered—at both ends to one another in such a way that along the rest of their length they do not touch one another, and the temperature of one junction is raised above the temperature of the other, then in the closed circuit of the rods an electromotive force will appear, the magnitude of which depends on the temperature difference of the junctions and on the nature of the metals used. By measuring this force and knowing the temperature of one of the junctions, one can determine the temperature of the other junction.

Choice of a thermocouple. In choosing metals for a thermocouple, two principal considerations must be kept in mind: first, the magnitude of the electromotive force and the law of its variation, and then the physical and chemical properties of the given materials; among other things, an important condition for a good thermoelement is the absence of secondary currents.

As regards the magnitude of the electromotive force, it should be the greater the lower the temperature being measured, and the law of its variation with temperature should desirably be as close as possible to the law of an inclined straight line.

As regards the physical and chemical properties of the metals selected, they must satisfy the following requirements: the metals should be as pure as possible, as little subject to oxidation as possible, should not change their structure under successive heatings, should not be brittle, and, finally, should be ductile, so that wire of uniform cross-section along its length can be made from them.

In view of all that has been said above, for measuring low temperatures, from \(0^\circ\) to \(100^\circ\) C., thermocouples of iron and constantan should be used—constantan being an alloy of 60% nickel and 40% copper.

The dependence of the electromotive force \(e\) of this thermocouple on the temperature \(t\) may be expressed, taking the temperature of one of the junctions as equal to \(0^\circ\) C., by

\[ e = 0.0481\,t + 0.0000027\,t^2 . \tag{27} \]

As is seen from equation (27), the electromotive force increases almost directly proportionally to the temperature.

For temperatures up to \(360^\circ\), one may use either the same iron–constantan thermocouple, or copper–constantan or silver–constantan thermocouples. Preference should be given to the latter thermocouple at high temperatures, as being less subject to oxidation, i.e., less variable also with respect to its readings. The law of variation of the electromotive force of the copper–constantan thermocouple may be expressed by the equation

\[ e = 0.0403\,t + 0.0000255\,t^2, \tag{28} \]

and for the silver–constantan thermocouple—

\[ e = 0.035\,t + 0.000025\,t^2 . \tag{29} \]

§ 18. Thermoelements.

As we see from Eqs. (28) and (29), the curve for the silver–constantan thermocouple is only slightly flatter than the curve for the copper–constantan pair, i.e. its sensitivity is only slightly less.

It should be noted, however, that the numerical coefficients in Eqs. (27)–(29) are not entirely constant, but represent only average values, since it is very difficult to have chemically pure metals, and still more difficult to obtain completely identical and homogeneous alloys. Therefore, when using thermocouples, \(f(e,t)\) is found experimentally for each pair of pieces of wire, and the results obtained are presented in the form of a table or, which is considerably more convenient, in the form of a diagram.

Methods of measurement. The actual measurement of the electromotive force that develops as a consequence of a temperature difference may be carried out in two ways: by direct measurement of the voltage with the aid of a sensitive millivoltmeter, and by the so-called zero method.

The zero method, or the method of compensating connection, is used for more accurate measurements, since it is more sensitive. It consists in balancing the unknown electromotive force of the thermoelement by another, known electromotive force.

The scheme of this method is shown in Fig. 147: \(t\) is the thermoelement, \(a\) a small electric accumulator, \(w_1\) a constant resistance, \(w_2\) an adjustable resistance, \(m\) a milliammeter, and \(g\) a galvanometer. The current from the accumulator \(a\), regulated by means of the resistance \(w_2\), produces in the resistance \(w_1\), equal, for example, to \(0.1\) ohm, a difference of potentials which must balance the unknown electromotive force of the thermoelement \(t\); for this, the contact on \(w_2\) is moved until the needle of the galvanometer \(g\) comes to 0; the reading on the milliammeter \(m\) will make it possible to find the temperature \(t\).

Fig. 147.

Fig. 148.

If, in the preceding circuit, instead of the resistance \(w_2\), the resistance \(w_1\) is varied when making the reading, we obtain the circuit of Fig. 148:

the current from the accumulator \(a\), which produces across each element of the resistance \(w_1\) a definite potential difference, goes through the main circuit \(w_1 w_2 w_3 a\) and branches off into the section \(tcg\); the greater the electromotive force of the thermocouple \(t\), directed against this current, the farther the contact on the resistance \(w_1\) must be moved, i.e., it must be increased, so that both electromotive forces balance each other, as will be indicated by the needle of the galvanometer \(g\); the position of the contact \(w_1\) then gives directly the potential difference in millivolts, whence the temperature \(t\) is usually found.

Since the voltage drop in the main circuit over the section \(w_1 w_2 w_3\) must always be exactly the same, while the electromotive force of the accumulator \(a\) varies, the voltage drop must first be adjusted by means of the resistance \(w_2\). The adjustment is made by comparison with the normal element \(n\), which is connected by means of the switch \(c\), so that the needle of the galvanometer is again brought to zero.

The method according to the diagram in Fig. 148 is more reliable than the method according to the diagram in Fig. 147, since in it the accuracy of the readings depends only on the constancy of the electromotive force of the normal element \(n\) and of the resistance \(w_1\), which is in fact attainable, whereas in the method according to Fig. 147 the accuracy depends on the accuracy of the readings of such a delicate instrument as the milliammeter \(m\).

With the zero method, thermocouples made of thinner wire, down to \(0.2\) mm, may be used, which further increases the sensitivity of the instrument.

The disadvantages of the zero method are the greater complexity of carrying out the readings and the impossibility of measuring rapidly fluctuating temperatures, as well as the high cost of the measuring apparatus.

Corrections for resistance. When working with a thermoelement, it must be remembered that the certificate of the P.T.I., with which every good thermoelement should be supplied, indicates the electromotive force \(e\) of the element itself. A millivoltmeter connected to the thermoelement measures the voltage at the terminals, which is less than \(e\) by the magnitude of the voltage drop in the element itself; the latter is equal to the product \(ir\), where \(i\) is the current strength and \(r\) is the internal resistance of the element. Since \(i\) depends on the external resistance, i.e. chiefly on the galvanometer, the voltage at the terminals of the element will also be different, depending on the galvanometer used. In addition, the galvanometer is usually placed at some distance from the thermoelement and is connected to it by copper conductors, the resistance of which must also be taken into account, since, in the case of a considerable distance and a small resistance of the galvanometer, their influence may be quite significant.

§ 18. Corrections to the readings of thermoelements.

Thus, in order to obtain accurate results, the reading of the instrument must be multiplied by a certain coefficient, calculated on the basis of Ohm’s law. If \(e'\) is the reading of the galvanometer, \(r_1\) the internal resistance of the thermoelement, \(r_2\) that of the copper conductors, and \(r_3\) that of the galvanometer, then the actual electromotive force \(e\), from which the desired temperature is to be determined with the aid of the certificate of the F.-T. I. I., is

\[ e = e'\frac{2(r_1+r_2)+r_3}{r_1+r_2+r_3}. \tag{30} \]

The magnitude of the correction may be judged from the following example: a thermoelement of silver-constantan; the wires have \(d=0.5\) mm; their length \(l=1000\) mm; \(r_1=2.49\) ohms; the length of the copper conductors is \(L=15\) m each; their diameter \(d_2=1.0\) mm; the resistance of the millivoltmeter is \(r_3=357\) ohms.

First let us find the resistance \(r_2\) of the conductors: the specific resistance of copper \(c=0.017\); with the aid of the expression

\[ r = c \cdot L/f, \tag{31} \]

where \(f\) is the cross-section of the conductor in \(\mathrm{mm}^2\), we obtain for both conductors

\[ r_2 = 2 \cdot 0.017 \cdot \frac{15}{0.7854} = 0.66\ \text{ohm}; \]

then, by equation (30),

\[ e = e'\frac{2(2.49+0.65)+357}{2.49+0.65+357} = 1.009\,e'. \]

The correction is almost \(1\%\); at a temperature of \(+360^\circ\) it amounts to \(+3.2^\circ\), which is already very large.

For practical use, on the basis of such a calculation, a temperature curve is compiled from the table in the certificate of the F.-T. I. I. for the entire installation: thermocouple, conductors, and millivoltmeter. Such a diagram makes it possible, from the reading of the millivoltmeter, immediately to obtain the graphically corrected temperature.

If the thermoelement has been supplied without a certificate, but with a millivoltmeter having a scale graduated directly in \({}^\circ\mathrm{C}\), then the indicated corrections have already been introduced in the manufacture of the instrument. However, in the case of using long connecting conductors, it is useful to carry out a check at several temperatures at the principal points: melting of ice for \(0^\circ\), boiling of water for \(+100^\circ\), and boiling of mercury for \(+357.2^\circ\).

Influence of cold junctions. The second important condition for the accuracy of the readings is that the free ends, the so-called cold junctions, of the thermoelement should have the same temperature as during calibration. At the F.-T. I. I. thermoelements are verified by immersing these ends in melting ice. This is the most correct method. In technical measurements one often confines oneself to cooling the ends with running water, whose temperature is measured and added to the readings of the thermoelement.

Sometimes the ends are not cooled, and the temperature of the surrounding air is simply added to the instrument readings. This latter method, however, cannot be regarded as correct: owing to radiation and heat transfer from the heated junction, the temperature of the cold junctions may be considerably higher than the air temperature, and the error may amount to several degrees, while at the same time there is no way to take it into account.

In millivoltmeters having a temperature scale and a device for resetting the pointer, the correction for the temperature of the cold junctions can be avoided by setting the pointer, before switching on the millivoltmeter, not at \(0^\circ\), but at the temperature of the cold junctions immersed in running water. Of course, for precise measurements this method is not suitable, since the electromotive force increases, according to equations (27)–(29), not directly in proportion to the temperature, but somewhat faster.

Influence of the ambient temperature. Finally, it must also be borne in mind that the resistance of the windings of millivoltmeters, and consequently their readings, depend on temperature. Therefore the millivoltmeter must be installed so that it has the normal room temperature. If its heating cannot be eliminated, its readings will be lower than the true ones, and a certain correction must be introduced. For modern portable instruments, the readings must be multiplied by \(\alpha = (1 + 0.0013 \Delta t)\), where \(\Delta t\) is the excess of the instrument temperature over the normal room temperature \((+15^\circ \mathrm{C})\).

For more accurate observations, the numerical coefficient at \(\Delta t\) must be calculated, requiring from the instrument manufacturer exact data on the magnitudes of the resistance of the whole instrument and of its winding separately.

Finally, in general it is necessary to ensure that all connections where different metals touch have the same temperature, equal to the room temperature; otherwise thermoelectric currents will also arise at these points, affecting the reading of the thermoelement.

The accuracy of the readings of the thermocouples indicated above, in connection with good millivoltmeters, amounts, if all the corrections given are observed, to \(\pm 1^\circ\), and in the best case to \(\pm 0.5^\circ\). When using the zero method of measurement it is easy to obtain an accuracy of \(\pm 0.5^\circ\) and even down to \(\pm 0.2^\circ\).

19. Design and Accessories of Thermoelements.

The wire for thermoelements is taken about 100 cm long; the actual length has no significance, so long as it is sufficiently large that the heat communicated to one end of the thermocouple wires does not heat the other ends.

If several identical thermoelements are required, the simplest and cheapest way is to order from the Physico-Technical Institute a thermocouple, supplied with a certificate, made of two wires of such length that, by cutting them into pieces of approximately 100 cm each, the required number of thermo—

§ 19. Design of Thermoelements

...the thermocouple. It is then still necessary to have a corresponding millivoltmeter or an instrument for zero measurement and a switch. The mounting for thermoelements for all measurements with steam turbines can be made on site, and for some measurements, as we shall see below, one cannot even proceed otherwise.

Thermoelements are most often made from wire 0.5–1.0 mm thick. Although thermocouples of constantan in combination with iron, copper, and silver may be made with a thickness of up to 2 mm, such a thickness is useless, and sometimes even harmful, when the temperature being measured is subject to fluctuations.

The joining of the ends exposed to the temperature being measured is done either by fusing them or, at low measured temperatures, by soldering with pure tin; in doing this, no acids may be used, but only rosin, since acids eat away the wires and change the resistance of the thermoelement.

It is most reliable to join the ends of the wires by twisting them together over a length of about 5 mm and fusing the tips in a gas flame. Twisting alone is unreliable, since the wires may become covered with oxide, which greatly increases the resistance.

The free ends of the thermoelement are connected to insulated copper conductors leading to the instrument by means of which the electromotive force is measured. This connection is made either by clamps or, better, by soldering with tin and rosin. In view of the negligible voltage of the current, the insulation of the conductors may be simple, as for electric bells.

The resistance of these conductors should not be great; it is desirable to make it no more than 1 ohm; for this purpose, with each conductor up to 20 m long, it is sufficient to use copper wire 1 mm thick, and with a length up to 100 m—2 mm.

The wires of the thermocouple must be carefully insulated from one another along their entire length. This can be done by putting a thin glass tube or glass beads on one of them; the whole element is also inserted into a glass tube sealed at one end. A thermoelement equipped in this way may be introduced into the steam or water space by the same methods as mercury thermometers.

If it is desired to increase the sensitivity of the thermoelement, an open tube may be used and the hot junction may even be allowed to protrude slightly from it. In this case the thermocouple must be made of wires which, at the given temperatures and in the given medium, do not oxidize, for example, of constantan and silver. In this case measures must be taken, such as the use of a stuffing-box arrangement, to preserve the tightness of the space in which there is steam or water under a pressure different from atmospheric pressure.

Chapter III. Measurement of Temperatures. § 16.

In Fig. 149 is shown a specimen of such a thermoelement²⁵: \(a\) is the heated junction of the thermoelement, \(b,b\) are glass tubes, \(c\) is a plaster filling, \(d\) is a glass tube enclosing the thermoelement, \(e\) is an insulating sheath, glass or rubber, in the copper plug \(f\), screwed into the iron tube \(g\), which itself is screwed into the cast-iron flange \(h\); the outer iron tube \(g\) protects the outgoing ends of the thermoelement from mechanical damage; \(i\) is a plug, rubber or even wooden.

Fig. 149.

In Fig. 150 is presented a simpler arrangement used by the author: one of the wires of the thermocouple is inserted into a thin glass tube \(b\), soldered to the broader tube \(c\), into which plaster is poured, and on top of it Mendeleev cement \(d\); then both wires are inserted into the glass tube \(e\) with a flaring \(f\) at the top and are likewise filled with plaster \(g\) and, above, with Mendeleev cement \(h\). The thermoelement so fitted is inserted into the steam space by means of a union of the type shown in Fig. 143.

Figs. 150–151.

Fig. 152.

Fig. 153.

Finally, in Fig. 151 is shown the mounting of a thermoelement used by the author for screwing into the casing of a multistage turbine for investigating the temperature in the different stages: \(a\) is the measuring junction, \(b\) and \(b\) are two thin glass tubes, which, after being put onto the thermocouple, are heated until softened and flattened so that they can pass through as narrow a—

§ 19. Thermoelement Frames

a large opening, 5–6 mm, in the bronze plug \(d\); further on, the wires are passed through the rubber plug \(c\), into which the ends of the tubes \(b,b\) also enter; the rubber is compressed by the nipple \(e\); \(f,f\) are likewise glass tubes. The merit of this apparatus is the very small thickness of the part projecting into the steam space, and its tightness at any steam pressure.

To make a thermoelement of iron-constantan more sensitive to temperature fluctuations, and bearing in mind the easy oxidizability of iron, which does not allow the hot junction to be left open, the firm of Keiser and Schmidt manufactures, for steam lines with superheated steam, a special thermoelement with a fitting made of a thin steel tube, provided near the hot junction with 8–10 thin ribs \(a\), increasing the surface of the tip 10–20 times, Fig. 152. In order that, should the steel tube begin to let steam pass through, the latter could not burst outward or seep into the cable leading to the galvanometer, a stuffing box is arranged in the head \(c\).

To increase the electromotive force of a thermoelement, for a given temperature difference between the hot and cold junctions, and thereby also the accuracy of the instrument, several thermocouples may be connected in series according to the scheme of Fig. 153: \(a,a\), the left wires in each of the 4 pairs, for example, are of constantan, while \(b,b\), the right ones, are of iron, copper, or silver. The electromotive force of such a complex thermoelement is, of course, when the electromotive forces of all the individual thermocouples are equal, 4 times the force of each thermocouple, and the deflection of the millivoltmeter pointer is likewise that many times greater for a given temperature difference. With such thermoelements, with corresponding numbers of pairs, it is possible to measure the most insignificant temperature fluctuations, down to \(0.1^\circ\) and even less. It must be borne in mind, however, that a series connection of several elements reduces the sensitivity of the instrument, i.e., its rapid following of temperature fluctuations.

In this way, in the thermoelement according to Fig. 152, for example, 2 iron-constantan thermocouples are connected in series, which makes it possible to measure temperatures from 0 to \(50^\circ\) with an accuracy of up to \(0.25^\circ\), owing to the fact that sufficient sensitivity has been preserved.

Cold junctions. As already stated above, the cold junctions of thermoelements must be cooled either with melting ice or with water.

Ice may be kept either simply in a glass beaker, or better in a vessel with an opening at the bottom for draining the melt water. As such a vessel one may use, for example, the vessel shown in Fig. 145.

When cooling with running water, the temperature of which must be measured with a thermometer, one may use a small bath of the type used in photography for washing negatives, with inflow and outflow of water by rubber tubes, or a glass vessel into which the water enters near the bottom through a rubber tube from a vessel placed higher up—

...a bucket or a small barrel, and run down directly over the edge into the vessel placed underneath.

At the present time there exist instruments in which not only the need to maintain a constant temperature of the cold junctions is eliminated, but also, in general, the need to introduce any corrections to the readings of the millivoltmeter.

One of such devices—the “compensator” of Prof. Bristol²⁶, Fig. 154—consists of an additional resistance that decreases as the temperature rises. This is a mercury-filled sealed glass vessel with a high, narrow neck; in the mercury is immersed a loop made of platinum wire, connected to it and passed through the glass by means of copper ends soldered in—one to one of the free ends of the thermocouple, the other to one of the conductors leading to the millivoltmeter.

Fig. 154.

When the ambient temperature rises, the temperature of the cold junctions also rises, and, consequently, the readings of the millivoltmeter decrease. At the same time, however, the temperature of the mercury in the compensator also rises; the mercury expands, its level rises, and the length of the free ends of the loop decreases, while with this its resistance decreases, which in turn increases the deflection of the millivoltmeter needle. By selecting the length of the loop, the capacity of the vessel with mercury, and the diameter of its neck in accordance with the internal resistance of the millivoltmeter, it is possible to achieve complete elimination of the influence of changes in the temperature of the cold junctions. Bristol’s compensator is very convenient, especially when millivoltmeters with not particularly large internal resistance are used.

Another analogous device, designed by Schwarz and manufactured by the firm Keiser & Schmidt, consists in the following²⁷: the copper conductors leading to the millivoltmeter are separated; to their clamps the thermocouple wires—iron and constantan—are connected directly, and a length is assigned to them according to the distance at which the millivoltmeter stands. In other words, the cold junctions have the same temperature as the whole millivoltmeter; the latter is provided with a device that automatically adds to the temperature difference between the heated and cold junctions the temperature increase. An iron-constantan thermocouple is used because the law of variation of its electromotive force comes closest to an inclined straight line, which is especially important when the temperature of the cold junctions varies.

§ 19. Cold Junctions.—Millivoltmeters.

When using several thermocouples according to the diagram in Fig. 153, the intermediate unheated junctions of iron and constantan are also brought out to the galvanometer, so that they too have the same temperature.

In Fig. 155 a diagram is shown of such a connection and of the corresponding galvanometer: \(c\) and \(c\) are two thermoelements connected in series by means of the compensating loop \(l\); the spiral \(b\), soldered from two strips with different coefficients of expansion under a change of temperature, is fixed immovably at its left end, while its right, free end is attached to the spring holder \(h\), which carries the spiral \(s\). When the temperature rises the spiral \(b\) unwinds and communicates to the movable system of the instrument and to the pointer \(c\), under the action of the spring \(f\) and the spiral \(s\), a rotation clockwise; when the temperature falls the pointer \(c\) turns somewhat in the opposite direction. By means of this device the pointer of the millivoltmeter, without the action of the thermocurrent, is set to the temperature of the surrounding air. This temperature, being equal to the temperature of the cold junctions lying at the instrument itself, is thus automatically added to the temperature indicated by the millivoltmeter under the action of the thermocurrent.

Millivoltmeters. As the measuring instrument one usually takes a precision millivoltmeter with a pointer, most often of the Deprez-d’Arsonval system.

For operational measurements, instruments of the firm Keiser and Schmidt are fairly widespread; in them the vertical axis of oscillation of the moving part of the instrument, the coil with the pointer, ends in points resting in jewels. These instruments are comparatively sturdy and give correct readings even if they are not installed strictly level, or if the support trembles slightly.

Instruments of the same firm according to the diagram of Fig. 155 are made with a horizontal axis of oscillation; their external appearance, with a round casing, resembles a manometer. These are good stationary instruments, but they are not suitable for precise measurements.

Very accurate and convenient instruments are manufactured by the Siemens & Halske works. In Fig. 156 there is shown, at \(1:5\) natural size, a millivoltmeter with a moving part on points. In Fig. 157 an instrument of the same firm is shown, but with a winding suspended on a tautly stretched wire. A mirror located next to the scale makes it possible to take very accurate readings: when reading, the eye must be placed so that,

Chapter III. Measurement of Temperatures. § 19.

so that the pointer covers its image in the mirror. Before the reading is taken, the instrument must be brought, by means of the leveling screws, into a strictly horizontal position, as indicated by the circular level \(a\). On the side there is a clamp \(b\), which should be lowered before the reading is taken, turning it upward, and after the reading again closed; failure to observe this rule shortens the service life of such a delicate instrument and may even easily cause it to break. By turning the upper part of the tube in which the conducting wire is located, the pointer can be set to the temperature of the cold junctions. Generally all precision instruments, including that shown in Fig. 156, are furnished with a clamp and a scale with a mirror.

Fig. 156.

Fig. 157.

Instruments with a suspended coil are more sensitive, but also more fragile; they require careful leveling and extremely cautious handling.

Fig. 158.

Fig. 159.

The instruments of Hartmann & Braun are likewise distinguished by great accuracy and sensitivity; they are made with a suspended coil. A specimen of such an instrument, also on a scale of \(1 : 5\) natural size, is shown in Fig. 158.

Some firms also manufacture wall-mounted galvanometers, with the pointer arranged at the side. A specimen of such an instrument by the Cambridge Scientific Instrument Co. is shown in Fig. 159. Such instruments are especially convenient for permanent installation in the engine room, where it is difficult to find a fully suitable, secluded place for setting up a table-type instrument.

In order to reduce the influence of accessory resistances that may vary—for example, of connecting wires or switches—millivoltmeters are deliberately made with a large internal resistance of 300–600 ohms.

The millivoltmeters described above usually have, in addition to the scale graduated in millivolts, a second scale graduated in degrees C., making it possible to take readings directly, without consulting tables or curves of the relation between electromotive force and temperature. In doing so, however, one must not forget that the temperature scale is determined empirically for the given thermocouple; it may not be suitable for another.

Finally, Fig. 160 shows, at 1:5 natural size, a compact set of instruments for measurement by the zero method according to the diagram in Fig. 148, manufactured by Siemens and Halske; identical letters, but capitalized, designate the same parts as in Fig. 148.

Fig. 160.

For continuous monitoring of temperatures—for example, of superheated steam—recording galvanometers are useful. For turbine testing they are not indispensable, although they are also desirable in order to determine how well the requirement of constancy of the temperature before the turbine has been satisfied.

A convenient and comparatively compact instrument by Hartmann & Braun is shown at 1:5 natural size in Fig. 161. It consists of a millivoltmeter of the Deprez–d’Arsonval system, combined with a special self-recording device. Its action is as follows: a clockwork mechanism rotates uniformly a drum on which paper is fixed, and at the same time every 30 or 45 seconds causes an arc with divisions, located over the entire width of the tape, to descend and for an instant press against it the pointer of the voltmeter, fitted with a special pen for recording; this gives a successive series of points replacing a continuous curve; the drum makes one revolution in 24 hours. Since the pointer, during its movements, does not touch the paper, the sensitivity of the instrument is not impaired by the pressure of the recording device.

Fig. 161.

To measure the ordinates of the resulting diagram, a transparent glass scale is supplied. The arcs printed on the paper, and the distances between them corresponding to \( \frac{1}{2} \) hour, make it possible to determine the time of any point of the diagram.

Switches and change-over switches. In order not to keep the millivoltmeter under current all the time, whereby it inevitably wears out, it is better to switch it on only when taking readings—except, of course, for the monitoring instruments that are needed to watch the turbine and therefore are switched on once and for all.

As a switch one may use either a push button, as used for electric bells, or a small switch,

§ 19. Switches and commutators.

used for lighting; but, in view of the possible variability of the resistance of these devices, for precise measurements one should use a mercury switch. It can be made simply from a small glass jar, around which the conductor coming from the millivoltmeter is wound and thereby fastened to it; the end of this conductor, stripped of insulation, is constantly immersed in the mercury, while the end of the conductor connected to the thermoelement is passed through a glass tube, bent around its axis, and is immersed together with it in the mercury only when the temperature reading is being taken.

Since several thermoelements have to be connected in turn to a single millivoltmeter, this is very conveniently done by the same mercury switch: the ends of the conductors soldered, for example, to the negative pole of the thermocouples, i.e. to the constantan wires, are all clamped under one terminal of the millivoltmeter, while the ends from the other pole, in the manner indicated above, are immersed at the appropriate moments in the mercury.

If no more than 5 thermoelements are switched successively, it is convenient to use the commutator shown full-size in Fig. 162: through the ebonite board \(a\) passes the axis of rotation of the pawl \(b\), provided, for better contact, with a gold tip; this pawl is connected behind the board with one of the terminals of the millivoltmeter; \(c_1, c_2 \ldots c_5\) are brass spring plates, by means of which the pawl \(b\) can be brought into contact; under the screws fastening \(c, c\) to the board \(a\), the ends of the conductors soldered to the corresponding thermocouple wires are clamped; the stop adjusting screws \(d_1, d_2, \ldots\) are connected by conductors behind the board \(a\) with the pawl \(b\) and ensure switching-on; the key at the pawl \(b\) is provided with a pointer indicating which of the plates \(c, c\) is at the given moment connected into the circuit with the millivoltmeter. This commutator can also be actuated by a clockwork mechanism, when using a self-recording millivoltmeter.

Fig. 162.

20. Resistance thermometers. General remarks.—These instruments are based on the increase in the electrical resistance of a platinum (rarely gold, nickel, or iron) wire as the temperature rises.

According to the latest experiments of Callendar, this dependence from \(0^\circ\) to \(600^\circ\mathrm{C}\) can be well expressed for platinum by the equation

\[ r = r_0 \left(1 + 0.0034675\,t - 0.00000000075\,t^3\right), \tag{32} \]

where \(r_0\) is the resistance at \(0^\circ\mathrm{C}\).

Chapter III. Measurement of Temperatures. § 20.

In practice, good instruments are always calibrated by experiment.

Methods of measurement. All the numerous resistance-measurement circuits, very diverse at first glance, may be reduced to 4 basic ones.

Method 1: the unknown variable resistance \(r_t\), Fig. 163, is determined from a known constant resistance \(r\); namely, the current from an accumulator or dry cell \(a\) branches at point 1, and, according to Kirchhoff’s law,

\[ i_1 : i_2 = \frac{1}{r} : \frac{1}{r_t}, \]

whence

\[ r_t = r \cdot i_1 / i_2; \tag{33} \]

knowing the magnitude \(r\) and measuring the current strength \(i_1\) and \(i_2\) in each of the branches by means of the corresponding instruments \(i_1\) and \(i_2\), Fig. 163, one can find the unknown resistance \(r_t\), and from it the corresponding temperature.

Fig. 163.

Fig. 164.

Method 2: Koepchen proposed the circuit, Fig. 164, with two cells \(a_1\) and \(a_2\) and one ammeter \(g\); the electromotive forces of the cells are taken equal, each equal to \(e\). Through the branch \(1—2\) there will flow a current whose strength, according to Kirchhoff’s law, is

\[ i = \frac{e(r_t - r_1)}{r_t(r_1 + r) + r_1 r_2}, \tag{34} \]

i.e. the current strength \(i\), measured by the milliammeter \(g\), is approximately proportional to the difference of the resistances; a small change in the resistance \(r_2\) causes a considerable change in the current strength \(i\), and, consequently, a large deflection of the pointer \(g\).

The value of the resistance from which the temperature is found is, from eq. (34),

\[ r_t = \frac{r_1(e + i r_2)}{e - i(r_1 + r_2)}. \tag{35} \]

§ 20. Resistance thermometers.

Method 3, with a Wheatstone bridge, Fig. 165; if \(r_0\) is the resistance of the bridge and of the milliammeter \(m\), \(r\) the resistance in the section \(1-a-2\), \(e\) the electromotive force of the cell \(a\), and \(i\) its current strength, then, denoting the current strengths passing through the separate branches respectively by \(i_1, i_2, i_3\) and \(i_4\), and through the bridge by \(i_0\), and bearing in mind that all the resistances are made equal, \(r_1=r_2=r_3\), we obtain, by Kirchhoff’s law, the following expression for \(r_t\):

\[ r_t=\frac{e r_1^{\,2}+i_0 A}{e r_1-i_0 B}, \tag{36} \]

where

\[ A=r^3+2r_0r_1^{\,2}+2rr_1^{\,2}+3rr_0r_1, \]

\[ B=rr_0+2rr_1+2r_0r_1+3r_1^{\,2}. \]

Despite their somewhat complicated form, the quantities \(A\) and \(B\) do not make the calculations difficult, since they do not change and for each given installation may be computed in advance once and for all.

Since the voltage \(e\) must be known, by measuring \(i_0\) we have all the data for determining \(r_t\).

In practice they proceed so that, at \(0^\circ\text{C}\), all four resistances are equal, \(r_t=r_1\); the scale is marked experimentally in such a way that the deflection of the milliammeter needle directly indicates the required temperature in \(^\circ\text{C}\).

Fig. 165.

Fig. 166.

Method 4: this is a zero method, obtained from method 3 if one of the constant resistances \(r_1\), \(r_2\), or \(r_3\) is replaced by an adjustable one, Fig. 166, and, when \(r_t\) changes, it is adjusted so that the needle of the galvanometer \(g\) returns to 0; in this case, obviously, directly

\[ r_t=r_3. \tag{37} \]

Comparing all the methods examined with one another, one may say that the most convenient and simple is method 3; more sensitive and especially convenient for small changes in temperature is method 2; the zero method 4 is somewhat more complicated, but it is the most accurate: with it one may use a much more sensitive galvan—

nometer, since its scale may, for the same length, have only a small number of very large divisions; moreover, this method does not depend on changes in voltage and current strength, nor on the accuracy of the graduation of the galvanometer scale, provided only that its zero is correct; and, finally, as will be seen below, with it the harmful influence of additional resistances is easily eliminated.

Method 1 has now been abandoned, as insufficiently sensitive and accurate owing to the presence of two ammeters.

Sources of errors and their elimination. When using the most widespread method 3, the expression for the resistance \(r_t\), eq. (36), includes, besides the current strength, also the voltage \(e\) in the main circuit. Instead of measuring \(e\) each time, in practice it is preferable to work with a constant \(e\). In order that, despite a change in the voltage of element \(a\), a constant \(e\) should remain in the circuit, the diagram in Fig. 165 must be supplemented by two additional resistances \(r_4\) and \(r_5\), Fig. 167. The control resistance \(r_4\) is made of such magnitude that, when it is switched in by means of switch \(c\) in place of the thermometer resistance \(r_t\), at the proper \(e\) the pointer of the milliammeter comes to a definite mark. If the voltage of element \(a\) has decreased, the deflection of the pointer will be smaller; then part of the resistance \(r_5\) is cut out until the pointer assumes the required position. If, with \(r_5\) completely cut out, the pointer still does not reach the mark, then the accumulator must be recharged.

Fig. 167.

Fig. 168.

In instruments according to method 2, Fig. 164, the checking of \(e\) is performed by the same switching over to a control resistance; in this case the setting of pointer \(g\) to the required mark is attained by regulating the resistance \(r_2\), which serves as a shunt for ammeter \(g\). To use expressions (34) and (35), it is further necessary to ensure that the voltages of the currents sent by elements \(a_1\) and \(a_2\) into branch \(1—2\) are strictly identical. To regulate any possible small difference, the connection to point 2 is made by means of pe-

§ 20. Measurement Circuits with Resistance Thermometers

of a large resistance slider, installed so that, at a certain temperature of the thermometer \(r_t\), \(0^\circ\text{C}\), the pointer \(g\) stands at 0.

In method 4 the voltage of the current has no significance.

The second source of errors is the change in temperature not only of the platinum thermometer coil, but, owing to heat transfer and radiation, also of the wires connected to it that lead to the measuring resistance. In view of the uncertainty as to what length of the wires is affected by heating, and according to what law their temperature falls from the measured \(t\) to \(t_0\), that of the surrounding air, it is analytically very difficult to allow for the additional, “harmful” resistance which occurs and raises the instrument reading; therefore efforts are made to eliminate its influence by the appropriate design.

For the zero method this influence can be completely eliminated by means of Callendar’s compensating loop, Fig. 168: the \(c,c\) conductors, the “harmful” resistance of which is to be eliminated, are made of wire of the same metal as the resistance \(r_t\), but of a considerably larger cross-section in order to lessen their influence; the \(e\) loop is of the same metal, of the same cross-section and of the same length as \(c\), arranged parallel to \(c\) and connected into the section \(4-r_3\). Thus, to exactly the same extent as the harmful resistance increases, the resistance \(e\), i.e. of the section \(4-r_3\), also increases, and we still have exactly \(r_t=r_3\). A certain drawback of this loop is the necessity of leading 4 conductors from the resistance thermometer.

For method 3 the compensating loop cannot fully eliminate the influence of the harmful resistance, as is seen from Eq. (36), but it does give some improvement; the main point is that the harmful resistance should be made as small as possible, and then its change will not be so appreciable.

In order that temperature fluctuations in the room not affect the readings of the instruments, all the remaining conductors must have as small a resistance as possible. These conductors are taken as insulated copper wires of such cross-section that their total resistance is not more than 1 ohm; in precise measurements the conductors are made as short as possible, so that their resistance is only 0.1, or even 0.01 ohm.

To be certain that the resistance of the conductors will not change with time, all connections should be made by soldering with tin, and not by clamps or screws, whose contact surfaces easily become covered with oxide, greatly increasing the resistance. Where clamps are unavoidable, the contact surfaces must be inspected and cleaned.

For the correctness of the readings, the constant resistances are made of manganin, whose temperature coefficient of change of resistance—

of which is only 0.00001. The adjustable resistances, Fig. 166 or 168, in precise measurements are better made in the form of resistance boxes with plugs; the latter should have a large, well-lapped surface.

Finally, care must be taken that there are no thermocurrents in the circuit, for which purpose all connections should, as far as possible, be of the same metals and have the same temperature.

The current strength from the accumulator should not be great, only about 0.1 ampere. For especially precise measurements, for example by the null method, the current strength is taken still smaller, about 0.01 amp., so that the current does not noticeably heat the platinum spiral.

Verification. In conclusion it may be mentioned that the verification of these instruments is carried out exactly as for mercury thermometers, and with the same instruments.

21. Construction of resistance thermometers.—At not especially high temperatures, from +100° to 600°C, platinum wire may be replaced, for the sake of economy, by nickel wire. Such an instrument, for measuring the temperature of superheated steam, screwed into the wall of a pipe, using Kapeller’s circuit, method 2, and manufactured by the firm G. A. Schultze, is shown in Fig. 169; the resistance is made in the form of a spiral of nickel wire wound on a porcelain rod; the casing is of iron.

Next we shall indicate several instruments for measurement by the most common method 3.

In Fig. 170 is shown, approximately at 1:2 natural size, a thermometer manufactured by the firm Braun, screwed directly into the wall of a pipe. The spiral is of nickel; the casing is steel; length \(l = 150\) mm.; the instrument is usable up to 500°C.

In Fig. 171 is shown, at 1:2 natural size, an instrument of the same firm for measuring the temperature of a liquid by direct immersion of the whole instrument in it: a thin nickel wire \(a\) is wound on a porcelain tube, open at both ends; the wire is enclosed

§ 21. Construction of resistance thermometers.

hermetically with air from the copper tube \(b\); the conductors to the galvanometer consist of a flexible two-core cable with lead sheathing \(c\). Owing to the contact of the instrument with the liquid both inside and outside, a very rapid following of its indications after changes in the temperature of the liquid is attained.

Fig. 171.

In Fig. 172 is shown, at 1:4 natural size, an instrument of the firm Hartmann & Braun: in a flat metallic casing there is enclosed a thin platinum strip, wound spirally on a mica plate. The flange at the lower part of the head is fastened to a coupling for screwing into a steam pipe; in the case of a flat wall of a vessel with the liquid being tested, the instrument may be screwed by its flange directly to this wall. The instrument can measure temperatures from \(-100^\circ\) to \(+500^\circ\) C. The galvanometer is made directly with a temperature scale. Fig. 173 shows an example of a wall-mounted galvanometer for the instrument of Fig. 172, with a scale for temperatures from \(-20^\circ\) to \(+60^\circ\) C.; galvanometers of the same type are also made with scales for other temperature limits, e.g. \(+150^\circ\) to \(+400^\circ\) C for superheated steam.

Fig. 172.

Fig. 173.

Chapter III. Measurement of Temperatures. § 21.

The most successful construction to date should be considered that which appeared 3–4 years ago and is manufactured by the firm W. C. Heraeus, figs. 174 and 175: the platinum wire is wound, in the form of a spiral, onto a rod of quartz glass heated until softened, and is inserted into a thin-walled tube of the same glass; then the tube is heated until softened, and the air is pumped out of it, as a result of which the tube fits tightly onto the rod, so that the turns of the spiral

Fig. 174 and 175.

are brought close to the surface of the tube, fig. 175; owing to the absence of an air space such a thermometer responds almost instantaneously to changes in the measured temperature and is not afraid of the sharpest vibrations, by virtue of the properties of quartz glass, which has an extremely small coefficient of expansion. From the platinum resistance to the terminals in the head run two conductors, made, up to \(+400^\circ \mathrm{C}\), in order to reduce cost, of silver wire; connection with the platinum ends is made by fusing.

In fig. 176 such a finished thermometer for precise measurements is shown at \(1:2\) natural size; the lower thin part has a thickness of only 4 mm, the length of the platinum spiral is 60 mm, its resistance at \(0^\circ \mathrm{C}\) is 50 ohms; similar instruments are made with a total thickness of 3 mm, with a spiral length of 20 mm and a resistance of 25 ohms.

Fig. 176.

Specimens of instruments for technical purposes, provided with a sheath of iron or steel tube, are given in figs. 177 and 178, both at \(1:5\) natural size; spiral length 60 mm, its resistance 50 ohms; limits of application from \(-200^\circ\) to \(+700^\circ \mathrm{C}\); the thickened part of the actual measuring instrument, having a length of 100–150 mm, at the top may have any length from 0 to 500 mm.

§ 21. Design of Resistance Thermometers.

In Fig. 179 there is shown, at 1:5 actual size, the external appearance of a Weston bridge for thermometers according to Figs. 177–178.

Finally, a specimen of an instrument from the Cambridge Scientific Instrument Company for measurement by the zero method is shown in Figs. 180–182: a a platinum spiral wound on a cross of mica plates, b four platinum conductors, including 2 conductors and the compensation loop of Callendar; c mica disks supporting these conductors, d a farfor tube, e a steel tube-casing, f also a steel tube; the head g is made, for laboratory work, of beech wood; i clamps for the conductors to the Weston bridge.

Fig. 179.

Fig. 180–182.

The Weston bridge and the galvanometer may be taken of the ordinary type, but the set made by the Cambridge Scientific Instrument Company, where the bridge, galvanometer, and cells are assembled in one small box, Fig. 183, at about 1:7

Fig. 183.

actual size, is also very convenient.

... namely: $I$ the thermometer itself, $B$ the galvanometer, the pointer of which is brought to zero by changing the resistance, corresponding to $r$, in Fig. 166, for which purpose the knob $H$ is turned; $F$ a push-button switch for closing the current; the moving scale $A$ gives the resistance $r_t$, or even directly the temperature sought $t_n$ in °C; $C$ a pair of accumulator cells, and $R$ an adjustable resistance for setting the required voltage.

As the source of electric current in modern designs, accumulator cells are most often used—one, or sometimes two, with a voltage of about 2 volts and a capacity of 10–15 ampere-hours. In view of the negligible current consumption in the above-mentioned arrangement, and since the current is closed only at the moments of taking readings, the cells have to be charged only once every few months.

22. Measurement of temperatures at turbines.—In testing steam turbines it is necessary to measure the temperatures of steam, water, and oil; moreover, the latter measurement has no direct bearing on the working process in the turbine as determined during the test, and therefore we shall discuss it separately in the chapter on lubrication.

Steam temperatures. In order to establish, during a test, the conditions under which the turbine is operating, the steam temperatures must be measured:

1. at the end of the steam pipe, before the very inlet into the turbine, i.e., in most turbines before the regulating throttle valves, in order to know whether the turbine has saturated or superheated steam, and in the latter case by how much;

2. in a more detailed test, measurement of the steam temperature between the throttle valve and the inlet into the turbine itself already pertains to the investigation of the working process of the turbine, but in method of measurement it does not differ in any way from the first measurement;

3. further, it is necessary to measure the temperature of the steam at the outlet from the turbine: on the one hand, to determine the state of the steam if it emerges superheated—which, however, happens rarely—and, on the other, in the more usual case, to check the readings of the vacuum gauge;

4. sometimes the temperatures of the steam in the condenser are measured at the beginning of the steam path, in the middle, and at the end, in order to assess the operation of the condenser;

5. finally, in factory tests of a new type of multi-stage turbine and in scientific laboratory investigations, the steam temperature is measured in individual stages of the turbine in order to determine the actual working process and ways of improving it.

For the measurements under items 1 and 2, mercury glass thermometers are most often used. In recent times, however, thermoelements and resistance thermometers have been gaining ever wider application. Both these types of instruments have substantial advantages, both in respect of the convenience of taking readings and, chiefly, in view of the possibility of taking them at a distance.

§ 22. Measurement of steam temperature.

In the sense of measurement accuracy, mercury thermometers made of Jena 59^III glass, with graduations in 1°, thermoelements with readings by millivoltmeter, and resistance thermometers with readings by milliammeter may be considered approximately equivalent. With careful treatment and observance of the precautions indicated above, the accuracy is about ±1° at high temperatures and up to ±0.5° at temperatures of 150–180°; in general, about ±0.3%.

Greater accuracy is hindered by the necessity of introducing thermometers by means of a fitting of the type shown in Fig. 144, or the fittings of thermoelements and resistance thermometers. In any case, an accuracy higher than ±0.3% is not required. The temperatures indicated in many test reports with an accuracy down to 0.1° are simply the results of averaging from a series of consecutive readings and testify not at all to the accuracy attained, but to so-called “fascination with decimal places” and to an insufficiently thoughtful attitude toward the results obtained.

Although the velocity of steam in pipes is generally small, some projection or rib near the thermometer fitting may cause local superheating of the steam at the expense of kinetic energy, as will be explained in detail below. Such superheating causes an increase in the instrument reading.

In view of this, if the steam temperature proves to be only 2–5° higher than the saturated-steam temperature corresponding to the given pressure, then before deciding that the steam is slightly superheated it is necessary to verify whether the superheating is not merely apparent, and whether, on the contrary, the steam may not even be wet.

For measuring the temperature of low-pressure steam, the 3rd and 4th measurements, it is simplest to use a mercury glass thermometer, introduced directly by means of a rubber stopper. Thermometers should be taken with graduations of 0.5°, which, when the corresponding corrections are applied, makes it possible to determine temperatures with an accuracy of up to ±0.5°.

Sometimes thermoelements or resistance thermometers are also used for these measurements, but more rarely, since they offer only one advantage—the possibility of taking readings at a distance—while for these measurements they are less accurate and, moreover, comparatively expensive. However, once one of these methods has been chosen for measuring the temperature of live steam, the connection of the same instruments for exhaust steam is already inexpensive.

The greatest attention and especially accurate instruments are required for measuring the temperature in the individual stages.

In Fig. 184 there is shown, at 1:5 natural size, the corresponding device with a mercury thermometer, installed in the turbine of the Rato system at the Danzig Polytechnic.^52) The device has only one advan—

^52) Z. V. d. I. 1904, S. 1531.

Chapter III. Measurement of Temperature. § 22.

...by its extreme simplicity, but it also has a whole series of substantial shortcomings: the use of a fitting is itself the source of a number of errors indicated above in § 19, but in the present case one more is added to them—the influence of the velocity of the steam, before which the influence of the temperature of the walls of the casing vanishes; for this reason the thermometer \(t\) is inserted into the fitting by means of a wooden plug \(c\).

Steam which, on leaving the moving wheel, has a considerable velocity, strikes the fitting; the kinetic energy of the impact is converted into heat, part of which goes to heating the fitting, and, consequently, the thermometer reading will be higher than the true temperature of the steam in the given stage.

Let us try to calculate, at least approximately, the possible increase \(\Delta t\) in the thermometer reading. As an example, take the steam velocity \(c=200\) m/sec, its pressure \(p=9\) kg/cm\(^2\) abs.; take the dimensions of the fitting from Fig. 184: \(d=14\) mm, the length protruding into the steam space \(l_1=30\) mm, the total length \(l=75\) mm; wall thickness 1.5 mm; material—brass.

The heat \(Q\) developed by the steam on impact against the fitting is equal to its kinetic energy multiplied by the thermal equivalent of work \(A=1/427\):

\[ Q=\frac{1}{2}Mc^2 \cdot A. \tag{38} \]

The mass of steam striking in 1 sec may be found from the corresponding volume \(V\) m\(^3\)/sec, the specific weight, equal at 9 kg/cm\(^2\) (considering the steam dry saturated) to \(\gamma=4.54\) kg/m\(^3\), and the acceleration of gravity \(g=9.81\) m/sec\(^2\):

\[ M=V\gamma/g. \]

The second volume of steam \(V\) may be found as the product of the area of the projection of the fitting \(l d\) by the velocity \(c\). But, in view of the cylindrical outline of the fitting, only those particles of steam will lose all their velocity whose motion is directed along the normal to the curvature of the cylinder, i.e., directed toward its axis; the remaining particles will strike the fitting and be deflected from their path, losing only part of their velocity. The influence of the cylindrical outline is taken into account by assuming that not the full volume of steam participates in the impact, but multiplied—

§ 22. The Influence of Steam Velocity

... by a certain coefficient \(\psi < 1\). The value of \(\psi\) may be taken, on the basis of purely geometrical calculations, confirmed fairly well by some experimental data, as equal to 0.67.

Then, for our case, we obtain

\[ M = 0.67 \cdot 0.03 \cdot 0.014 \cdot 200 \cdot 4.54 / 9.81 = 0.0259, \]

whence, by equation (38),

\[ Q = \frac{1}{427}\cdot \frac{1}{2}\cdot 0.0259 \cdot 200^{2} = 1.21\ \text{heat units/sec.} \]

From the amount of heat found, it is necessary to determine the rise in steam temperature \(\Delta t\), assuming that it is distributed over the entire quantity of steam

\[ V\gamma = 0.03 \cdot 0.014 \cdot 200 \cdot 4.54 = 0.382\ \text{kg/sec.} \]

Taking the heat capacity of steam \(c_p = 0.575\), we find

\[ \Delta t = \frac{1.21}{0.575 \cdot 0.382} = 5.5^\circ \text{C}. \]

Then we shall find the amount of heat \(q\) which, out of the \(1.21\) heat units found, will pass from the steam to the fitting, using the known expression

\[ q = \alpha f z (t_2 - t_1), \tag{39} \]

where \(\alpha\) is an empirical coefficient, which for saturated steam is \(4000 \div 6000\); we shall take \(\alpha = 5000\); \(f\) is the area in \(\text{m}^2\), in our case this is the front half of the cylinder surface, i.e.

\[ f = 0.5 \cdot \pi \cdot 0.014 \cdot 0.03 = 0.00066\ \text{m}^2; \]

\(z\) is the time in hours; in our case \(z = 1\ \text{sec} = 1/3600\ \text{hr}\); \((t_2 - t_1) = \Delta t = 5.5^\circ\). Thus

\[ q = \frac{5000 \cdot 0.00066 \cdot 5.5}{3600} = 0.00504\ \text{heat units/sec.} \]

From the dimensions indicated above, the total weight of the fitting is found to be

\[ 4.89\ \text{cm}^3 \cdot 8.55 = 41.7\ \text{g}; \]

its heat capacity may be taken as \(0.092\); the oil in the fitting is approximately

\[ 2.060\ \text{cm}^3 \cdot 0.92 = 1.9\ \text{g} \]

with heat capacity \(0.40\), and, finally, the weight of mercury in the thermometer is approximately

\[ 0.25\ \text{cm}^3 \cdot 13.56 = 3.4\ \text{g} \]

with heat capacity \(0.0033\).

From these data we find

\[ \Delta t = \frac{5.04}{41.7 \cdot 0.092 + 1.9 \cdot 0.40 + 3.4 \cdot 0.033} = 1.07^\circ. \]

Although the value found, \(1.07^\circ\text{C}\), cannot lay claim to great accuracy—the possible error is \(\pm 20\%\), perhaps even \(\pm 30\%\)—it nevertheless clearly shows that, in measurements where an error of \(0.5^\circ\) is significant, this method must be recognized as undesirable.

Moreover, it must be borne in mind that the velocity \(c = 200\ \text{m/sec}\) taken by us is by no means limiting; in modern large turbines with

\[ n = 3000\ \text{rev/min} \]

\(c\) reaches \(400\ \text{m/sec}\); in this case \(\Delta t\) increases...

proportional to \(c\), i.e., for the preceding branch pipe, at \(c = 400\) m/sec., one obtains \(\Delta \tau = 2.14^\circ\) C. This circumstance explains why, in the tests by Prof. Josse of the Ehrmann turbine, in which the velocity \(c\) reaches 800 m/sec., i.e. the value \(\Delta \tau\), calculated as indicated above, would be about \(+4.3^\circ\), the measurement of temperatures not only with mercury thermometers but also with thermoelements gave, however, such exaggerated data that they could not be used²⁸.

Instead of a mercury thermometer with a measuring branch pipe, these measurements should be made by means of a silver-constantan thermoelement with an open heated junction, according to Figs. 150 or 151, and with a cold junction immersed in melting ice; and the measurements themselves should be made by the zero method, Figs. 147 or 148, using the instrument shown in Fig. 160, or with the aid of precise resistance thermometers, Fig. 176, the measurements likewise preferably being made by the zero method, Figs. 166 or 168. The thermometer should be introduced directly into the steam space, generally as shown in Fig. 151, i.e., by means of a stuffing box with a rubber packing, screwed into an opening in the thickness of the casing.

Finally, it must be pointed out that even at a moderate steam velocity, up to 100 m/sec., when the error \(\Delta \tau\) calculated above is no more than \(0.2 \div 0.3^\circ\), a mercury thermometer with a branch pipe still cannot be used. The fact is that such a branch pipe, owing to its contact with the turbine casing, along which a heat flow moves from the high-pressure stage, where the steam is highly superheated, may be heated above the temperature of the steam in the given stage. Thus Stodola²⁹, comparing, at different turbine loads, the readings of thermometers, one inserted in a branch pipe screwed directly into the turbine casing and the other in a branch pipe insulated from the casing, found that the readings of the former were in all cases, owing to the aforementioned heat movement, approximately \(3^\circ\) higher than the readings of the latter. An error of \(+3^\circ\) is too large. True, by making the indicated comparison one can find the corresponding correction, but it is nevertheless not very reliable.

In general, every effort must be made so that the accuracy of measuring the steam temperature in the individual stages is no less than \(\pm 0.5^\circ\), and, if possible, \(\pm 0.25^\circ\). To achieve this, bearing in mind that there are 10–20 points of measurement, not counting temperature measurements outside the turbine, is not easy.

Temperatures of water. In turbine testing the temperatures of water usually have to be measured at three points: the temperature of the cooling water as it enters the surface condenser, its temperature as it leaves it, and the temperature of the condensate.

§ 22. Measurement of water temperatures.

When working with a spray condenser there remain, of course, only two measurements: that of the cooling water and of the mixture of condensate with the cooling water.

In all these cases it is simplest and most reliable to carry out the measurement by means of mercury-in-glass thermometers. It is sufficient to take its scale divided into \(0.5^\circ\), from which, with a certain amount of practice, readings may be taken by eye with an accuracy of up to \(0.1^\circ\).

It is best to insert the thermometer directly, or by means of a rubber stopper, or by means of a gland according to Fig. 143.

For the rest, one must bear in mind everything stated above in § 17.

Recently, for temperatures up to \(+50^\circ\) C., thermoelements have also begun to be used, chiefly according to the scheme of Fig. 153, or resistance thermometers, for example of the type shown in Fig. 171. Though less accurate than glass mercury thermometers, both of these latter types of instruments are very convenient, especially for the continuous observation of the temperature of the spent cooling water, allowing readings to be taken from the engine room without going down into the basement, where it is often dark and cramped.

In conclusion it should also be mentioned that, in some designs of surface condensers, the cooling water approaches the discharge pipe from different tubes at different temperatures. In this case, for the sake of accurately determining the mean temperature, measures must be taken to mix the water and give it a vortex motion. One may, for example, place in the discharge nozzle a tin spiral, or several—2 or 3—tin disks fastened on an axial rod, with round openings, shifted relative to one another in the series of disks according to the pattern of the oil nozzle of Diesel engines.

Chapter IV.

Measurement of pressures.

23. Spring pressure gauges.—A pressure gauge gives the so-called excess pressure \(p\), often called the manometric pressure, i.e. the difference between the given absolute pressure \(p_2\) and the atmospheric, or barometric, pressure \(p_0\), also expressed in kg/cm²:

\[ p = p_2 - p_0, \tag{40} \]

whence the absolute pressure \(p_2\) is found by adding the atmospheric pressure to the pressure-gauge reading \(p\),

\[ p_2 = p + p_0. \tag{41} \]

Atmospheric pressure is measured by means of a barometer, which gives it in the form of the height of a mercury column \(B\) in mm. In order to con—

to express the barometric pressure in kg/cm², it must be remembered that
\(1\ \text{kg}/\text{cm}^2 = 735.5\) mm Hg at \(0^\circ\)C, i.e.,

\[ p_0 = B/735.5. \tag{42} \]

In technical measurements it is often more convenient to take the temperature of the mercury as \(15^\circ\)C; then \(1\ \text{kg}/\text{cm}^2 = 737.4\) mm Hg.

The simplest of the spring manometers, the so-called Ducommun or Schaeffer manometer, as manufactured by the firm Schaeffer & Budenberg, is shown in Fig. 185: the pressure is received by a circular metal plate \(a\), the edges of which are clamped between the flanges of the instrument casing; the plate \(a\) is most often made of hardened steel and, for greater elasticity, is provided by stamping with wave-like concentric corrugations; the pressure being measured acts from below, and from above, at the center, a rod \(b\) is attached to \(a\); by means of levers and a toothed sector \(c\), the bulging of plate \(a\) when the pressure rises is transmitted to the pointer, seated on the axis \(d\), on a greatly enlarged scale. A thin spiral spring \(g\) presses all the joints in a constant direction, thereby weakening the effect of the unavoidable lost motion in them.

Fig. 185.

Fig. 186.

Despite the wave-like outline of plate \(a\), its bulging under pressures up to 10–12 atm does not exceed 2 mm, and in some instruments even 1 mm. Owing to such rigidity of the plate, the instrument is less sensitive to sudden pressure fluctuations and external shocks, but on the other hand there is less lost motion, and wear—

§ 23. Spring Pressure Gauges.

...slackness in the transmitting mechanism is reflected very noticeably in the accuracy of its readings.

With a strong and especially with a sudden increase of pressure, the plate may shift somewhat, as though it were drawn into the upper part of the instrument, and then the readings of the instrument become incorrect. To prevent this phenomenon, the works of Dreyer, Rosenkranz, and Droop first rivet the plate to a rigid iron ring and only then clamp it together with it between the flanges, Fig. 186.

In order to obtain, in the manufacture of the pressure gauge and also in its subsequent testing, the required setting of the pointer, as well as the required transmission ratio in its mechanism, the latter is usually provided with two adjusting devices: by changing the length of the rod \(e\), Figs. 185 and 186, and by the screws \(f\). In fact, for setting the pointer to 0 there are still other means: the pointer may be turned on the axis on which it is held only by friction, and it is also possible to turn by one or several teeth the gear engaging with the toothed sector.

Fig. 187.

A model of a pressure gauge of another type, invented by Schinz, but better known under the name of the Bourdon pressure gauge, as manufactured by the Schaeffer & Budenberg works, is shown in Fig. 187. The action of this instrument is based on the fact that a curved metallic spring tube \(a\), one end of which is soldered, and the lower end, soldered to the union \(b\), communicates with the liquid whose pressure is being measured. When the pressure inside the tube increases, the latter straightens and transmits this motion to the pointer \(n\) by means of the lever \(c\) and the toothed sector \(d\); when the pressure falls, the tube coils up again; shifting the hinge \(e\) makes it possible to set the required transmission ratio.

In pressure gauges for pressures up to 15 atm., the tube is made of brass, thin-walled, and, for greater flexibility, flattened into an ellipse. Its free end moves by 6–10 mm, owing to which the accuracy of these pressure gauges is higher than that of the preceding ones, Figs. 185 and 186.

In order that the readings of the Bourdon pressure gauge be correct, the spring tube must always have the same temperature as during graduation, i.e. room temperature. In view of this, when measuring steam pressure, measures must be taken so that steam does not enter the tube, and the pressu—

Chapter IV. Measurement of Pressures. § 23.

should not be transmitted by means of water that is not strongly heated, as will be discussed in greater detail below.

To protect the manometer from accidental heating, the Dreyer, Rosenkranz and Droop works arrange the tube \(R\), Fig. 188, so that its open end is at the top and communicates with the vertical tube \(H\); thanks to this, even in the absence of pressure, the condensation water cannot flow out of tube \(R\) and always stands at the level \(a—b\). To avoid accidental heating at the start of using the instrument, the works fills tube \(R\) with glycerine.

Fig. 188.

Fig. 189.

How much the heating of the tube distorts the readings and damages the manometer is evident from the following experiment: the manometer according to Fig. 187 was subjected to the direct action of steam; at a pressure of \(2.4\ \mathrm{kg}/\mathrm{cm}^2\) it indicated 2.6, at \(6.0\)—6.4 and at \(10.6\)—12.3; moreover, after cooling, the pointer began to indicate 1 atm. more than before. A manometer tested in parallel under the same conditions according to Fig. 188 gave correct readings and did not suffer from the action of the steam.

In addition, at Rosenkranz’s suggestion, the indicated works supplies Bourdon manometers with a spring \(D\), Fig. 189, made of hardened steel wire, which is concentric with tube \(R\) and is fixed rigidly at \(x\) with its immovable end \(K\), and at \(y\) with its movable end; spring \(D\) participates in the motion of tube \(R\), takes upon itself a certain part of the stress and, by partly unloading tube \(R\), increases the durability and accuracy of the instrument.

Finally, for especially precise measurements, and also for checking ordinary instruments, so-called control manometers are made, consisting of two independent manometers with independent pointers and exactly graduated scales. In addition to especially careful workmanship, the control manometer differs also in design—by a smaller number of transmission levers—

§ 23. Test Manometers.

...for the sake of reducing the lost motion, and with an eccentric scale with long hands. Finally, for better observation of the complete serviceability of the mechanism, they try not to cover it with the dial. In Fig. 190 such a manometer is shown: \(h\) is the shut-off cock; it is attached to the corresponding opening by means of flange \(e,e\) and two bolts \(f\); the opening in the flange is on the rear side and is not visible in the drawing.

Fig. 190.

Two independent mechanisms are made with the following aim: so long as the readings of both hands are exactly the same, one may be sure that the manometer is in good order, since it is almost impossible that the spring tubes should become distorted simultaneously and continue to give exactly identical readings.

Sometimes the mechanisms and hands are arranged one above the other; then it differs still less in appearance from an ordinary manometer. Other factories arrange the hands in yet another way: crosswise or one in the usual manner, and the other under the dial, so that only its upward-curved tip is visible from it, Figs. 191. In contrast to the instrument in Fig. 190, this one is provided with a shut-off valve \(h\) and a round flange \(e\), tightened by means of the more widespread and convenient clamp \(f\), Fig. 192, with a screw.

Figs. 191 and 192.

Chapter IV. Measurement of Pressures. § 23.

Self-recording manometers are very useful for monitoring the operation of a station, but in tests as well they are useful, and in some cases an indispensable aid, since they provide a document indicating to what extent, during the test, the requirement of constancy of operating conditions was met; and in some cases they give, in general, the necessary picture of the turbine’s operating conditions.

In Fig. 193 is shown one of the simplest Bourdon self-recording manometers, at the end of whose pointer there is a special pen or pencil; the dial, with a diagram paper fastened to it, makes, under the action of a clock mechanism concealed behind it, one revolution in 12 or 24 hours.

Figs. 194 and 195 show, approximately at \(2:7\) full size, a much more cumbersome and expensive, but also far more accurate, instrument of this kind.

The clock mechanism is located in the chart drum \(T\), which makes a complete revolution in 12 or 24 hours. The writing instrument may be either a very soft pencil or a special pen with aniline ink; in order not to reduce the sensitivity of the instru-

§ 23. Connection of pressure gauges.

the recording device should barely touch the paper. Owing to the considerable length of the pen arm, the transmission mechanism is reduced to only one small lever, which increases the accuracy of the instrument.

In Fig. 195 the rotation of the drum for changing the paper and winding the clockwork is shown by dotted lines.

The tube for transmitting pressure is connected to branch pipe \(G\), while flange \(S\) serves for fastening the instrument to a bracket or a wall, for which corresponding holes are drilled in it.

The remaining letters denote the same things as in Fig. 189.

Connection of pressure gauges. The correctness of the indications and the durability of metallic pressure gauges, especially of the Bourdon system, are adversely affected by two circumstances: high temperature and abrupt fluctuations of pressure. The influence of the first circumstance can be eliminated, or at least greatly weakened, by inserting a so-called water loop: the tube connecting the steam space with the pressure gauge, most often of copper, is bent in the form of a circular or elongated loop; Figs. 196–198, in which the condensed steam is retained, so that the pressure-gauge tube is filled not with steam, but only with heated water. In Fig. 198 the cock \(h\), to the branch pipe \(m\) of which the pressure gauge is screwed, is a three-way cock and is provided with flange \(e\) for the control pressure gauge.

Fig. 196–198.

It is useful to include such a loop in any case also with the pressure gauge shown in Fig. 189.

To weaken the harmful influence of sharp shocks during pressure oscillations, for example ahead of the regulating valves of Parsons turbines, two methods may be used: throttle the pressure and insert an elastic cushion.

The first method may be carried out, for example, by applying cock \(h\), Figs. 196 and 197, and, in the case of especially strong shocks, by inserting into the piping to the pressure gauge Walter’s device, used by the firm Schaeffer; Fig. 199: into the conical fitting \(a\) is inserted the lapped plug \(b\), with a helical channel cut on its surface; the spring \(c\) presses the plug; fitting \(d\) is connected with the tube, and

Chapter IV. Measurement of Pressures. § 23.

a pressure gauge is screwed into \(a\). Owing to the very long path to the screw channel, which offers considerable resistance, short-period pressure oscillations do not have time to be transmitted to the pressure gauge.

Fig. 199.

Fig. 200.

Fig. 201.

Fig. 202.

Another very simple device, resembling the diesel-engine nozzle, is shown in Fig. 200: in the nipple \(a\), into which the tailpiece \(b\) of the pressure gauge is screwed, 3–4 washers \(c,c\) are inserted, the openings of which are offset with respect to one another; the rings \(d,d\) provide the required spacing between the washers.

Fig. 201 shows a Shaffer and Budenberg device according to the second method, at the same time replacing the water loop: the steam, entering from below through the tube, condenses and remains at the bottom of the spherical enlargement \(B\); when the water rises to the lower edges of \(B\), air becomes trapped in the side channels, in the space \(A\), and in the pressure gauge itself, and this air serves as an elastic buffer that softens shocks. In addition, strong throttling occurs in the small openings \(C\), which lead into the ring \(A\), and in the small opening that connects the cavity \(A\) with the pressure gauge itself.

Fig. 202 shows an analogous device made by Eckardt & Co.

Figs. 203 and 204 show, approximately at \(1/6\) natural size, the same kind of protective device, but combined with a Focht mud separator: the steam pressure is transmitted to the pressure gauge through the tube \(a\), while the vessel \(u\), with the tube \(c\) lowered almost to its bottom, forms a water seal that prevents contact of the steam with the pressure-gauge spring; the upper part of the pear-shaped chamber \(b\) forms an air cap, and dirt, often carried along by the steam, settles in the lower part; the cock \(d\) serves for discharging the dirt, and the cock \(e\) for connecting a control pressure gauge. The instrument is attached by means of the flange \(f\) and two bolts to some bracket; Figs. 203 and 204 show the union \(g\), to which the instrument is attached in case of

§ 23. Connection of Pressure Gauges.

the installation of the pressure gauge at the steam boiler; \(g\) is set into the brickwork of the boiler.

Figs. 203 and 204.

Finally, when the connecting tube leading to the pressure gauge is of any considerable length, the height of the column of water condensing in the tube may affect its readings; for example, a difference in water levels of 1 m introduces into the pressure-gauge reading an error of \(0.1\ \mathrm{kg}/\mathrm{cm}^{2}\).

To avoid this error, which fluctuates with changes in pressure if the water does not fill the tube and either rises or falls in it, it is useful to fill the entire connecting tube with water beforehand and to include a device that keeps the difference in water levels at a constant height, which will make it possible to add to the pressure-gauge readings a constant correction known in advance.

Such a device is shown in Fig. 205: \(a\) is a vessel in which the water remains at one height, since the water from the steam gradually condensing in it flows through tube \(b\) into steam pipe \(c\); \(d\) is the tube to the pressure gauge, always filled with water; when the steam pressure increases, the displacement of part of the water from \(a\) into \(d\) cannot lower the level by any appreciable amount.

Fig. 205.

24. Mercury Pressure Gauges.—For the accurate measurement of small pressures of \(1 \div 1.5\) atm., it is sometimes useful to use pressure gauges with mercury, in which the steam pressure is balanced and measured directly by the corresponding column of mercury.

They are usually made in the form of two glass tubes communicating at the bottom, of which the upper end of one communicates

Chapter IV. Measurement of Pressures. § 24.

with the steam space, and the other—with the atmosphere; if the pressure being measured is above atmospheric, then in the first tube the level will fall, and in the second it will rise; the difference of levels \(h\) will give the required pressure in mm of mercury column. To convert the pressure into kg/cm\(^2\), \(h\) must be divided by 737.4, i.e., by the height of a column of mercury at \(15^\circ\)C corresponding to 1 kg/cm\(^2\). Since mercury expands appreciably when the temperature rises, at a higher temperature \(t^\circ\)C the column \(h'\) will be higher than the column at \(15^\circ\). To convert the observed column \(h'\) to the height \(h\) at \(15^\circ\), it must be multiplied by the corresponding coefficient, namely

\[ h = h'\,[1 - 0.00018\,(t - 15)], \tag{43} \]

Fig. 206 shows such a manometer for pressures up to 1400 mm Hg, i.e., approximately up to 1.9 atm. A rubber tube is put onto the corrugated nozzle \(a\), connecting the manometer with the steam space; the projection \(b\) is made on the open elbow so that, in the event of an accidental rise of pressure above the limit, the mercury will not splash onto the floor; for the same purpose, it is useful to place pieces of cotton wool in the funnel above the ball.

Fig. 206.

If, when both elbows are connected with the atmosphere, the mercury in them stands exactly at 0, and the diameters of the tubes are identical, then instead of the difference of levels one may simply take double the reading on one of the scales.

In order that the influence of capillarity not be excessively noticeable, the diameter of the glass tubes should be taken as no less than 8 mm.

For precise measurements, purified, dried mercury should be used, and the glass tubes should be thoroughly washed, first with a weak solution of nitric acid, and then with alcohol, and thereafter dried.

Finally, care must be taken that there be no water either above the mercury or in the tube connected to the steam space, since the column affects the difference of mercury levels, increasing it if it is in the manometer above the mercury on the side of the pressure being measured, and decreasing it if it is in the tube communicating with the atmosphere. If, nevertheless, water is found above the mercury, then the corresponding correction must be introduced, bearing in mind that 1 mm of water column is equal to 0.074 mm of mercury column.

By virtue of the construction of mercury manometers, they are very convenient to use when it is necessary to determine the difference between two pressures. Thus, a mano-

§ 24. Mercury Manometers.

With the manometer according to Fig. 206 it is possible to measure the difference of pressures in adjacent stages of impulse turbines, if one steam space is connected by a rubber tube to branch pipe \(a\), and the other to branch pipe \(b\). Of course, the thickness of both the rubber connecting tubes and the glass tubes of the manometer must correspond, in terms of strength, to the absolute magnitude of the pressures being measured.

Differential manometer. Still more convenient for the latter purpose, and more accurate for small pressure differences, as, for example, in adjacent stages of reaction turbines, is the differential manometer of Schaeffer and Budenberg, shown at \(1:5\) natural size in Figs. 207 and 208. This is the same kind of U-shaped instrument with mercury, but with a special pointer: in both glass tubes, iron balls float on the surface of the mercury; these pull along the ends of the rocker arms \(a\), made of magnetized steel; the pointer \(b\) indicates directly the pressure difference on a scale that permits readings down to \(0.001\ \mathrm{kg}/\mathrm{cm}^{2}\). The greatest pressure difference that can be measured with this instrument is about \(0.10\text{--}0.12\ \mathrm{kg}/\mathrm{cm}^{2}\).

Self-recording mercury manometer. Quite recently the firm of Hallwachs & Co. has put out an instrument called by it “Gasosa” and shown schematically in Fig. 209, p. 144: to the branch pipe \(d\) of vessel \(b\), in which the mercury is located, a tube is connected from the space in which the pressure is being measured; the measured pressure causes the mercury to rise in the glass tube \(c\). Platinum wires are soldered into tube \(c\) at equal intervals; the other ends of these wires are connected to various points of the electrical resistance \(r\), included in the circuit of the voltmeter \(v\); the higher the column of mercury, the greater the part of the resistance that is switched—

included, the greater the deflection obtained by the pointer \(v\); the current in the network is obtained from the accumulator \(a\). In order to equalize the resistances with long conductors and the changes in the voltage of the accumulator \(a\), there is an adjustable resistance \(c\); so that the current is not consumed in vain, the circuit is closed only at the moment of taking the reading by the switch \(s\).

The instrument is made for pressures from 0.01 to 1 atm. gauge; in this case the pressure steps—the divisions of the scale—are made, as desired, from 0.1 to 0.01 atm.; the accumulator \(a\) has a capacity of 28 ampere-hours at a voltage of 12 volts.

The voltmeter \(v\) is usually made self-recording, of the kind indicated above, Fig. 161, only more compact.

Fig. 210 shows, approximately at 1:10 of natural size, the external view of the manometer itself, with divisions of 0.02 atm., enclosed in a tin casing; and Fig. 211 shows the distribution board for it with a self-recording voltmeter by Siemens and Halske and the other accessories listed above.

25. Vacuum gauges.—Neither in their idea nor in their construction do vacuum gauges differ essentially from manometers; the difference is only that manometers measure the difference of pressures \(p_{2} - p_{0}\), where \(p_{0}\) is the atmospheric pressure and \(p_{2} > p_{0}\), while vacuum gauges measure \(p_{0} - p_{2}\), with \(p_{2} < p_{0}\).

Metal vacuum gauges are made chiefly according to the Bourdon system, since according to the Schäffer system they prove insufficiently sensitive.

Their scale is graduated either in cm of mercury column, i.e. from 0 to 76 cm, or, which is essentially the same, in inches of mercury column, i.e. from 0 to 30 in., or, finally, in kg/cm²: 0–1.0 kg/cm².

In practice, rarefaction is usually expressed in %, taking as 100% the case when the absolute pressure is equal to 0. Accordingly there are also vacuum gauges with a scale divided from 0 to 100%, but such a graduation—

§ 25. Vacuum Gauges.

...is quite incorrect. It is made so that 100% corresponds to a rarefaction of 760 mm Hg, and at that barometric pressure the readings of the instrument will be correct, while at any other pressure they will not. Namely, if the height of the barometer \(B < 760\), then the vacuum gauge will indicate the rarefaction in % as worse than it is in reality; at \(B > 760\)—as better.

Drawings 210 and 211.

Moreover, in general, the method of expressing rarefaction in % can cause confusion, and one cannot but express the wish that it should not obtain the undeserved right of citizenship which it enjoys even in scientific tests of turbines.

In fact, the very same reading of a vacuum gauge, with one and the same barometer height, has to be expressed by a different value in %, depending on what is being discussed—for example, whether one means the thermal state in the condenser or the work of the air pump.

Let us give an example: the vacuum gauge indicates a rarefaction of 610 mm Hg; the barometer height is 715 mm. The absolute pressure in the condenser is \(715 - 610 = 105\) mm Hg, or \(105 : 737.4 = 0.142\) kg/cm². Relati-

with the whole state of the steam, the vacuum in percent must be given as \((760 - 105) : 760 = 86.2\%\), while for the performance characteristic of the air pump the vacuum is \(610 : 715 = 85.3\%\). With poorer vacuums the difference will be still greater; with better ones, smaller.

In general, in test reports it is more correct to indicate the vacuum either in mm of mercury column or in kg/cm² of absolute pressure, adding what the height of the barometer \(B\) was.

Baro-vacuum meters. Recently vacuum meters have appeared with a scale in percent, but with the barometer height taken into account at the time of the report. This allowance, however, is made by the second method, i.e. by referring the vacuum to the given barometer height, and not to the normal height of 760 mm. For precise tests of steam turbines with determination of the state of the steam in the condenser, such instruments are unsuitable; but for monitoring the operation of a turbine they are, of course, much better than ordinary vacuum meters.

The essence of both instruments described below is the same: they are a combination of a Bourdon vacuum meter and an aneroid barometer.

In Paumann’s instrument, Fig. 212, the barometer pointer \(a\), when crossing the 100% line, shows the given barometric pressure; the reading of the vacuum is found at the intersection of pointer \(b\) with the corresponding concentric circle.

Fig. 212.

Fig. 213.

In the more convenient for reports, but less accurate by virtue of its construction, Frerichs instrument, Fig. 213, pointer \(b\) gives the corresponding reading on a scale which rotates under the action of the barometer; the height of the latter is indicated by pointer \(a\) on the outer scale.

Figs. 212 and 213 show the instruments at 1:4 natural size.

§ 25.

Baro-vacuum Gauges.—Mercury Vacuum Gauges.

The advantage of baro-vacuum gauges over ordinary vacuum gauges may be explained by the following example: the vacuum gauge shows 72 cm Hg, then begins gradually to fall, and after an hour shows only 69 cm. Such a decrease may be caused by some leak in the condenser, and then the engine driver must immediately take measures to find and eliminate it. But the same decrease may also occur from a fall of the barometer, for example from 770 to 740 mm. If readings are taken with a baro-vacuum gauge, then the cause of the fall in vacuum is immediately apparent.

Mercury vacuum gauges. For more accurate measurements, it is better to use mercury vacuum gauges, as being more precise and sensitive. In construction these instruments are of several types.

First, as a vacuum gauge one may use a U-shaped tube, for example, the apparatus in Fig. 206. If, when communicating with the atmosphere, the zero of the scale—the mercury level—stands at the middle of the height of the tube, then it is sufficient to take its length as 780–800 mm.

Secondly, the elbow communicating with the atmosphere may be replaced by a vessel of considerable cross-section. The level of the mercury in the vessel, although only slightly, will vary; its change may be allowed for in several ways: either the scale may be graduated accordingly, making the divisions somewhat smaller than a centimeter, or the mercury level and the zero of the scale may be brought to the same height, either by lowering the scale or by raising the mercury. The advantage of all instruments with one tube is that only one reading need be taken instead of two.

In Fig. 214 there is shown a convenient vacuum gauge of the following type: \(a\) is a glass vessel with a stopper, through which passes, freely and tightly, a glass tube \(b\), connected tightly by a thick rubber tube \(c\) to a flexible metallic spiral tube \(d\), which communicates with the corresponding space; by means of the screw \(e\) the vessel \(a\) is moved up or down until the mercury level coincides with the zero of the scale marked on the tube \(b\).

Fig. 214.

In Figs. 215 and 216 there is shown a convenient instrument that permits measuring both vacuum and pressure up to 1 kg/cm² above atmospheric pressure, the so-called mano-vacuum gauge. In view of the instrument’s dual purpose, the cast-iron vessel \(a\) with mercury is placed in the middle; the tube \(b\) communicates with the space whose pressure is being measured, and in the ball \(c\) there is an opening communicating the instrument with the atmosphere; the stuffing-box—

... d, d with rubber or leather padding; the scale is graduated empirically according to the cross-section of vessel \(a\).

The instrument is especially convenient when the turbine is tested under different conditions, with exhaust either to the condenser or to the atmosphere, or when measuring the steam pressure in an intermediate stage, where the pressure is sometimes above and sometimes below atmospheric, depending on the load.

Drawings 215 and 216.

Finally, it is possible to make an instrument that will indicate not a vacuum in comparison with the variable barometric pressure, but directly the absolute pressure; this is the so-called shortened barometer, Drawing 217: the left-hand elbow \(a\) of a glass tube is sealed or is supplied with a corresponding stopcock so that neither air nor water is above the mercury; the right-hand one—\(b\)—communicates with the condenser; the height \(h\) gives directly the absolute pressure in mm Hg. The mercury for this instrument must be thoroughly boiled and dried, and it must also be ensured that no air bubbles enter elbow \(a\), for which purpose the constriction \(c\) is useful. Air and vapors of liquid, having entered \(a\), lower the column \(h\), and the readings of the instrument give a vacuum as if better than the actual one; in general it must be borne in mind that the instrument has this defect.

Drawing 217.

Drawing 218 shows a shortened barometer, manufactured by the English firm Brady and Martin, of Newcastle-on-Tyne, improved in details and called by the firm a “kinotometer”³⁰.

In the “kinotometer,” manufactured specially for work with a steam turbine, two shortcomings of the simple arrangement have been eliminated: first, in the left, widened elbow \(a\) of the barometric U-shaped tube, thanks to the inclusion of a second U-shaped glass tube—with calcium chloride—steam cannot penetrate, condense, and change the mercury level; and second, even with abrupt fluctuations of pressure in the condenser, it cannot enter

§ 25. Mercury Vacuum Gauges

mercury, which is rather dangerous with copper tubes of surface condensers. This latter condition is achieved in the following manner: first, to the upper opening of tube \(a\) there is soldered a glass tube inserted into \(a\), the tip of which is drawn out to such a small diameter that mercury cannot get into it; but even if it were to penetrate into the connecting tube, and from there into \(b\), it would be retained by a second safeguard—a glass vessel \(c\), which communicates with the manometer by a tube soldered into the middle of its height, and with the condenser by a tube soldered in at the top.

Fig. 218.

height; and with the condenser—by a tube soldered in above. The scale of the instrument has two divisions: in inches \((1/10'')\) of absolute pressure and in % of vacuum. If, as is done in most cases, the vacuum is referred to the given barometric pressure, then the latter divisions will, of course, not be quite accurate under the influence of changes in barometric pressure; however, if the vacuum is referred to the normal barometric pressure \(B = 737\) mm Hg, then the instrument at once gives correct readings. To bring the zero of the scale to the level of the mercury in \(a\), the scale can be shifted somewhat with the aid of a rack; \(d\) is the head of the rack screw. For transport the instrument is fastened in a box; the separate glass parts are secured by thick rubber tubes; the dimensions of the box are \(100 \times 270\) with a height of 430 mm. Of course, the box must not be laid on its side, so that air does not enter the right-hand sealed bend of tube \(a\), the further presence of which would give readings with an exaggerated vacuum.

The firm Negretti and Zambra also manufactures a baro-vacuum gauge specially for steam turbines; this instrument consists of a mercury barometer, the lower bend of which can be connected alternately either with the condenser, for measuring the absolute pressure there, or with

with the outside atmosphere—for reading off the barometric pressure. The entry of water into this knee is prevented by inserting into the connecting pipeline a glass vessel with strong sulfuric acid; this same vessel traps the mercury and does not allow it to enter the condenser.

The firm Gallenkamp & Co. manufactures mercury “Goerz” vacuum gauges with readings at a distance and self-recording ones according to the same scheme as the manometers described above, Figs. 209–211. The divisions on these instruments are made in 0.01 atm., i.e., about 7.4 mm Hg, which is convenient when the instrument is used as a station control instrument, but is not sufficiently accurate for careful tests of steam turbines.

Connection of vacuum gauges. One of the chief conditions for the correctness of vacuum-gauge readings is the tightness of all connections in the pipe from the apparatus to the instrument. It is better to connect metal tubes with a union nut than with sleeve clamps, and to use thick-walled rubber tubes, so-called analysis tubes. The tightness of all valves must be checked with particular care.

It is convenient to test for tightness by admitting air into the connecting tubes under a slight pressure, for example by pumping it in with a bicycle pump, and by coating all places where leakage is possible with soapy water. The formation of soap bubbles will reveal a leak.

Fig. 219.

To preserve the accuracy of readings and the serviceability of metallic spring vacuum gauges, their springs must be protected from sudden pressure fluctuations. The means for doing this are almost the same as for manometers: either grind in a small cock, or insert a resistance as in Figs. 199 and 200, or, finally, mount the vacuum gauge on a fitting as in Fig. 219: the cavity \(B\) plays the role of an air buffer, and the narrow openings \(c\) and from the cavity \(A\) to the vacuum gauge play the role of an additional resistance—an air cataract.

Finally, the last requirement, equally important for all vacuum gauges, is that water should not collect in the connecting tubes, since a column of it may noticeably distort the instrument readings. The spirals \(d\), Fig. 214, served the same purpose.

In the extreme case, if water has entered a mercury vacuum gauge, its effect can be allowed for with sufficient accuracy by adding to the instrument readings the column of water converted to the specific weight of mercury, i.e., multiplied by 0.073.

26. Calibration of manometers and vacuum gauges.—The methods of calibrating manometers may be divided into two principal ones: comparison with control manometers, and testing by direct loading.

§ 26. Checking pressure gauges by comparison.

In checking by comparison, one may use, as the control instrument, either an accurate metal pressure gauge according to Figs. 190 or 191, or a large mercury manometer. The latter is made in the form of a cast-iron vessel \(a\), Fig. 220, with mercury, to which a tube \(b\) and a fitting \(c\) are attached for connection with the pressure gauge being tested and with the liquid producing the required gradual increase in pressure.

Fig. 220.

The tube \(b\) is made of thick-walled glass tubes with an internal diameter of about 10–12 mm and a length of about 2 m; the joints of the separate sections are connected by means of cast-iron couplings and glands with leather or rubber packing; the scale is marked directly on wooden bars fastened to the wall, on which the entire instrument is assembled.

For observing the column of mercury, a ladder is made in front of the manometer, which one of the observers has to climb. Checking is greatly facilitated if the manometer is provided with the device shown schematically in Fig. 220: along the scale two wires are stretched, serving as guides for the carriage \(d\), to which are fastened a mirror \(s_1\), inclined downward at \(45^\circ\), and an incandescent electric lamp or kerosene lamp \(e\); the carriage is suspended on a thin steel cable passed over a pulley fixed at the top of the instrument; by means of this cable the observer can move the carriage up or down, while himself standing in one place and at the same time watching the mercury level, reflected in the mirror \(s_1\), through the annular sighting tube or a simple tube \(f\) with a second mirror \(s_2\), whereby it is convenient for the observer to watch the change in the mercury level. The wire to the lamp is made with a block and a counterweight descending at the side of the manometer.

Of course, in view of the considerable height of the mercury column, it is necessary to introduce, with the greatest possible care, the correction for the influence of temperature according to Eq. (43).

When comparing the readings of the accurate gauge and the gauge being tested, one notes which divisions of the tested gauge correspond to 1, 2... kg/cm² of the control gauge. From these observations a table of corrections is compiled, and, in the case of considerable errors, an attempt is made to correct the readings—

...readings with the aid of the above-mentioned resetting devices, or, finally, the manometer is provided with a new scale.

The checking should be carried out first with increasing pressure, then with decreasing pressure, and the mean values should be taken.

In order to eliminate the effect of static friction during the check, it is useful to tap the manometers lightly with the fingers before taking readings; the same should be done when taking readings while using the manometer.

The pressure to which the manometer being checked and the control manometer are subjected may be produced in various ways. Fig. 221 shows a corresponding water press: by means of the vessel \(a\), into which water is poured, and the cock \(b\), the pump cylinder is filled with water, which is drawn in when the plunger is screwed out by rotating the flywheel \(c\) counterclockwise; on the fittings \(d\) and \(e\), communicating with the chamber—the rear end of the press—the manometer being checked and the control manometer are placed by means of transition fittings screwed into them, or of the fitting \(f\); the cock \(b\) is closed, while \(d\) and \(e\) are opened, and, by screwing the plunger in by rotating the flywheel \(c\) clockwise, the pressure is raised.

Fig. 221.

It is quite convenient to obtain pressure by connecting a small cast-iron cylinder, provided with fittings to which the manometers being checked are screwed, with a vessel containing liquefied carbonic acid or compressed air. By gradually admitting the compressed gas into the cylinder, the required pressure can be obtained.

The required pressure may also be obtained by means of special steam boilers. Thus, Figs. 222 and 223 show Prof. Bach’s device³¹: \(A\) is a boiler heated by an internal coil, through which high-pressure steam is passed through valve \(B\); tube \(F\) serves to increase or decrease the quantity of water in the boiler; tube \(K\) serves for discharging the spent water from the coil, the boiler \(A\), and the surrounding casing \(E\); tube \(G\) communicates—

1. Z. V. d. I. 1911, p. 1311. ↩

2. Z. V. d. I. 1911, S. 1504; 1912, S. 1483. ↩↩

3. See, for example, Josse, Neuere Wärmekraftmaschinen, Berlin 1905, pp. 27 and 77; Moyer, Power Plant Testing, New York, 1911, p. 286; Z. Turb. 1906, p. 221, etc. ↩

4. Z. Turb. 1905, p. 214. ↩

5. Z. V. d. I. 1907, p. 607. ↩

6. Z. Turb. 1908, p. 230. ↩

7. Engng. 1909, LXXXVIII, p. 805. ↩

8. Mém. et Comptes rendus d. travaux d. la Soc. d. Ing. Civ., 7. Serie, LXVI, No. 4; Zeitschr. Dampfk. u. Versich.-G. A.-G. 1913, p. 101. ↩

9. Eng. 1909, p. 575. ↩

10. Forsch. H. 25, S. 73. ↩↩

11. Eng. 1909, p. 471. ↩

12. Z. V. d. I. 1912, S. 1219. ↩

13. Engng. 1908, p. 197; Eng. 1908, p. 506. ↩

14. Z. Turb. 1911, p. 132; Z. V. d. I. 1912, p. 1327. ↩↩

15. Engng. 1908, LXXXV, p. 197. ↩

16. Buchetti, N. guide, p. 154. ↩

17. Eng. 1908, CVI, p. 614; Buchetti, N. guide, p. 159. ↩

18. Engng. 1911, XCII, p. 715. ↩

19. Engng. 1911, XCII, p. 605; Z. Turb. 1912, S. 142. ↩

20. Eng. 1908, CVI, p. 505. ↩

21. Eng. 1908, CVI, p. 506. ↩↩

22. Eng. 1908, CVI, p. 615. ↩

23. In compiling §§ 17–21 the author made use, along with other material, of the corresponding chapters of his book: Measurement of Temperatures for Technical Purposes. Tomsk, 1910. ↩↩

24. The indicated types of glass are produced by German firms, from which thermometers are chiefly ordered for Russia. ↩

25. Forsch. H. 12. S. 10. ↩

26. Sc. Amer. 1906, 94, p. 415; Iron Age. 77, p. 1610; Eng. News, p. 159. ↩

27. Z. V. d. I. 1912, S. 259. ↩

28. Z. Turb. 1908, S. 231. ↩

29. Z. V. d. I. 1911, S. 1347. ↩

30. Engineering, 1912, XCIII, p. 539. ↩

31. Z. V. d. I. 1902, p. 1577; or see also V. Malyshev, Testing of Indicators. St. Petersburg, 1905, p. 24. ↩