Proceedings of the Tomsk Technological Institute

of Emperor Nicholas II.

Vol. 10. 1908. No. 2.

II.

A. M. Krylov.

THEORY AND CALCULATION OF THE INJECTOR.

Chapters IV, V, VI with an appendix of 9 tables of drawings.

69–155.

Intake Nozzle

The mixture of water and as-yet uncondensed steam, on leaving the condensing nozzle, enters the intake nozzle. The latter is a pipe composed of a short and a longer cone, facing one another with their vertices; at the place where they join it is useful to have a cylindrical insert of small length, which determines the direction of motion of the water particles parallel to the axis of the pipe. It is precisely at this place that the nozzle has the smallest diameter. Having repeatedly observed the operation of his apparatus, Giffard came to the conclusion that its capacity, i.e. its ability to deliver a certain quantity of water under all other identical conditions, depends directly on this dimension; it may be expressed by the empirical formula \(E = 28d^2\sqrt{p}\), where \(d\) denotes the diameter of the mouth of the intake nozzle and \(p\) the pressure of the boiler from which the steam is taken. Indeed, if the velocity of the jet and its density are the same at the entrance into the intake nozzle, then the quantity of water delivered will vary in proportion to the variation of the area of the mouth, or to the square of its diameter.

If it were possible to regard the working process as taking place without losses from friction, impacts, changes of section, etc., we would have a very simple method for determining the capacity of the injector: the jet of water that has entered the intake nozzle must overcome the pressure from the boiler side upon the feed valve; it is obvious that the velocity of the jet at the mouth must be only a little greater than that with which hot water would flow out of the boiler under the difference of heads corresponding to the pressure in the boiler and the pressure before the nozzle. Multiplying the velocity determined in this way by the area of the mouth, we would have the per-second discharge of water by the injector. However, harmful resistances and, especially, the decrease in the density of the jet in comparison with the density of water, depending on incomplete condensation, make such a method inapplicable in more or less exact tests. It is necessary to determine by observation and direct weighing the actual discharge of the injector; if we then divide it by the discharge computed theoretically from the velocity, we obtain a ratio, always less than unity,

which may serve as the characteristic of the given apparatus; this will be its coefficient of efficiency. Such a method of comparison can be applied to almost all single injectors. Suppose, for example, that there is an apparatus whose orifice diameter is \(12\ \mathrm{m}/\mathrm{m}\). Experiment has shown that in one second \(2.683\ \mathrm{kgr.}\) of water was delivered and \(0.228\ \mathrm{kgr.}\) of steam was consumed, i.e. the total weight of the mixture was \(2.91\ \mathrm{kgr.}\)* The working pressure of the boiler was \(8\ \mathrm{atm}\); corresponding to it is a head of \(82.664\ \mathrm{met.}\) (the pressure before the orifice being atmospheric); the velocity of outflow of the water would be \(40.27\ \mathrm{mtr.}\). Through the orifice of this injector \(4.55\ \mathrm{kgr.}\) of water could pass; hence the ratio

\[ E=\frac{2.910}{4.55}=0.64. \]

The smaller the back pressure against which the injector can work, the higher this ratio \(E\) will be in it; but in reality almost every injector is always capable of forcing water at a greater back pressure than the steam pressure used for its operation. Since an injector is installed for each boiler and must operate almost exclusively with the steam of that boiler, such an increase of the limit of possible back pressure is of no importance. It is only necessary that the velocity in the orifice be so great that, after subtracting all harmful resistances, the jet should possess kinetic energy sufficient for entering the boiler. Since an injector is the better the more remote are the limits within which it can deliver water at each pressure, an increase of \(E\) would mean at the same time an increase of the possible interval between maximum and minimum discharge. Therefore the sometimes encountered indication of the difference between the working steam pressure and the possible back pressure should rather be regarded as a negative characteristic; it means that either not all the kinetic energy of the jet is used in impact and the velocity of the jet is too great when it passes through the orifice, or, if increasing the quantity of water is accompanied by loss through the overflow opening, incomplete condensation is connected with a considerable decrease in the density of the jet. In calculating \(E\), the question may arise as to the temperature of the water delivered by the injector: one may force it hotter, another less heated; less hot water must pass, since its volume is greater; but this is not essential, since the specific volume of water changes very little with temperature.

Thus, according to Hirn’s formula, the dependence between the specific volume of water \(v\) and its temperature \(t\) is given by the following equality:

\[ v=0.001\left(1+0.00009t+0.0000034t^2\right). \]

* Ann. d. Mines, 1860, vol. XVII, op. Deloy.

Theory and Calculation of the Injector

Calculation gives, for temperatures from

\[ \begin{array}{rcl} -20^\circ \text{ to } +115^\circ & & v=0.001,\\ 120^\circ \text{ to } 125^\circ & & v=0.00106,\\ 130^\circ \text{ to } 135^\circ & & v=0.00107,\\ 200^\circ & & v=0.00115. \end{array} \]

In view of this, independently of temperature, the calculated quantities of water will correspond to the actual ones with sufficient accuracy. Thus, by calculating the coefficient \(E\) for a series of injectors of different firms, but of one and the same size and type, we sometimes obtain the possibility of judging the degree of perfection and the suitability of one or another for its purpose. The experimental conditions, of course, apart from changing the injectors themselves, must remain unchanged, i.e. there must be one and the same steam pressure, temperature of the suction water, suction height, etc. For purposes of comparison one may also calculate the discharge of an injector by referring it to \(1\) sq. mm of the area of the orifice; in this case the superiority of one apparatus over another will be expressed more distinctly and the figures will be more easily remembered.

The area of the orifice of the receiving nozzle gives us the possibility of determining the capacity of the injector; but the value of the coefficient \(E\) does not depend on this nozzle; it receives a jet of mixture in a known state, and its role consists in the conversion of the kinetic energy of this jet into potential energy.

One or another value for \(E\), although it will be calculated according to the size of this nozzle, depends chiefly on the correctness of the dimensions and outline of the condensing nozzle; the shape of the receiving nozzle chiefly affects whether the injector can force water only at boiler pressure, or whether the back pressure may be higher, or must be lower than the working pressure of the steam. When the jet of the mixture of water and steam enters the receiving nozzle, its further motion in it may take place in very diverse ways.

Exactly how this motion will take place will depend on the angle of conicity of the diverging part of the nozzle, on the condition of its walls, on the velocity of the jet, and very probably on the physical properties of the material of the tube, i.e. whether it is wetted by the jet, whether there is much adhesion between the water and the walls, etc. The role of the nozzle is already sufficiently clear: the kinetic energy of the jet must be converted in it into potential energy for overcoming resistances, including the feed valve; while a part of it must remain in its original form, so that the jet, after passing the valve, may move through the feed pipe to the outlet into the boiler. If the receiving nozzle is given the form indicated in Fig. 28, then the walls of the nozzle will have no influence on the motion of the jet; the jet from such a nozzle will flow out just as it does in free discharge into the atmosphere.

Its kinetic energy will almost entirely be expended on internal vortical motions, eddies, and molecular motions of particles along the surface of the jet; such a jet cannot yield much useful work. The greater the angle of conicity at a considerable inlet velocity, the less, in such a case, the jet will be capable of performing a certain useful work; conversely, with a small angle of conicity, the water, passing one after another through successively increasing sections of the pipe, will fill the pipe, it will slide along its walls; apart from the loss due to friction against these walls, there should be no other loss in it, given a proper form of the nozzle. The jet, passing from one section of the nozzle to another, will slow its motion, but in each section, owing to the decrease in velocity, the pressure in the jet will increase, and this pressure is transmitted uniformly to the walls in the given section. This increase of pressure is due to the support from behind of moving particles having the greater velocity upon those going ahead with a reduced velocity. At the moment of leaving any section, the jet by inertia tends to move with the same velocity, but it meets the water particles lying ahead and exerts pressure upon them. Let us imagine that a ball is rolling along a plane with a certain velocity; if we block its path, then this object will experience from the ball a pressure depending on the mass and velocity of the ball; if we wished to restrain the ball by some flexible connection fastened at the point of departure of the ball, then at the moment when the ball has traveled a path equal to the length of the connection, it will exert upon the latter a tensile action. These two phenomena also take place in the receiving nozzle, in which the jet, filling the section, moves more slowly. A series of successive pushes, occurring without impacts because of the infinitely small difference of velocities in two adjacent sections, produced by the particles coming from behind upon those lying ahead, is summed at the outlet section into work that may be equal to or greater than the work done by the external pressure, relative to the receiving nozzle, upon the jet at its exit from it. A series of impulses, acting with tension, produced by the particles lying ahead upon those situated behind them, with which they are connected by cohesion, causes the phenomenon of suction, which also explains the suction action of diverging nozzles, called Venturi nozzles, who first studied their action. From this it is already clear that the shape of the nozzle must play a large role and influence the magnitude of that back pressure which may occur in a given injector.

What, then, is the law governing the motion of the jet and the transformation of its kinetic energy into potential energy as it passes through this nozzle? If the angle of conicity of the diverging part of the nozzle is small, i.e.

if the jet fills every cross-section of it, then, obviously, neither eddies nor whirlpools can arise anywhere.

Let us trace, in its very course, the motion of certain particles of the liquid jet from the moment it enters the mouth. The central particle of the jet, moving translationally, will follow a trajectory coinciding with the axis of the nozzle; all the other particles lying around it will describe trajectories that recede more from the axis of the nozzle, i.e., deviate toward the periphery, the farther they are situated from the center; the smaller the angle of conicity, the greater, evidently, will be the radii of curvature of these trajectories. For this case we may assume that the tangents to the trajectories in any (vertical) section perpendicular to the axis will be inclined at a very small angle to the axis, or almost parallel to it. Such an assumption simplifies the problem of consideration, since in the given case we have to do only with the translational motion of each particle in one and the same direction, and this in turn conditions a uniform distribution of pressure over the area of the jet in any of its arbitrary cross-sections.

Let us now consider the motion of the central particle, and the conclusions obtained for it, by virtue of what has been said above, apply directly to the entire jet of liquid. Let $\alpha$ (Fig. 30) be a section perpendicular to the axis of the nozzle, and therefore also to the central jet itself, at a distance $l$ from the entrance into the nozzle; let the area of the central jet be $\omega$; denote by $u$ the velocity with which the liquid particles pass through this section $\alpha$, and by $p$ the pressure normal to the area of the section; for an infinitely close section, situated at a distance $dl$ from the first, let $du$ and $dp$ represent the increments of velocity and pressure; $\gamma$ is the weight of a unit volume of liquid.

The element of the central jet bounded by these sections has volume $\omega dl$; on the left it is acted upon by the pressure $\omega p$, on the right by $\omega(p+dp)$; the resultant of these two pressures, directed in exactly opposite directions, is equal to $\omega dp$ and is negative. The mass of the element will be

\[ \frac{\omega \cdot dl \cdot \gamma}{g}, \]

where $g$ is the acceleration of gravity; assuming the motion to occur without resistance (without friction), we, according to the equation of motion of mechanics, shall write

\[ -\omega dp=\frac{\omega \cdot dl \cdot \gamma}{g}\cdot\frac{du}{dt}\ldots\ldots\ldots (1) \]

or

\[ \frac{du}{dt}=\frac{g\cdot dp}{\gamma\cdot dl}\ldots\ldots\ldots (2) \]

where $dt$ is an infinitely small element of time during which the particle moves from section $\alpha$ to the adjacent one. In order to bring both parts of this

equation to one and the same independent variable, we shall turn our attention to the following. Let the initial area of the nozzle be $\omega_0$ and the initial velocity $u_0$, and in the section $\alpha$—$\omega$ and $u$; for steady motion and with continuity of the jet there must exist the equality

\[ \omega_0 u_0 = \omega u = \mathrm{const} \ldots\ldots\ldots (3) \]

The velocities of the jet vary depending on the areas of the transverse section, and the latter, for a known and definite angle of conicity, are functions of the distance $l$ from the initial section with area $\omega_0$. Let us choose as the element of time that time which is required for an element to pass, with velocity $u$, the distance $dl$, i.e. let us take $dt = \frac{dl}{u}$; then, making the substitution for one and the same instant, we obtain the equality

\[ -\frac{gdp}{\gamma \cdot dl} = \frac{udu}{dl} \ldots\ldots\ldots (4) \]

or, passing to differentials, we shall have

\[ -gdp = \gamma \cdot udu, \ldots\ldots\ldots (5) \]

whereby $p$ and $u$ are independent of time and functions of one and the same independent variable $l$; let $u_0$ and $p_0$ be the velocity and pressure at the entrance; integrating within the limits from $(u_0, p_0)$ to $(u, p)$, we obtain:

\[ u^2 - u_0^2 = \frac{2g(p_0 - p)}{\gamma} \]

Such is the relation between velocities and pressures for the central streamlet in two of its sections situated at a finite distance from one another.

Let us suppose that the receiving nozzle begins at the entrance with a small cylindrical part and then passes into a diverging cone; it is evident that all particles of the liquid, at the instant of passing through the cylindrical insert, will have one and the same velocity, the direction of which will be parallel to the axis of the nozzle; upon leaving it, the trajectories of the particles lying nearer to the walls of the nozzle will deviate somewhat toward the periphery, but if the angle of conicity is small, so that their radii of curvature are very large, then they will be almost parallel to one another; by virtue of this, the condition of uniform distribution of pressure over the whole area of the jet and of equal velocity for all elements of the given section will be almost observed. The relation derived may in this case be referred to the whole jet with that accuracy with which our assumptions permit this to be done, and the resistance from friction of the particles among themselves and against the walls, as well as the influence of gravity, which, in

THEORY AND CALCULATION OF THE INJECTOR.

in reality, owing to the small length of the nozzle, is negligible. The relation between velocities and pressures in the various sections of the jet is clearly represented by a diagram (Fig. 31). To construct it, we divide the volume of the nozzle into equal-volume parts, so that the greater the diameter of a section of the nozzle, the closer this section is to its neighbor. On the verticals drawn in the planes of these sections, the corresponding velocities and pressures are laid off. The diagram shows that at first the velocity of the jet decreases very rapidly, while the pressure increases very rapidly; since we are speaking of the pressure of a liquid that transmits it equally in all directions, the pressure on the walls of the nozzle evidently increases just as rapidly, and in these places the greatest wear is to be expected. In fact, most often in repairing the receiving nozzle it is necessary to bore out its receiving cone, in order to smooth out the depressions that have formed; the wear will be especially considerable in the case of using water containing dirt, sand, or a large amount of dissolved salts, which are deposited on heating in the form of hard precipitates.

The question therefore arises whether it is possible to give the nozzle a more advantageous form, in which the transmission of pressure to the walls would occur more uniformly; in that case, of course, the wear would also be more uniform and the action of the nozzle more perfect.

Conical divergent nozzles were first investigated by Venturi. Observing the outflow of water from a nozzle into the atmosphere*), he noted a great non-uniformity in the quantity of water flowing out, and even the presence of vortices inside the nozzle. This non-uniformity of outflow is readily explained by the instability of the pressure at the mouth of the nozzle, which, as stated above, possesses a suction capacity; the latter changes, and this is immediately reflected in the quantity of water flowing out. The presence of vortices is undesirable, since they absorb part of the live force which can no longer be used to perform work. The most favorable form evidently should be one in which the increase of pressure proceeds uniformly; the pressure curve in the diagram will then be a straight line.

If this condition is imposed in determining the dimensions of the nozzle, then, obviously, in the equation

\[ \frac{u^2-u_0^2}{2g}=\frac{p_0-p}{\gamma} \]

the second part, referred to the length of the nozzle, must be constant. If the pressure increases according to the equation of a straight line, then it is clear that

*) Lowell Hydraulic Experiments, Francis, J. B.

the force acting on the elements of the separate jets in each cross-section perpendicular to the axis of the nozzle will increase proportionally to the tangent of the angle of this straight line with the axis of abscissas. Since force is equal to the product of mass and acceleration, and the mass, by the law of continuity of the jet, remains constant, the acceleration will likewise be constant; that is, the velocity will vary uniformly, and in the present case the acceleration will be negative, i.e. the motion uniformly retarded. The uniform transfer of pressure to the walls of the nozzle will determine the uniformity of its wear, while the gradual application to the elements of an ever greater and greater moving force must also be accompanied by the least losses from frictional resistance and impacts.

To determine the longitudinal profile of the nozzle, let us divide its length \(L\) into \(n\) parts \(s\) of equal magnitude, i.e. \(L = ns\); let the diameter of the orifice be \(d_0\) and the initial velocity \(u_0\); the exit velocity must be \(u_n\); let the acceleration of the jet in its uniformly retarded motion be \(j\).

By the formula for such motion we have

\[ L = u_0 t - j \frac{t^2}{2}, \ldots\ldots (6) \]

and the acceleration

\[ j = \frac{u_0 - u_n}{t}; \]

determining \(t\) from this equality and making the substitution, we find:

\[ j = \frac{u_0^2 - u_n^2}{2ns} \ldots\ldots (7) \]

Since \(s\) is constant, this equality contains the condition that the acceleration \(j\) also be the same; for this it is necessary that the difference of the squares of the velocities on adjacent sections be constant.

Thus, let the initial velocity of the jet be known to us; we consider the jet at the orifice of the receiving nozzle to be entirely homogeneous and liquid. It may be determined in two ways: either by the theorem of quantities of motion, or by the difference of pressures in the boiler and at the orifice of the receiving nozzle. Let the pressure in the boiler be \(p\) and at the orifice of the receiving nozzle \(p_0\); if \(\delta\) is the density of the jet at the temperature of injection, then the height of a column of water corresponding to these pressures (by the manometer) will be

\[ \frac{p - p_0}{\delta}\cdot 10000 \]

and, for \(\delta = 1000\), \(h = (p - p_0)10\); under such a head the jet will have the velocity

\[ u_0' = \sqrt{2g \cdot 10(p - p_0)} = 14\sqrt{p - p_0}, \]

where \(p\) and \(p_0\) are in atm. \((\mathrm{kg}/\mathrm{cm}^2)\); since harmful resistances absorb part of the kinetic energy in overcoming them, the actual velocity \(u_0\) must be equal to \(\alpha u_0'\), where \(\alpha > 1\), and, according to Giffard’s data, \(\alpha = 1.06\), or, for the sake of reserve, in order to be assured of excess-

the pressure in the pipe over the boiler pressure may be taken as $\alpha=1.1$.

The quantity of water delivered by the injector will be $\dfrac{\pi d_0^2}{4}\cdot u_0$, since $u_0$ depends on the pressure in the boiler and at the mouth of the nozzle; this is the second reason for using a divergent nozzle in the receiver. The lower the pressure at the mouth, the greater will be $u_0$, and consequently the quantity of water delivered. In experiments and in determining the quantities of water flowing out of such nozzles, Brownlee and Francis succeeded in attaining an almost complete vacuum at the mouth of the nozzle. With an open injector such a rarefaction is impossible; the pressure at the mouth must be somewhat higher than that which corresponds to the temperature of the mixture, in order to avoid steam formation; with a closed overflow this rarefaction may be considerably lower. But even with an open overflow it is possible to make good use of the properties of a divergent nozzle for increasing the quantity of water delivered. Usually the receiving nozzle begins with an inlet short converging cone; its purpose is to catch the whole jet issuing from the condensing nozzle. Because of the large angle of conicity of this short appendage, the relation derived above for velocities and pressures cannot be fully applied to it; nevertheless, it is evident that, under favorable conditions, the jet embraced by it, moving with acceleration toward the mouth, will be, at the moment of passing through the smallest section, under the least pressure, and the velocity of the jet will therefore be the greatest possible and necessary for the maximum of water delivered.

If the quantity of water $Q$, in kgr., delivered by the injector in the course of an hour is known, then, knowing $u_0$, one can find the diameter of the mouth.

$$ \frac{Q}{3600\cdot \delta}=\frac{m}{\delta}=\frac{\pi d_0^2}{4}\cdot u_0,\ldots\ldots (8) $$

where $m$ is the quantity of water in kgr. per second and $\delta=1000$, $d_0$ and $u_0$ in meters.

Let $d_n$ and $u_n$ be the diameter and velocity at the outlet. Since the motion has been assumed by us to be continuous, then

$$ \frac{u_0\pi d_0^2}{4}=\frac{u_n\pi d_n^2}{4}, $$

whence we find

$$ u_n=u_0\frac{d_0^2}{d_n^2}\ldots\ldots (9) $$

The acceleration $j$ is equal to $\dfrac{u_0^2-u_n^2}{2sn}$, or, making the substitution for $u_n$,

$$ j=\frac{u_0^2}{2ns}\left(1-\frac{d_0^4}{d_n^4}\right)\ldots\ldots (10) $$

Under ordinary conditions the value of the ratio \(\dfrac{d_0^4}{d_n^4}\) is very small, and it may be neglected without great error in the results of the calculation; then for \(j\) we obtain the simpler expression

\[ j=\frac{u_0^2}{2ns}=\frac{u_0^2}{2L}\ldots\ldots(11) \]

Let us now compose the equation of the curve which is to be taken as the generatrix of the solid of revolution, and which will represent the receiving nozzle.

Take the axes \(x,y\); let \(ab\) be the required profile (Fig. 32). We have

\[ j=\frac{u_0^2}{2L}\left(1-\frac{d_0^4}{d_n^4}\right) \]

Substituting \(2x\) for \(d_n\) and \(y\) for \(L\), we find

\[ j=\frac{u_0^2}{2y}\left(1-\frac{d_0^4}{16x^4}\right)\ldots\ldots(12) \]

Solving this with respect to \(x\), we obtain:

\[ x=\frac{d_0}{2}\sqrt[4]{\frac{u_0^2}{u_0^2-2jy}},\ldots(13) \]

where

\[ j=\frac{u_0^2-u_n^2}{2L} \]

is a positive quantity. This is the equation of the profile curve for the receiving nozzle, in which the pressure of the jet on the walls of the nozzle will increase uniformly. If, instead of \(j\), we substitute the approximate value \(j=\dfrac{u_0^2}{2L}\), then we obtain

\[ x=\frac{d_0}{2}\sqrt[4]{\frac{L}{L-y}}\ldots\ldots(14) \]

Let us take an example; let \(u_0=50\) mt., \(d_0=0.010\) mt.; \(u_n\) is to be 5 mtr.; the length of the nozzle \(z=20d_0=0.200\) mtr.

The acceleration

\[ j=\frac{50^2-5^2}{2.0,2}=6187,5; \]

the equation of the profile curve is

\[ x=\frac{0,010}{2}\sqrt[4]{\frac{50^2}{50^2-2.6187,5.y}} =0,005\sqrt[4]{\frac{1}{1-4,95y}}. \]

By the second, simplified formula,

\[ x=0,005\sqrt[4]{\frac{0,2}{0,2-y}}. \]

According to these formulas, for any value of \(y\) we obtain the value of \(x\); Fig. 33 shows the nozzle profile obtained for the given example. It is evident that its diameter at first changes very little; near the outlet end of the nozzle it increases more rapidly and at the exit reaches a value equal to infinity. The nozzle shape obtained in this way differs considerably from the usual one in the form of a straight diverging cone. It would be the best for an injector in the case where it had to operate under constant, unchanging conditions; in reality this is not so: for example, the steam pressure may vary considerably, determining the magnitude of the initial velocity \(u_0\); but the latter may also vary considerably depending on the completeness of condensation, i.e. on the density of the jet \(\delta\). Only when \(\delta = 1000\), i.e. with an absolutely liquid jet, will the action of the apparatus be the best, and it will deliver, overcoming the greatest possible pressure, the maximum quantity of water possible for it. The amount of air introduced with the water or sucked in because of leakage of the joints will also be reflected in the velocity \(u_0\). Giffard therefore gave the profile of the receiving nozzle different outlines, depending on the greatest pressure at which the injector would have to operate. The nozzle profile was obtained by the joining of two arcs of different radii (Fig. 34); for high and medium steam pressures he made the radius of the arc equal to 300 diameters of the mouth, and for low pressures—\(200d_0\); correspondingly, for the inlet converging cone, 7 and 8. Both arcs are tangent to a straight line parallel to the axis of the nozzle in a section passing perpendicular to the axis through \(d_0\). Since, according to \(d_0\), he also took the other dimensions of the apparatus, for each number of injector not only its own profile of the receiving nozzle was obtained, but also, in general, all the dimensions of the injector. Theoretically this should be correct, but it must be noted that the length of the nozzle in such a case is insignificant, whereas it, like the shape of the profile, plays an important role. It was already pointed out at the beginning that, with a short nozzle and with the high velocity at which the jet usually passes through it, the walls of the nozzle play no role whatever. The four nozzle forms indicated in Figs. 35–36 were tested by Kneass; he evaluates the effect of each of them by the magnitude of the back pressure, overcoming which the injector can deliver water.

The pressure of the working steam remained constant, and the quantity was regulated so that one and the same volume of water was delivered without its loss through the overflow orifice. With a working-steam pressure of 4.5 atm., the possible back pressure for the short cylindrical nozzle of Fig. 35 proved to be 2.5 atm.; the pressure ratio \(4.5 : 2.5 = 1.8\) indicates that in this case almost 50% of the kinetic energy of the steam jet was absorbed without benefit for the work of forcing. Especially significant

there must be a loss here from impact, since the jet issuing from such a nozzle possesses the greatest velocity and meets ahead of it the water moving slowly in the pipe. The nozzle shown in Fig. 36—a long cylindrical one—proved still worse, since the possible back pressure decreased. Bored out so that the profile of the nozzle took a shape close to a parabola (Fig. 37), this nozzle improved the action of the apparatus: the back pressure rose to 4.3 atm.; the nozzle of Fig. 38—longer and with the profile of a curve of large radius of curvature—gave a back pressure of 6.2 atm.; finally, with the most correct outline of the nozzle, the back pressure was raised to 6.5 atm. Thus, both the form of the profile and the length of the receiving nozzle play an important role in its perfect action in transforming kinetic energy into potential energy.

The diameter of the mouth of the receiving nozzle is usually in a known ratio to the outlet section of the condensation nozzle; the interval between them is made about 1.9–2.0 diameters of the mouth; the mixed jet, upon leaving the condensation nozzle, while passing through this interval, is under atmospheric pressure when the discharge is open.

By virtue of this, the sectional area of the receiving nozzle was given the dimension that the jet freely flowing into the atmosphere must have, the pressure at the moment of its passage through the mouth of the nozzle being, evidently, assumed equal to atmospheric pressure.

It was already noted above that it is advantageous to have as small a section as possible here. The angle of conicity of the converging short cone in front of the receiving nozzle differs little from the same angle for the expanding part; although the dependence derived earlier cannot be applied to the present case with the same accuracy, nevertheless to a certain degree it will be satisfied here as well. Let the jet, passing through the interval, have section \(\omega_0\), \(u_0\)—its velocity, and \(p_0\)—atmospheric pressure; let some arbitrary section of the converging cone be \(\omega_1\), and \(u_1\) and \(p_1\) the corresponding velocity and pressure of the jet; since we consider the density of the jet constant and equal to \(\delta = 1000\) for water, which is incompressible, the equality \(u_0 \omega_0 = u_1 \omega_1\) is necessary, or

\[ u_1 = \frac{\omega_0}{\omega_1} u_0 . \]

The relation between the velocities and pressures in the sections of the jet in the interval and as it passes through the inlet cone may be written as follows:

\[ p_1 = p_0 + \frac{\delta}{2g}\left(1 - \frac{\omega_0^2}{\omega_1^2}\right) u_0^2 \ldots (15) \]

since in it \(\omega_0 > \omega_1\), the expression in parentheses is a negative quantity, and therefore \(p_1 < p_0\), i.e. less than atmospheric pressure. As was noted, the press—

the cross-section of the jet will decrease up to the mouth of the nozzle, where it will be smallest. Thus, if the area of the mouth of the receiving nozzle is less than the cross-sectional area of the jet while it passes through the interval between the nozzles, then this still entails inconvenience; the opposite relation will have a far more unfavorable effect on the operation, i.e., when the area of the mouth is greater than the cross-sectional area of the jet.

In this case the jet may also fail to fill the cross-section of the mouth, and then there is no probability that each element of the jet in this cross-section will have a velocity whose direction is parallel to the axis of the nozzle; therefore the theory of the nozzle presented above will prove inapplicable.

Both a large positive difference and a negative difference between the cross-sectional areas of the mouth and of the jet are undesirable; with complete and perfect condensation of the steam it is advantageous to have this difference as close to zero as possible and, in any case, negative. The inlet cross-section of the converging cone should be equal to the outlet cross-section of the condensing nozzle, or slightly greater than it, in case of inaccurate installation and noncoincidence of the axes of both nozzles.

We have seen that, under the condition of uniformly retarded motion of the jet in the receiving nozzle and a uniform increase of its pressure, the outlet diameter of the nozzle must become infinitely large; in reality this cannot be done; the velocity of the jet at the outlet will be greater than the velocity with which the water moves in the delivery pipe. Owing to this there will occur an impact, in which the loss of energy will be the greater, the more these velocities differ from one another. It is impossible to avoid this loss completely; but if the transition from the receiving nozzle to the delivery pipe is outlined by a smooth curve, then this loss can be considerably reduced. Therefore the arrangement of the nozzle according to Fig. 39 must be considered irrational; its arrangement according to Figs. 60 and 62 would be correct if the outlet end of the nozzle were outlined more smoothly up to the diameter of the feed pipe.

The lost head, in meters of water column, in the given case will be equal to

\[ h=\left(\frac{d_1^2}{d_0^2}-1\right)^2 \frac{v_1^2}{2g} \]

or, in atmospheres,

\[ p=0.1\,\frac{v_1^2}{2g}\left(\frac{d_1^2}{d_0^2}-1\right)^2 \]

If, for example, \(d_1 = 50\ \mathrm{m}/\mathrm{m}\), \(d_0 = 30\ \mathrm{m}/\mathrm{m}\), and \(v_1 = 5\ \mathrm{mtr.}\), then

\[ h = 4\ \mathrm{mtr.}\quad \text{and}\quad p = 0.4\ \mathrm{atm.} \]

With a final velocity \(v_1 = 10\ \mathrm{mtr.}\), this loss will amount to

\[ 0.4\left(\frac{10}{5}\right)^2 = 1.6\ \mathrm{atm.}; \]

it is evident that it is advantageous to make the transition of the outlet section of the nozzle to the delivery pipe as smooth as possible. In addition to this more or less avoidable loss, part of the energy will also be absorbed by friction against the walls of the nozzle.

Theory of Operation.

On the basis of the indications given in the preceding three chapters, for a given definite diameter of the orifice of the steam and receiving nozzles we can construct the most advantageous profile for them; the task of the present chapter is to consider the general theory of the operation of the injector and to determine the dimensions of the nozzles in their relation to one another.

It should, however, be noted from the very outset that at the present time it is not yet possible to embrace mathematically, by a general formula, the entire working process of the injector; it is therefore necessary to confine ourselves to such a solution of the question as would correspond to the existing practical relations, and so that this aim be attained in the simplest manner, easily and clearly representing the matter.

It has already been indicated that the action of the injector is based on two principles: the mechanical action of impact and the thermodynamic one—the conversion of heat into kinetic energy. Thus we shall obtain two equations by means of which the dimensions of the injector nozzles must be determined.

One of these equations has already been derived by us in the chapter on the condensation nozzle. Assuming that the steam nozzle of the nozzle has such a size that one kgr. of steam flows out per second, at its given initial state, for the final temperature of the feed water we had

\[ t_e = \frac{q_2 + r_2 x_2}{1 + P} + \frac{A(u_1^2 - u^2)}{2g(P + 1)} + \frac{A(u^2 - u_2^2)}{2g(P + 1)} P + \frac{P}{P + 1} t_a \ldots (1) \]

In this equation we neglect the loss of heat by radiation, as well as the positive and negative work of gravity, depending on the position of the injector with respect to the steam and water space of the boiler.

The loss of heat by radiation was determined by Giffard and found equal to 15% of all the heat contained in the forced water, i.e. the loss amounts to \(0.15 (P + 1)(t_e - t_a)\); this figure, however, seems somewhat large, but it will have to be used until there are other, more exact determinations.

A. M. Krugov.

Solving equation (1) with respect to \(P\), we shall find:

\[ P=\frac{q_2+r_2x_2-t_c+A\,\dfrac{u_1^2-u^2}{2g}} {t_c-t_a+\dfrac{A}{2g}\left(u^2-u_2^2\right)} \ldots\ldots (2). \]

Here the velocity of the steam \(u\) may be replaced by the general expression for it in terms of the heat content before and after outflow and the expansion connected with this, and we obtain:

\[ P=\frac{q_1+r_1x_1-t_c-\dfrac{Au^2}{2g}} {t_c-t_a+\dfrac{Au^2}{2g}-\dfrac{Au_2^2}{2g}} \ldots\ldots (3). \]

For a given steam pressure and its steam content \(x\), \(\lambda=q_1+r_1x_1\) will be known to us; the temperature of the feed water \(t_a\) may be specified; we may also provisionally assume the temperature \(t_c\), approximately taking the heating of the water as \(40\)—\(50^\circ\); we must determine the velocities \(u\) and \(u_2\) in order that we may calculate \(P\). For this we shall compose a second equation, using the theorem on quantities of motion.

One kg of steam, flowing out of the nozzle with velocity \(u_1\), will have \(\dfrac{u_1}{g}\) quantity of motion; the water flowing into the condensation nozzle will have \(\dfrac{P}{g}u_2\) quantity of motion; after impact \((P+1)\) kg of mixture will have \(\dfrac{P+1}{g}u\).

On leaving the condensation nozzle, in the interval between it and the receiving one, the mixture is subjected to compression by atmospheric pressure (with an open discharge pipe); if the atmospheric pressure is \(p_0\) and the pressure in the condensation chamber is \(p_1\), and, of course, \(p_0>p_1\), then the impulse of the force due to the difference of these pressures, when it acts on the jet during one second, will be equal to the increment of the quantity of motion; if \(p_0\) and \(p_1\) are expressed in kg per mtr.\(^2\), and \(\gamma_0\) is the density of the mixture, then we have

\[ u_1+Pu_2+\frac{g}{\gamma_0}(p_0-p_1)=(P+1)u \ldots\ldots (4) \]

and

\[ P=\frac{u_1-u+\dfrac{p_0-p_1}{\gamma_0}g}{u-u_2} \ldots\ldots (5) \]

In deriving this formula, we have not yet taken into account the existing losses, so that the velocities \(u_1\), \(u\), and \(u_2\) do not correspond to the actual ratios.

To calculate the possible losses, let us set up a series of equations of motion of the jet according to Bernoulli’s theorem (Fig. 40).

In section I the velocity of the steam is known to us, and depends on the form of nozzle arrangement that we have assumed; the existing losses of velocity head were also discussed in considering the steam nozzle.

In section II Bernoulli’s equation is written as follows:

\[ \frac{p_0}{\gamma} = \frac{u_2^2}{2g} + h_2 + \frac{p_1}{\gamma} + \xi_2 \frac{u_2^2}{2g} \ldots (6) \]

Here \(p_0\) is atmospheric pressure (kgr/sq. m.), \(p'\) is the pressure in the condensation chamber, \(\xi\) is the coefficient characterizing the losses of velocity on the path from the reservoir to the entrance into the condensation nozzle. For \(\xi_2\) Grashof gives the value 4; Prof. Kondrat’ev, 0.5, i.e. a value eight times smaller; this speaks only in favor of the method of calculation proposed by us below.

From equation (6) the velocity \(u_2\) is determined by the formula

\[ u_2 = \sqrt{ 2g\left( \frac{p_0-p_1}{\gamma} - h_2 \right) \frac{1}{1+\xi_2} } \ldots (6a) \]

In a suction injector \(h_2\) enters under the radical with a minus sign; in a non-suction injector, with a plus sign; in the first case \(p_1\) must be less than \(p_0\), the atmospheric pressure, while in the second it may also be greater than \(p_0\).

If \(\xi_2\) is known exactly, then from (6) the pressure in the condensation chamber may be found, and, consequently, the vacuum produced by the steam jet:

\[ \frac{p_1}{\gamma} = \frac{p_0}{\gamma} - h_2 - (1+\xi_2)\frac{u_2^2}{2g} \ldots (6b) \]

In section III the velocity \(u_3\) depends on the velocities of the water and steam and on their masses; it can be calculated from the equality indicated above, derived on the basis of the theorem of quantities of motion. In view of the assumption, stated in the chapter on the steam nozzle, regarding the possibility of compression of the steam, the question remains open whether this equality is applicable without further corrections for determining this velocity \(u_3\).

In section IV we have

\[ \frac{u_4^2}{2g} - \frac{p_1'}{\gamma_1} = \frac{u_5^2}{2g}(1+\xi_5) + \frac{p_2'}{\gamma_1} \ldots (7) \]

Since sections III and IV are situated very close to one another, and the influence of the force caused by the pressure difference \(p_0-p'\) is very small, it may be assumed that \(u_3\) is equal to \(u_4\), although in reality they will differ from one another.

In equality (7), \(p_1'\) is the pressure at the mouth of the receiving nozzle; it is always lower than \(p_0\), owing to the suction action of the receiving nozzle; \(p_2'\) is the pressure of the mixture at the end of the receiving nozzle; it is always greater than the pressure under which the reservoir is, into which the water is being forced; \(\xi_5\) is the coefficient accounting for losses of head as the jet passes through the receiving nozzle. These losses depend both on friction and, to an even greater extent, on possible vortex motions of particles in the jet itself; \(\gamma_1\) is the density of the mixture in the receiving nozzle. Whether it has one and the same value at the beginning and at the end of the nozzle cannot be stated exactly; if complete condensation does not take place in the condensing nozzle, and the jet leaves it containing a certain quantity of steam, these densities at the beginning and at the end of the receiving nozzle will be different; the value of \(\gamma_1\) is also affected by the admixture of air, which may be released in the condensing nozzle from the water and, with an open overflow pipe, may be drawn in owing to the suction action of the working receiving nozzle.

Thus, we have

\[ (1+\xi_5)\frac{u_5^2}{2g} = \frac{u_4^2}{2g} + \frac{p_1'-p_2'}{\gamma_1} = \frac{u_3^2}{2g} + \frac{p_1'-p_2'}{\gamma_1} \ldots (7a) \]

In section V:

\[ (1-\xi')\frac{u_5^2}{2g} + \frac{p_2'}{\gamma_1} = h_1+\frac{p}{\gamma_1}+\frac{p_0}{\gamma_1}+\frac{u_0^2}{2g} \ldots (8) \]

In equation (8), \(\xi'\) is the coefficient for the resistances from the end of the receiving nozzle to the outlet of the water from the pipe into the reservoir into which it is being forced; \(h_1\) is the height of the water level in this reservoir above the axis of the injector nozzles; \(p\) is the pressure in the reservoir; \(u_0\) is the velocity of discharge of water from the pipe supplying water to the reservoir; \(u_0\) is taken within the limits up to 2 mtr., i.e., from the assigned value of the velocity, we always know the velocity head

\[ \frac{u_0^2}{2g}. \]

For brevity, denote the sum

\[ h_1+\frac{p}{\gamma_1}+\frac{p_0}{\gamma_1}+\frac{u_0^2}{2g} \]

by \(H\). Then we have

\[ \frac{u_5^2}{2g} = \frac{H-\dfrac{p_2'}{\gamma_1}}{1-\xi'} \ldots (8a) \]

Substituting in (7a) the value found for \(\dfrac{u_5^2}{2g}\), we obtain

\[ \frac{1+\xi_5}{1-\xi'} \left( H-\frac{p_2'}{\gamma_1} \right) = \frac{u_3^2}{2g} + \frac{p_1'-p_2'}{\gamma_1}, \]

hence

\[ \frac{u_3^{\,2}}{2g} = \frac{1+\xi_5}{1-\xi'} \left(H-\frac{p_2'}{\gamma_1}\right) - \frac{p_1'-p_2'}{\gamma_1}. \]

\[ u_3 = \sqrt{ 2g\left\{ \frac{1+\xi_5}{1-\xi'} \left(H-\frac{p_2'}{\gamma_1}\right) - \frac{p_1'-p_2'}{\gamma_1} \right\} } \ldots\ldots (9) \]

Using now the values found for \(u_2\) and \(u_3\), and knowing \(u_1\), we shall compose the equality according to the theorem of quantities of motion. We shall have:

\[ \frac{\xi_1 u_1}{g} + \frac{P}{g} \sqrt{ 2g\left(\frac{p_0-p_1}{\gamma}-h_2\right)\frac{1}{1+\xi_2} } = \frac{P+1}{g} \sqrt{ 2g\left\{ \frac{1+\xi_5}{1-\xi'} \left(H-\frac{p_2'}{\gamma_1}\right) - \frac{p_1'-p_2'}{\gamma_1} \right\} }. \]

\(\xi_1\) is the coefficient of resistance in the steam nozzle; we have omitted the term \(\dfrac{p_0-p_1}{\gamma}\) in view of its small influence on the sum.

From equality (10) it would be possible to find the value of \(P\); but the expression for \(P\) turns out to be too complicated and practically inconvenient, especially since, besides the coefficients \(\xi_1\), \(\xi_5\), \(\xi_2\), and \(\xi'\), which are rather uncertain, it includes \(\gamma_1\), the density of the jet of mixture, whose actual value is unknown in advance.

Therefore, we shall introduce a general coefficient embracing all possible losses in the working process, assuming that they occur at the very impact of the steam jet upon the water. If this coefficient is denoted by \(\mu\), then under the stated condition we may write

\[ \mu\left(\frac{u_1}{g}+\frac{P u_2}{g}\right) = \frac{P+1}{g}u \ldots\ldots (11) \]

Whence we have

\[ P=\frac{\mu u_1-u}{u-\mu u_2} \ldots\ldots (12) \]

or, more exactly,

\[ P= \frac{ \mu u_1-u+\dfrac{g}{\gamma_0}(p_0-p_1) }{ u-\mu u_2 } \ldots (12a) \]

In calculation it will be necessary to use chiefly equation (12); for \(\mu\) one should take the value \(0.6\).

Thus the course of calculation of the injector will be as follows.

It is required to determine the dimensions of an injector for a boiler whose working pressure is \(9\) atm., and whose evaporative capacity is \(1200\) kg of steam per hour \((1\ \text{atm.} = 1\ \text{kg}/\text{cm}^2)\). The temperature of the feed water is \(15^\circ\) C.

Usually the injector is calculated so that it can deliver 2 or 3 times the amount of water.

According to Mollier’s tables for water vapor, we find that \(t = 178.9^\circ\text{C}\); the volume of one kg of steam is \(0.1993\) cubic m.; the heat of the water in 1 kg is \(181.5\) cal.; the latent heat of evaporation \(r = 484.6\) cal.; we shall regard the steam as dry saturated; the total heat of evaporation is \(666.1\) cal.

First of all, let us determine the theoretical velocity with which the water would issue from the mouth of the receiving nozzle under the head corresponding to the given pressure.

Let us assume that in the interval the pressure is equal to atmospheric pressure; in fact this is not quite correct, since, owing to the suction action of the diverging nozzles, at the mouth of the receiving pipe it will be less than atmospheric.

Since the working pressure of the boiler is \(9\) atm., the head of \(90\) meters will serve as the starting point in determining the velocity of outflow.

The general formula for calculating this velocity is as follows:

\[ u' = \sqrt{2g\left(h + \frac{p - p_0}{\gamma}\right)} \ldots\ldots (13) \]

Here \(h\) is the height of the water level in the boiler above the axis of the receiving nozzle; \(p\) is the absolute pressure in the boiler in \(\mathrm{kg}/\mathrm{cm}^2\), \(p_0\) is the atmospheric pressure, and \(\gamma\) is the density of water.

Since \(h\) is small (2–4 meters), in the general case we neglect this term. Thus,

\[ u_1 = \sqrt{19.62 \cdot 90} = 42.0 \text{ meters}. \]

To determine the velocity \(u_2\), we use formula (6a)

\[ u_2 = \sqrt{2g\left(\frac{p_0 - p_1}{\gamma} - h_2\right)}, \]

in which we omit the factor

\[ \frac{1}{1 + \xi_2}, \]

taking \(\xi_2 = 0\), since, according to the foregoing, we have included the influence of the resistances in the coefficient \(\psi\).

Although in practice we encounter injectors sucking to a height of up to \(5\) mtr., for reliability we shall assume that the suction height cannot be more than \(1.5\) mtr.

Such a limitation of the suction height is also useful because, with a known rarefaction in the condensation nozzle, we may have a higher velocity of entry of the cold water, which is necessary for better condensation of the steam as it flows through it in a thin layer.

Let us now assume that the pressure in the condensation chamber is \(0.6\) atm.; then, for determining \(u_2\), we have

\[ u_2=\sqrt{2g(10-6-1.5)}=4.43\sqrt{2.5}=7\ \mathrm{mtr}. \]

(We note that Grashof estimates the resistance to the flow of water from the lower reservoir into the condensation chamber by the coefficient 4; knowledge of it is necessary for determining the actual velocity of entry and, from it, the inlet section of the condensation nozzle.)

By equation (12) we now determine \(P\), the number of kgr. of water that must be supplied to the injector,

\[ P=\frac{0.6u_1-42.0}{42.0-0.6\cdot 7}. \]

The velocity of the steam \(u_1\) is determined from Tables A and D in the chapter on the steam nozzle. (We assume that the steam nozzle will have the form of a diverging cone.)

According to Table A, the velocity of the steam at the mouth of the nozzle will be \(451.8\ \mathrm{mtr.}\); according to Table D, with the ratio

\[ \frac{p_1}{p}=\frac{10}{0.6}\approx 16.6, \]

the velocity will be 2 times greater, i.e. approximately \(900\ \mathrm{mtr.}\). Substituting into the formula written above, we compute \(P\):

\[ P=\frac{540-42.0}{42.0-4.2}=13.17\ \mathrm{kgr}. \]

With such a \(P\), the temperature of the water will be, according to the table given in the chapter on the condensation nozzle, about \(60^\circ\) C.

The figures obtained by computation give mean values, which we encounter in practice.

Taking the threefold quantity of supplied water per hour, we must have \(1\ \mathrm{kgr.}\) of water per second.

This serves to determine the diameter of the suction pipe and the inlet section of the condensation nozzle; in order not to increase the resistances in the suction pipe, it is better to determine its size so that the velocity in it is about one meter \((0.8\) to \(1.2)\). Then we obtain \(F\) in sq. meters,

\[ F\times 1000\times 1=1 \]

or

\[ F=0.001\ \mathrm{sq.\ mtr.}=1000\ \mathrm{sq.\ mm}. \]

Hence \(d=36\ \mathrm{m/m}\), i.e. \(\approx 1.5''\).

To determine the area of the inlet into the condensing nozzle, we compute the actually possible and expected velocity, taking \(\xi=4\).

It will be less than 7 in the ratio \(\sqrt{\frac{1}{5}}\), i.e. it will be

\[ \frac{7}{2.24}=3.13\ \mathrm{mtr}. \]

Since for \(1\ \mathrm{kgr.}\) of steam there are \(13.17\ \mathrm{kgr.}\) of water, and in one second only \(1\ \mathrm{kgr.}\) of water enters, the steam nozzle must deliver per second

\[ \frac{1}{13.17}\simeq 0.08\ \mathrm{kgr.} \]

of steam.

Let us now check what the final temperature of the water will be. For this, in formula (3) we substitute the values known to us for the letters and find \(t_e\). We have

\[ 13.17= \frac{ 666.1-t_e-\dfrac{42.0^2}{19.62\cdot 427} }{ t_e-15+\dfrac{42.0^2}{19.62\cdot 427}-\dfrac{7^2}{19.62\cdot 427} } \]

\[ \frac{A}{2g}=\frac{1}{19.62\cdot 427}=\frac{1}{8388}; \]

the influence of all terms containing this factor is very insignificant; we omit them and find:

\[ 14.17t_e=666.1+197.55. \]

\[ t_e=60^\circ.9. \]

Let us now determine the area of the mouth of the receiving nozzle. Introducing the coefficient \(\mu\) earlier, we now assume that the velocity of the jet passing through the mouth will be equal to \(u=42.0\ \mathrm{mtr.}\), and that in the jet there is neither steam nor air, which would increase its volume.

We have:

\[ F_s\cdot u=v_{t_e}\,{}^{*}). \]

Here \(v_{t_e}\) represents the volume of \(1.08\ \mathrm{kgr.}\) of water (\(1\ \mathrm{kg.}\) of water \(+0.08\ \mathrm{kgr.}\) of steam per second) at the temperature of the mixture, \(61^\circ\) C. To compute \(v_{t_e}\), one may use the formula

\[ v_{t_e}=v_0\left(1+at+bt^2+ct^3\right), \]

where \(v_0\) is the volume of water at \(4^\circ\) C., and the coefficients \(a\), \(b\), \(c\) have the values

\[ a=-0.0000603;\quad b=0.00000793\quad\text{and}\quad c=-0.0000000426. \]

*) If the calculation is carried out by the formula

\[ F\cdot u\cdot \gamma_s=G, \]

For \(v_{t_e}\) at 1000 kgr. we obtain \(1.0169\) cu. mtr.

We shall have

\[ F_s \cdot u=\frac{1.0169\cdot 1.08}{1000}=0.001098\ \text{sq. mtr.} \]

\[ F_s=\frac{0.001098}{42.0}=0.00002614\ \text{sq. mtr.},\quad \text{or} \]

\[ F_s=26.14\ \text{sq. m/m.}\quad \text{and} \]

\[ d_s=5.8\ \text{m/m.}\sim 6\ \text{m/m.} \]

(For Friedmann’s injector No. 6 the catalogue gives, at \(p=8\) atm., a capacity per hour of 3500 liters and a diameter of the water-supply pipes of 35 m/m.).

Knowing \(F_s\), it is easy to find also the area of the orifice of the steam nozzle. We shall have, with a velocity of steam outflow at the orifice of \(451.8\) mtr. and a volume of 1 kgr. of steam of \(0.346\) cu. m., by the formula

\[ F_0=\frac{0.08\cdot 0.346}{451.8} \]

(The volume \(0.346\) cu. m. corresponds to \(5.57\ \mathrm{kg}/\mathrm{cm}^2\), which is the pressure that approximately must be at the orifice of the steam nozzle).

\[ F_0=0.00006126\ \text{sq. m.},\quad \text{or} \]

\[ F_0=61.26\ \text{sq. mm.}\quad \text{and} \]

\[ d_0=8.86\sim 9\ \text{m/m.} \]

then for \(\gamma_s\) the values may be taken from the appended table.

\(t^0\) C.	\(\gamma_s\)	\(t^0\) C.	\(\gamma_s\)	\(t^0\) C.	\(\gamma_s\)	\(t^0\) C.	\(\gamma_s\)
40	0.99233	56	0.98530	72	0.97674	88	0.96682
41	195	57	481	73	615	89	616
42	157	58	432	74	555	90	550
43	117	59	382	75	495	91	483
44	077	60	331	76	435	92	416
45	035	61	280	77	375	93	348
46	0.98993	62	228	78	314	94	280
47	949	63	175	79	253	95	212
48	905	64	121	80	191	96	143
49	860	65	067	81	129	97	074
50	813	66	012	82	066	98	005
51	767	67	0.97957	83	004	99	0.95934
52	721	68	902	84	0.96941	100	863
53	674	69	846	85	876
54	627	70	780	86	812
55	579	71	733	87	746

Since \(t_c=60^\circ\), we shall therefore obtain

\[ F_s\cdot 1=\frac{1.08}{984.32}=0.001098\ \text{sq. m.} \]

The ratio \(\dfrac{d_0}{d_s} = 1.5\), which is in complete agreement with practical data.

It is already known that the area of the outlet of the condensing nozzle is made equal to the cross-section of the mouth of the receiving nozzle. It remains only to find the area of the inlet opening into it; this can be done if the size of the outlet section of the expanded part of the steam nozzle and the thickness of its walls are found.

With regard to the length of the condensing nozzle, its profile, and the receiving and steam nozzles, directions have already been given in the corresponding chapters.

We shall now indicate the second method of calculating the injector. As its basis we shall take the experimental data obtained by Rosenhain in his study of the question of the discharge of steam from nozzles.*) In addition, we shall note that, by introducing the coefficient \(\mu\) into the left-hand side of the equation obtained by us from the theorem on the quantities of motion of masses before and after impact, we intended to include in it all possible losses for the jet of steam, water, and mixture. It is evident that the reciprocal of \(\mu\), equal to 1.66 when \(\mu = 0.6\), which we shall call, through \(\psi\), so that \(\psi = 1.66\), may be placed on the right-hand side of the above-mentioned equation. It will show us for what back pressure we wish to carry out the calculation of the injector at a given working pressure of the steam, i.e. \(\psi\) will represent the ratio of the calculated back pressure to the working pressure of the steam.

In reality, the injector can always force water against a greater back pressure than is necessary for feeding the boiler. The magnitude of this back pressure depends on the design of the apparatus and the conditions of its operation; the better the design, and the more closely the operating conditions correspond to the principle of its action, the greater the quantity of water it delivers against the greater back pressure.

By experiment Rosenhain determined the reaction of the issuing jet of steam and gave an empirical dependence of the magnitude of the reaction on the diameter of the mouth of the steam nozzle and on the initial pressure of the steam.

His tests relate to nozzles of diameter \(^{3}/_{16}'' \sim 4.77^{m}/_{m}\); their length and the outline of the inlet for the steam were varied.

The magnitude of the reaction of the jet at different steam pressures was as follows:

\(p\ \mathrm{kg}/\mathrm{cm}^2\)	\(R\ \mathrm{kgr.}\)
4	0.69
6	1.17
8	1.67
10	2.18
12	2.65
14	3.24

*) Proceed. of the Instit. of Civ. Eng., v. 140, p. 199.

The steam pressure in Rosenhain’s experiments was not below 50 pounds per square inch, and therefore the formula given is not applicable for pressures below 3 atm.

If \(d_0\) is measured in inches, the pressure \(p\) in pounds per square inch, and \(R\)—the reaction—also in pounds, then the relation between these quantities is

\[ R=d_0^2(1.08p-12). \]

With sufficient accuracy for metric units, the same relation may be represented by the formula

\[ R=d_0^2(1.08p-0.84), \]

where \(d_0\) is in centimeters, \(p\) in \(\mathrm{kg}/\mathrm{cm}^2\), and \(R\) in kg.

Assuming the expansion of the steam to atmospheric pressure, we can find the velocity \(w\) from the formula given by Rosenhain,

\[ w=\frac{Rg}{G}, \]

where \(G\) is the weight of the steam flowing out per second, and \(g\) is the acceleration due to gravity, equal to \(9.81\ \mathrm{mtr}/\mathrm{sec}\).

Let us assume that the steam nozzle is of such a size that \(G=1\ \mathrm{kg}/\mathrm{sec}\).

It is evident that \(R=\frac{G}{g}w\) is the quantity of motion of 1 kg of steam.

Keeping the same notation, we obtain

\[ d_0^2(1.08p-0.84)+\frac{Pu_2}{g}=(P+1)\frac{u}{g} \ldots\ldots (14) \]

Let us denote the diameter of the mouth of the receiving nozzle by \(d_s\) (centim.).

Then

\[ \frac{\pi d_s^2}{4}\gamma_s u\cdot 10^{-4} \]

represents the weight of the mixture passing per second through the mouth of the nozzle. It will be equal to \((P+1)\).

We have, on substituting,

\[ d_0^2(1.08p-0.84)+\frac{Pu_2}{g} = \frac{\pi d_s^2}{4}\frac{\gamma_s}{g}u^2\cdot 10^{-4}\ldots\ldots (15) \]

or

\[ d_0^2(1.08p-0.84)+\frac{P}{g}u_2 = \frac{u^2}{2g}10^{-4}\cdot \frac{\pi d_s^2}{2}\gamma_s \ldots\ldots (15a) \]

Let us write Bernoulli’s equation for the receiving nozzle and for the motion of the jet within the limits of sections IV and V:

\[ \frac{u^2}{2g}+\frac{p_s}{\gamma_s} = \frac{u_5^2}{2g}+\frac{p_5}{\gamma_5}+h_5 \ldots\ldots (16) \]

Here \(p_s\) is the pressure of the jet at the mouth; \(u_5\), \(p_5\), and \(\gamma_5\) are the velocity, pressure, and density in section 5; and \(h_5\) is the head lost to resistance. With regard to the velocity \(u_5\), let us note that in the feed pipe it is taken as about one meter; consequently, \(u_5^2/2g = 1/19.62\), as a small quantity, may be omitted in equation (16), and we shall find

\[ \frac{u^2}{2g}=\frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5 \ldots\ldots (17) \]

Substituting into equation (15a), we obtain

\[ d_0^2(1.08p-0.84)+\frac{P}{g}u_2 = 10^{-4}\cdot \gamma_s \cdot \frac{\pi d_s^2}{2} \left( \frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5 \right) \ldots (18) \]

We could determine \(u_2\) from one of the formulas indicated above and replace \(P\) by a value equal to it,

\[ \left(10^{-4}\cdot \frac{\pi d_s^2}{4}\gamma_s u-1\right), \]

and, under certain assumptions, find a relation between \(d_0\) and \(d_s\), expressed only as a function of \(p_s\), \(p_5\), \(\gamma_s\), and \(h_5\); but such a formula would be of no practical interest because of its complexity.

For simplification we shall assume that \(\frac{Pu_2}{g}\) is so small a quantity that we may neglect it. Then we obtain:

\[ \left(\frac{d_0}{d_s}\right)^2 = \frac{ \pi \gamma_s \left( \frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5 \right) }{ 2(1.08p-0.84)10000 } \ldots (19). \]

In formula (19) we have the ratio of the diameters of the steam and receiving nozzles as a function of the pressures of the steam and of the mixed jet, of the resistances in the receiving nozzle, and of the densities of the jet.

The pressure \(p_5\)—at the end of the receiving nozzle—for a given profile of it and for the velocity \(u\) and \(p_s\), could be found; we know that it must be greater than \(p\), the pressure in the boiler, otherwise there will be no delivery of feed water.

Having specified a certain value of \(P\) and determined the temperature \(t_e\), we could, by Grashof’s formula,

\[ \gamma_s=1100-5t_e \]

find the density of the jet \(\gamma_s\).

The density of the jet \(\gamma_5\) could be referred to the hot water of temperature \(t_e\). There remains, however, the unknown \(h_5\)—the lost head in the receiving nozzle. It has already been indicated above that it will depend not only on friction, but to a greater degree on wave-like and vortex...

...of motion of the jet and of the water particles. For the present we have no data by which to judge, even approximately, its magnitude; therefore our calculation will be somewhat indeterminate, and it is simpler in this case to make one assumption that would encompass particular cases.

Let us assume that \(h_5=0\); we shall take \(\gamma'_5=\gamma'_s\)—corresponding to a feed-water temperature of \(61^\circ\) C., i.e. equal to 983 kg; we take \(p_s\) equal to atmospheric pressure.

Under these assumptions we shall calculate the injector so that it can force the water against a back pressure \(\alpha p\), where \(\alpha=1.5\text{–}1.75\).

Let us see how the ratio \(\dfrac{d_0}{d_s}\) will vary; we shall calculate it by the simplified formula

\[ \left(\frac{d_0}{d_s}\right)^2 = \frac{\pi'_s\left(\dfrac{p_5}{\gamma'_5}-\dfrac{p_s}{\gamma'_s}\right)} {2(1.08p-0.84)\cdot 10000} \ldots (20) \]

which, after substitution of the numerical values, will have the following form:

\[ \left(\frac{d_0}{d_s}\right)^2 = \frac{1.57p_5}{1.08p-0.84} \]

The values of the ratio \(\dfrac{d_0}{d_s}\) for various \(p\) and ratios \(p_5:p\) are given in the following table.

\(p\)—kg/cm² by the pressure gauge	\(\dfrac{d_0}{d_s}\), \(p_5=p\).	\(\dfrac{d_0}{d_s}\), \(p_5=1.5p\).	\(\dfrac{d_0}{d_s}\), \(p_5=1.6p\).	\(\dfrac{d_0}{d_s}\), \(p_5=1.75p\).	\(\dfrac{d_0}{d_s}\), \(p_5=2p\).
3	1.4	1.71	1.77	1.85	1.98
4	1.34	1.64	1.70	1.77	1.90
5	1.31	1.60	1.66	1.73	1.86
6	1.29	1.58	1.63	1.71	1.83
7	1.28	1.56	1.62	1.69	1.80
8	1.27	1.55	1.61	1.67	1.80
9	1.26	1.55	1.60	1.67	1.79
10	1.25	1.54	1.59	1.66	1.77
11	1.25	1.53	1.58	1.66	1.76
12	1.24	1.53	1.57	1.65	1.75

As can be seen from the table, the ratio \(\frac{d_0}{d_s}\) at \(p_5=(1.5—1.75)p\) remains, for all pressures, within the limits with which we have to deal in practice.

The proposed method makes it possible to find this ratio and the size of the steam nozzle very quickly.

For the example indicated above we had \(d_s=6^{m}/_{m}\); take \(p_5=1.6p\); then, from the table, \(d_0=1.59\cdot 6=9.54^{m}/_{m}\).

In the preceding table the calculations were carried out on the assumption that the density of the jet corresponds to the density of water at \(61^\circ\) C.

If this density were known to us as a function of the amount of uncondensed steam or entrained air, or if we wished to carry out the calculation for another temperature, then the data in the table for the ratio \(\frac{d_0}{d_s}\) would have to be multiplied by \(\sqrt{\frac{\gamma'_s}{983}}\), where \(\gamma'_s\) is the assumed density of the jet.

In determining above the velocity of entry of the water into the injector, we supposed that the rarefaction reaches 0.4 atm. Experience shows that in many cases the injector can suck water from a height of up to 7 mtr., provided only that such action is not impeded by the temperature of the feed water. On the other hand, the possibility of such a rarefaction may be confirmed by Zeuner’s experiments*), carried out to elucidate the action of a steam jet in increasing the draft in the firebox of a locomotive boiler.

By experiment Zeuner established that, at a steam pressure of 1.75 atm. and with a ratio of the diameters of the pipe and the steam nozzle of 4, the rarefaction reached \(108.25^{m}/_{m}\) of mercury column, while at the same pressure and a ratio of diameters \(\sim 2.8\), it was \(202.5^{m}/_{m}\) of mercury column.

The rarefaction increased both with an increase in the steam pressure and with a decrease in the ratio of the diameters of the pipe into which the steam flowed and of the steam nozzle.

By virtue of this we may suppose that the pressure we have adopted in the condensing nozzle of the injector, 0.6 atm., is entirely possible and attainable.

Let us now turn to the consideration of other questions connected with the operation of the injector.

First of all let us clarify what its capacity is and on what it depends.

The greatest weight of water that an injector of a given size can deliver per hour, at given steam pressure and dryness, initial water temperature, and suction height, we shall call the maximum—

) Zeuner, Das Locomotiven-Blasrohr*, Zürich, 1863, S. 29.

... capacity. With a change in one of the indicated conditions, the weight of the water delivered will decrease; by minimum capacity we shall mean that quantity of water by weight which the injector can deliver, at the given back pressure, without losses through the overflow pipe.

The greater this difference, the greater will be its percentage ratio to the maximum, and the better the delivery of water by the injector can be regulated in accordance with the steam consumption.

If, for example, the maximum capacity is 3600 kgr. per hour under certain definite data \(t_a\), suction height, \(p\) and \(x\), and the minimum under the same conditions is 2000 kgr. per hour, then the ratio will be 55% of the maximum capacity; consequently, within the limits of variation of the steam consumption up to 55%, the injector can continuously feed the boiler with water.

Depending on the capacity developed by it, the temperature of the feed water \(t_e\) will vary.

Hutton) gives the following table, indicating the approximate variation of the temperature of the feed water, at \(t_a = 10^\circ\) C. and a suction height from 0.6 to 1.2 mtr.*), depending on the quantity of water delivered by the injector.

Working steam pressure kg/cm²	Variations of feed-water temperature in degrees C.	kg/cm²	Degrees C.	kg/cm²	Degrees C.
2.8	38°—63°	7.7	52°—85°	12.6	60°—116°
3.5	38°—65°	8.4	52°—88°	13.3	60°—118°
4.2	38°—68°	9.1	54°—90°	14.0	63°—124°
4.9	43°—71°	9.8	54°—96°
5.6	46°—74°	10.5	54°—102°
6.3	46°—76°	11.2	57°—107°
7.0	49°—79°	11.9	57°—110°

With an unchanged inflow of steam, the following fluctuations may be obtained in the quantities of feed water, expressed as a percentage of the maximum, at the same \(t_a\) and suction height.

) Steam-boiler Construction*, Hutton. 1898., p. 468.

**) Feed-water temperature above 100° C. can occur only in injectors operating with a closed overflow, or in double injectors.

Working steam pressure, kg/cm²	$\dfrac{\max.-\min.}{\max.}\cdot 100$	Working steam pressure, kg/cm²	$\dfrac{\max.-\min.}{\max.}\cdot 100$	Working steam pressure, kg/cm²	$\dfrac{\max.-\min.}{\max.}\cdot 100$
2.8	45%	6.3	56%	9.8	57%
3.5	50%	7.0	46%	10.5	65%
4.2	55%	7.7	48%	11.2	66%
4.8	45%	8.4	52%	14.0	76%
5.6	44%	9.1	50%

The weight of the mixture passing per second through the mouth of the receiving nozzle is equal to $(p+1)$ kg; retaining the previous notation, we have

\[ F_s u\gamma_s=P+1 \]

\[ u=\frac{P+1}{F_s\gamma_s}\ldots\ldots\ldots\ldots\ldots\ldots (21) \]

Omitting in equation (14) the term of the sum representing the quantity of motion of the cold water, and substituting for $u$ from (21), we shall find

\[ d_0^2(1.08p-0.84)=\frac{(P+1)^2}{F_s\gamma_s g}\ldots\ldots\ldots (22) \]

or

\[ d_0^2(1.08p-0.84)=\frac{(P+1)^2}{7.7\,d_s^2\,10^{-4}\gamma_s}\ldots\ldots (23) \]

Hence we find $(P+1)$ kg/sec.

\[ (P+1)=d_0d_s\sqrt{(1.08p-0.84)\cdot 7.7\cdot 10^{-4}\gamma_s}\ldots\ldots (24) \]

But according to equation (19)

\[ d_0=d_s\sqrt{ \frac{\pi\gamma_s\left(\dfrac{p_5}{\gamma_5}-\dfrac{p_s}{\gamma_s}+h_5\right)} {2(1.08p-0.84)\cdot 10000} }. \]

Replacing $d_0$ in the preceding formula by the indicated quantity, we obtain

\[ P+1=0.0003475\,d_s^2\gamma_s \sqrt{\frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5} \ldots\ldots (25) \]

and per hour

\[ Q=1.25d_s^2\gamma_s \sqrt{\frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5} \ldots\ldots (25a) \]

From equality (25) we see that the quantity of water delivered by the injector, for a given \(d_s\), depends on the density of the jet \(\gamma_s\), which is a function of the initial temperature of the water, of the perfection of condensation of the steam jet (and partly of the air sucked in through leaks and contained in the water), and of the velocity with which the jet passes through the mouth of the receiving nozzle; the term \(\dfrac{Pu_2}{g}\), omitted by us for the sake of simplicity, would also indicate a dependence on the suction height, but we shall consider this question separately.

From the same equality it is evident that the arrangement of a diverging nozzle as the receiving nozzle is advantageous, since, owing to its suction action, we shall have in the mouth a pressure \(p_s\) lower than atmospheric pressure, and the smaller it is, the better, since this increases \((P+1)\), the quantity of water delivered.

Let us assume, as above, that \(h_5=0\), \(\gamma'_5=\gamma_s\), and \(p_s=\) atmospheric pressure. If feeding takes place at a water temperature of \(60^\circ\) C., then \(\gamma_5=953\), and if \(p_5\) and \(p_s\) are given in kg./cm.\(^2\), then \(\gamma_5=0.0983\). Thus we find

\[ Q=0.04d_s^2\gamma_s\sqrt{p_5-p_s}\ldots\ldots(26). \]

Here \(d_s\) is to be taken in mm, \(p_5\) and \(p_s\) in kg./cm.\(^2\), and \(\gamma_s\) refers to one cubic meter.

Hutton gives the following table for the quantity of water delivered by an injector in kgr. per hour in the case where the water flows into the condensing nozzle by gravity.

Diameter of the mouth of the receiving nozzle in millimeters	2.8	3.5	4.2	4.9	5.6	6.3	7	8.4	9.8	11.2	12.6	14
Working steam pressure in kg/cm.\(^2\)	2.8	3.5	4.2	4.9	5.6	6.3	7	8.4	9.8	11.2	12.6	14
Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector	Quantity of water delivered by the injector
2	230	250	275	300	320	340	360	385	410	430	455	475
3	500	550	635	680	725	770	815	860	950	970	995	1020
4	900	1000	1100	1200	1290	1380	1425	1470	1600	1700	1835	2000
5	1400	1600	1700	1835	1970	2100	2200	2400	2580	2670	2760	2900
6	2000	2300	2500	2680	2900	3050	3230	3550	3820	3950	4100	4280
7	2750	3100	3400	3700	3950	4175	4400	4800	5200	5380	5550	5730
8	3600	3950	4450	4800	5100	5500	5815	6350	6850	7075	7250	7560
9	4600	5100	5600	6050	6500	6860	7260	7935	8565	8880	9000	9300
10	5675	6450	7000	7540	8040	8760	8980	9935	10750	11560	11785	12100

Hutton indicates that, for a suction height of 0.9 mtr., the data of the table should be reduced by 7%, for 1.8 mtr. by 12%, for 2.7 mtr. by 20%, and by 30% when suction is at 3.6 mtr.

The table was compiled for an initial water \(t_a\) of \(+10^\circ\) C. If \(t_a = 21^\circ\) C., then the tabular data must be reduced by 3%; at \(t_a = 30^\circ\) by 5%; at \(t_a = 38^\circ\) by 10%; at \(t_a = 49^\circ\) by 15%; and at \(57^\circ\) by 25%.

Let us replace, in formula (26), \(p_5\) by the equal quantity \(\alpha p\), where \(\alpha = 1.5\text{–}1.75\), etc.; taking pressures from the manometer, we shall have

\[ Q = 0.04 d_s \gamma_s \sqrt{\alpha p}\ldots \tag{26a} \]

and, for \(\alpha = 1.5\),

\[ Q = 0.0488 d_s^2 \gamma_s \sqrt{p}\ldots \tag{26b} \]

For injector No. 8, working with steam at 10 atm. pressure, from the table we have \(Q = 6850\).

Consequently, we obtain

\[ 6850 = 0.0488 \cdot 64 \gamma_s \sqrt{10} = 9.876 \gamma_s \]

and

\[ \gamma_s = 693, \]

i.e., the density of the jet at the mouth of the nozzle is considerably less than the density of water which it should have at the feed temperature.

By experiment Giffard determined that the quantity of water delivered by his apparatus can be represented by the formula

\[ Q = 28 d^2 \sqrt{n - 1}, \]

where \(n\) is the absolute pressure of the steam in the boiler.

With the value of \(\gamma_s\) found, the formula derived by us takes the form

\[ Q = 27.33 d_s^2 \sqrt{p_5 - p_s}. \]

We now arrive at an even shorter method for determining the diameter of the receiving nozzle, namely by formula (26b), in which, instead of \(\gamma_s\), one must put 700, and for \(p\)—the working pressure of the steam in the boiler.

To clarify the circumstances accompanying the operation of the injector, let us turn to equation (25a)

\[ Q\ \mathrm{kgr.}\ \text{per hour} = 1.25 d_s^2 \gamma_s \sqrt{\frac{p_5}{\gamma_5} - \frac{p_s}{\gamma_s} + h_s} \]

We see that the capacity of the injector depends on the density of the jet at the mouth of the receiving nozzle, on the square of the diameter of this mouth, and is proportional to the square root of the difference of the heads corresponding to the required back pressure \(p_5\), combined with the head for harmful resistances, and the pressure at the mouth of the nozzle.

From the table that we have borrowed from Hutton, one clearly sees a fourfold increase in capacity when the diameter of the receiving nozzle is doubled.

The greater the density of the jet \(\gamma_s\), the greater \(Q\) will be.

Obviously, \(Q\) will be greatest for the case when \(\gamma_s\) corresponds exactly to the temperature of the feed water, i.e., when there is no uncondensed steam in the jet.

\(Q\) will decrease as \(\gamma_s\) decreases; in order for \(Q\) to remain unchanged, it will be necessary to increase the velocity at the mouth of the receiving nozzle. This will be possible only by reducing the quantity of water being supplied; if much air is dissolved in it, or if the suction line is not fully tight, its release or suction makes the operation of the injector unstable, and it may stop feeding the boiler. To eliminate instability in operation, so-called restarting injectors are constructed.

Finally, \(Q\) is the greater, the smaller the back pressure that the jet of water must overcome. It is obvious that the greatest value of \(Q\) will be when the injector operates at a pressure lower than the working steam pressure.

But in this case it will not serve to feed the boiler, and heating the water will be associated with a wasteful expenditure of heat, as will be discussed further below.

Using equation (25), one can construct diagrams that indicate the law of variation of \(Q\) as a function of \(d_s\), \(\gamma_s\), or \(p_s\).

For every injector there are certain limits within which it can be put into operation.

If \(P\) kgr. of water are mixed with \(1\) kgr. of condensing steam, whose total heat at its given dryness is \(\lambda\), then we shall obtain \((1+P)\) kgr. of water heated from the temperature \(t_a\) to the final temperature \(t_e\).

We shall have

\[ \lambda + P t_a = (1+P)t_e; \ldots \ldots (27) \]

whence we find that

\[ 1+P=\frac{\lambda-t_a}{t_e-t_a}. \ldots \ldots (28) \]

Mollier*) gives the following dependence of \(\lambda\) on the steam pressure \(p\) and its temperature \(t_p\):

\[ \lambda = 594{,}735 + 0{,}477t_p - Jp \]

The values of \(J\) are given in the table corresponding to \(t_p\).

) Neue Tabellen und Diagramme für Wasserdampf*, 1906.

The equality (28) will take the form

\[ 1+P=\frac{594.7+0.477t_p-Jp-t_a}{t-t_a}\ldots (28a) \]

For given \(p\) and \(t_a\), the quantity \((1+P)\) depends on the temperature difference \(t_e-t_a\), i.e. on the degree of heating of the feed water; the minimum of \((1+P)\) corresponds to the greatest degree of heating.

If we take for \(t_a\) the limit \(5^\circ\mathrm{C}\), and for \(t_e\)—\(90^\circ\mathrm{C}\), then

\[ \operatorname{minimum}(1+P)=\frac{594.7+0.477t_p-Jp-5}{85}, \]

\[ \text{”}\quad (1+P)=6.94+0.0056t_p-\frac{J}{85}p\ldots (29) \]

The coefficient \(J\) may be calculated for any steam temperature by the formula, where \(T\) is the absolute temperature,

\[ J=\frac{10000}{427}\left[0.325\left(\frac{273}{T}\right)^{\frac{10}{3}}-0.001\right] \]

or taken from the appended table.

\(t\) in deg. C.	Values of \(J\).	\(t\) in deg. C.	Values of \(J\).	\(t\) in deg. C.	Values of \(J\).
0	8	90	2.9	150	1.75
5–10	7	95	2.8	155	1.68
15–25	6	100	2.66	160	1.61
30–45	5	105	2.55	165	1.55
50	4.3	110	2.44	170	1.49
55	4.1	115	2.35	175	1.44
60	3.9	120	2.24	180	1.38
65	3.7	125	2.14	185	1.33
70	3.5	130	2.06	190	1.29
75	3.4	135	1.97	195	1.24
80	3.2	140	1.89	200	1.20
85	3.1	145	1.82

If we take \(p=3\ \mathrm{kg}/\mathrm{cm}^2\), whence \(t_p=132.8\), then for \((1+P)\) we compute the value \(7.61\ \mathrm{kgr}\).

\[ 1+P=6.94+0.0056\cdot 132.8-\frac{2.01}{85}3. \]

For one kgr. of steam there will be, therefore, 6.61 kgr. of water.

To determine the maximum \((1+P)\), let us turn to the equation

\[ u_1 + P u_2 = u(P+1) \]

If the velocity \(u\) is exactly equal to that velocity at which feeding of the boiler without loss of water through the exhaust pipe is possible, then \(P\) will be a maximum.

For the velocity \(u\) we had formula (17)

\[ \frac{u^2}{2g}=\frac{p_5}{\gamma_5}-\frac{p_s}{\gamma_s}+h_5 \]

When \((1+P)\) is to be a maximum, \(u\) must be a minimum, or the right-hand side of the above equality must be a minimum.

Replacing the right-hand side of the equality, as was done above, by the expression

\[ \frac{\alpha p}{\gamma_5}, \]

we find

\[ u=\sqrt{2g\frac{\alpha p}{\gamma_5}} \]

and, again taking \(\gamma_5\) equal to 983, we shall have

\[ u=14.1\sqrt{\alpha p}, \]

where \(p\) must be in \(\mathrm{kg}/\mathrm{cm}^2\).

Omitting in the momentum equation the term \(P u_2\), we find that

\[ 1+P=\frac{u_1}{14.1\sqrt{\alpha p}} \ldots \ldots \ldots \ldots \ldots \ldots (30) \]

For a conical converging nozzle the velocity \(u_1\), according to formula (16) of Ch. I, will be equal to

\[ u_1=323\sqrt{pv} \]

Making the substitution, we obtain

\[ P+1=\frac{323}{14.1}\sqrt{\frac{pv}{\alpha p}}=22.9\sqrt{\frac{v}{\alpha}} \ldots \ldots (31) \]

It is obvious that the maximum will occur when the velocity of entry into the boiler is very small; in other words, when the weight of water is so large that the velocity of the jet \(u\) is almost entirely transformed into potential energy for overcoming the pressure on the feed valve from the side of the boiler from which the working steam is taken.

In this case \(\alpha=1\), and the formula takes the form

\[ P+1=22.9\sqrt{v} \ldots \ldots (31a) \]

where \(v\) is the volume occupied by 1 kgr. of steam in its initial state.

Since \(v\) decreases as the steam pressure increases, \(P+1\) will be smaller for injectors operating with high-pressure steam than for those operating with low-pressure steam. Practice fully confirms this conclusion.

If we take steam at a gauge pressure of \(10\ \mathrm{kg/cm^2}\), for which \(v=0.1993\), then for \((P+1)\) we obtain

\[ P+1 = 22.9\sqrt{0.1993}=0.45\cdot 22.9 = 10.21\ \mathrm{kg}. \]

For an injector having a diverging steam nozzle, the velocity \(u_1\) will be greater; it is determined by formula (5) of Chapter I,

\[ u_1 = 91.53\sqrt{q_1-q_2+r_1x_1-r_2x_2}. \]

Allowing 15% for friction losses, we shall have

\[ u_1 = 77.8\sqrt{q_1-q_2+r_1x_1-r_2x_2}. \]

After substitution, equation (30) takes the form

\[ 1+P = 5.52\,\frac{\sqrt{q_1-q_2+r_1x_1-r_2x_2}}{\sqrt{\alpha p}}\ldots\ldots(31b) \]

For the example considered in Chapter I, at \(p=10\ \mathrm{kg/cm^2}\), the value of the square root in the numerator is \(\sqrt{88.439}=9.4\).

With \(\alpha=1\), we obtain

\[ 1+P = 5.52\,\frac{9.4}{3.16}=16.42 \]

and \(P\) maximum will be equal to \(15.42\ \mathrm{kg}\), i.e. an amount of water 1.67 times greater can be delivered by \(1\ \mathrm{kg}\) of steam.

Let us now consider the question of the influence of the suction height and the temperature \(t_a\) on the operation of the injector.

The suction height and the temperature of the supplied water \(t_a\) must lie within definite limits in order for injector operation to be possible. If we denote by \(t'\) the temperature of saturated steam corresponding to the pressure in the condensing nozzle, then we must have

\[ t_a < t'; \]

otherwise evaporation of the water will occur in the condensing nozzle; the steam released will cause an increase of pressure in the nozzle, i.e. will reduce the vacuum, and suction will cease.

If the atmospheric pressure above the water in the reservoir is \(p_0\), the pressure in the chamber is \(p'\), and the suction height is \(h_s\), then we shall have

\[ (1+\xi)\frac{u_2^2}{2g}+h_s=\frac{p_0-p'}{\gamma_a}10\ldots\ldots\ldots(32) \]

where \(p_0\) and \(p'\) are expressed in atmospheres \((\mathrm{kg/cm^2})\), and \(\gamma_a<1\).

From (32) we obtain

\[ p' = p_0 - \frac{\gamma_a}{10}\left[h_s + (1+\xi)\frac{u_2^2}{2g}\right]. \]

This equality gives us the possibility, for each suction height, taking \(\gamma_a = 1\), of finding the pressure in the condensing nozzle \(p'\) and, consequently, the temperature \(t'\) to which the water cannot be heated by the injector.

But the heating of the water is equal to \(t_c - t_a = \Delta t^0\); therefore, for the initial temperature \(t_a\), we obtain

\[ t_a < t' - \Delta t^0 . \]

Since, with an increase in the steam pressure, the amount of heat contained in 1 kg of steam increases, and, chiefly, the amount of outflowing steam increases considerably, the heating \(\Delta t\) will be greater in an injector operating with high steam pressure; and since the vacuum remains almost unchanged, the greatest possible temperature of the feed water which it can draw in is thereby reduced.

In Hartmann Knocke*), who sets forth the theory of the injector according to Grashof, we find the following table for the highest possible temperature \(t_a\), as a function of the suction height \(h_s\) and the steam pressure.

\(h_s\)	0	1	2	3	4	5 mtr.
\(p = 4\)	73	70	66	62	58	52
\(p = 6\)	70	67	63	59	55	49
\(p = 8\)	67	64	60	56	52	46
\(p = 10\)	64	61	57	53	49	43

In reality, for successful condensation of the steam it is necessary to have \(t_a\) less than the indicated values.

In the following table are given the limiting temperatures \(t'\) at various suction heights and pressures in the condensing nozzle.

\(h_s = 0\)	1	2	3	4	5 mtr.
\(p' = 0{,}9\)	0,8	0,7	0,6	0,5	0,4 atm.
\(t_s = 97{,}1\)	93,9	90,3	86,3	81,7	76,2° C.

In calculating \(p'\) it is assumed that 1 mtr. of head is lost to resistance.

) Die Pumpen*, Hartmann Knocke, S. 648.

A. M. Krylov.

The mechanical efficiency of the injector is very insignificant. This depends, as was already indicated above, on the great loss of velocity in the impact of water and steam. Retaining the previous notation, we have:

\[ \begin{aligned} &\text{vis viva of the feed water}\ldots\ldots\ldots\ldots &&\frac{(1+P)u^2}{2g} \\[4pt] &\phantom{\text{vis viva}}\quad \text{of the steam jet}\ldots\ldots\ldots\ldots &&\frac{u_1^2}{2g} \\[4pt] &\phantom{\text{vis viva}}\quad \text{of the cold water}\ldots\ldots\ldots\ldots &&\frac{u_2^2}{2g}\,P . \end{aligned} \]

The energy which we possessed in the separate jets of water and steam was equal to

\[ \frac{u_1^2+u_2^2P}{2g} \]

The ratio of the kinetic energy of the feed water, which is used for forcing it into the boiler, to that which existed before impact is equal to the efficiency

\[ \eta = \frac{\dfrac{(1+P)u^2}{2g}} {\dfrac{u_1^2+Pu_2^2}{2g}} = \frac{u^2(1+P)}{u_1^2+u_2^2P}. \]

For the example considered above,

\[ \begin{aligned} u_1 &= 900\ (452)\ \mathrm{mtr.}\\ u_2 &= 7\ \mathrm{mtr.}\\ u &= 42.0\ \mathrm{mtr.}\\ P &= 13.17\ \mathrm{kgr.} \end{aligned} \]

Calculating, we find

\[ \eta = \frac{(42.0)^2 \times 14.17}{(900)^2+13.17\cdot 7^2} = 0.0308, \]

i.e., only 3.08% of the available kinetic energy can be used to perform useful work.

The thermal efficiency, however, is very high. If it is assumed that the losses amount, according to Giffard’s determinations, to 15% of the heat of the feed water, i.e.

\[ 0.15(P+1)(t_e-t_a), \]

then it is evident that it will be no less than 85%, taking into account only the sensible heat; in reality it will be greater, since part of the heat is still contained in the work performed. According to Cario’s data, the thermal efficiency is equal to 0.95.

From this it is evident that the injector, as an apparatus for feeding a boiler, is very advantageous; but as a pump for delivering water to a given height it is uneconomical, if heating the water has no purpose.

Types of Injectors

Injectors are divided into those that suck in water and those that receive it under pressure. The manufacture of the latter is somewhat cheaper; the advantages they possessed—greater reliability of operation—now, with the appearance of so-called restarting injectors, play a considerably smaller role in the choice of the type of apparatus.

Their essential difference consists in the fact that, in a suction injector, before the action begins the jet of steam must produce sufficient rarefaction in the condensing nozzle so that water can rise into it. This is achieved by giving the steam nozzle a certain shape and, chiefly, by installing a sufficiently large overflow pipe, through which, at the moment of starting, steam together with air could freely escape into the atmosphere. The second difference consists in the fact that, in a suction injector, a valve or cock is installed by which, at the moment of starting, the quantity of steam flowing out is regulated; sometimes this is done by means of a sharp-ended spindle moving in the direction of the axis of the nozzle.

Depending on the kind of injector, the starting of one and the other differs. With a suction injector, a thin jet of steam is admitted with the valve or cock on the suction pipe fully open, and the opening of the steam nozzle is not increased until water appears through the overflow pipe; if, with the steam cock fully open, its outflow does not cease, this will indicate an excess of it, and it will be necessary to reduce its inflow, regulating it by the cock or valve on the suction pipe.

With a non-suction injector, first the water flowing in under pressure is admitted, and then steam is slowly let in.

This is for the most part necessary because the cross-section of the overflow pipe is very small; the steam, not having time to escape into the atmosphere, produces a back pressure on the water, throwing it out of the injector. Stalling, i.e. the escape of steam through the suction pipe, is also possible in suction injectors if, when starting it, an excessive quantity of steam is admitted into the passage through the nozzle. The arrangement diagram of each type of injector for boilers is shown in Fig. 41.

Non-Suction Injectors

Fig. 42 shows the Schau injector, often encountered on our railways. The condensing and delivery nozzles b and c constitute a single whole; in the narrow section of this tube there are openings g, through which water flows out before the injector is put into operation. Directly adjoining the injector is the cock E of the water-supply pipe, by which the inflow of water is regulated. It enters the condensing nozzle through the annular clearance between it and the steam nozzle and through the side openings in the condensing nozzle e. The cock of the overflow pipe may also be closed during starting; then the water fills the body of the injector, and when its operation has become established it may be taken for feeding, owing to the reduced pressure at the mouth of the receiving nozzle. If the steam pressure falls only slightly, the excess water is discharged into this body through the openings, and is again taken up when the steam pressure increases anew; the air contained in the water also escapes here, and can periodically be removed through the cock of the overflow pipe.

Sometimes, when there is an excess of steam in the boiler, the driver, while the train is standing, uses the injector to heat the water; in this case, with the cock of the overflow pipe open, the steam from it is directed through a pipeline to the tender.

Fig. 43 indicates a non-suction injector common on the Great Eastern Railway in England. Its body is of cast iron, while the cone is of bronze; the outlines of the nozzles are coarser than those of the Schau injector.

Schau injectors are manufactured in 8 sizes for delivering water in quantities from 450 to 9000 kgr. per hour.

Fig. 44 represents the Friedman injector, common on the railways of Austria. Its distinction is that the water is led to the jets of steam and of the moving mixture of steam and water by several nozzles. Owing to the more prolonged contact of the steam with the water, a more rapid and complete condensation of it is achieved; it can deliver water heated to \(65^\circ\) C.

The inflow of water can be regulated by a cock on the water pipe; the condensing and receiving nozzles are joined together by screws, which fasten them to one another by means of ribs cast onto the first nozzle.

At the outlet from the receiving nozzle a check valve C is installed; the same kind of valve is also present on the overflow pipe; by tightening a nut, the valve of the overflow pipe can be pressed against its seat; in this case the Friedman injector can deliver strongly heated water, owing to the increased pressure in the interval between the nozzles. Inspection and pro-

cleaning of the nozzles is carried out very easily, since all the nozzles are removed from the body through an opening closed by a threaded plug.

Friedmann injectors are manufactured in 9 different sizes, with working steam pressure up to 10 atm. and with a delivery from 1080 to 13800 liters per hour.

In Fig. 45 is shown the Nathan injector, which is used on the railways of America. The inflow of water takes place from below through a special channel in the body; the opening of the delivery pipe in the interval between the nozzles is shown by a circle; it is made pass-through on both sides and, depending on the position of the injector, the valve may be placed on either side; on the opposite side a threaded plug is fitted. For ease of starting, a regulating spindle is sometimes placed in the steam nozzle.

The inflow of water can be regulated by reducing the inlet area at the condensing nozzle. This is done in Webb’s injector, widespread on the London and North-Western Railway. The injector is shown in Fig. 46.

The condensing and receiving nozzles form a single whole and can have a progressive movement in special guides. The farther the condensing nozzle is pushed onto the steam nozzle, the smaller the quantity of water that enters the former.

This shifting of the nozzles is carried out by a long spindle, having a thread at the upper end and a handwheel \(W\) for rotating the spindle in the nut. The injector is placed under the driver’s platform; the steam inlet into it is directed upward. By means of the attachment \(P\), one can wash the platform with a jet of steam or wet the coal. When there is an excess of steam in the boiler, especially during stops at stations, it is possible, after closing the taps of the delivery and forcing pipes, to admit steam through the water-supply pipe into the tender.

In exactly the same way the inflow of water is regulated in the Rue injector, represented in Fig. 47. By inclining the handle to the right or to the left, we increase or decrease the annular cross-section between the nozzles for the inflowing water; by this means it is possible to change the capacity of the injector and to operate it at different steam pressures. For operation with suction of water, an additional nozzle-spindle is installed, with the discharge of steam into the condensing nozzle.

As was already indicated above, for feeding boilers by injectors one may use exhaust steam; this makes it possible to utilize the heat of the spent steam, while the heating of the water may reach 70–90°.

These injectors were first constructed by Hamer, Metcalfe and Davies.

In Fig. 48 is shown the injector of this plant, in the now generally used form for feeding stationary boilers up to \(5^{1}/_{2}\) atmospheres pressure. The exhaust steam is taken off by a side branch from the main line, with a slight fall in the direction toward the injector; the water is supplied either from a tank located above, or directly from the water main. By opening the cocks on the steam and water pipelines, the injector is put into operation. Its steam nozzle, corresponding to the low steam pressure and therefore to its considerable volume, has larger dimensions than in injectors working with live steam.

At its center there is a spindle B, whose purpose is to give the jet of steam the proper cylindrical form as it issues.

The condensing nozzle is also longer than usual and consists of two parts, of which one, D, is completely fixed, while the other, E, can rotate about the axis in the form of a valve. Both halves are accurately fitted to one another; to eliminate lateral displacement, the movable half has two ribs, between which the projection of the casing wall is placed. When the injector is in the vertical position, as indicated in the figure, the valve occupies a vertical position, so that the flow section of the nozzle is increased.

When the injector is installed in a horizontal position, the valve must be at the top and pressed against the fixed part of the nozzle by its own weight; when the injector is started in this position, the valve is lifted by the steam, and thereby the flow section of the condensing nozzle is again increased. The exhaust steam supplied from the engine exits through the side suction pipe located there; the latter has a vertical rib F, whose purpose is to create a water seal and not allow atmospheric air to enter; instead of such a device an air valve may also be fitted. When the pressure in the condensing nozzle falls below atmospheric, its movable half is closed by the excess pressure that appears, and the jet goes to the delivery nozzle and to the boiler.

In the lower part of the injector casing there is a plug, around whose circumference a scale is marked, while on the casing there is a pointer. By turning this plug, the condensing nozzle can be moved away from or brought nearer to the steam nozzle and thereby the inflow of water regulated. If the regulator is turned too far to one side or the other, water appears through the suction pipe, which indicates an incorrect position of the nozzles. The same injector can also work with suction lift of water. The general arrangement and installation are shown in Fig. 49. In order not to increase the back pressure on the piston of the engine, the branch should not introduce unnecessary resistances from changes in the direction of motion, etc.

As was already indicated earlier, the steam coming to the injector must be as dry as possible; the steam flowing from the engine, however, contains a considerable and very variable quantity of water. In order that it should not enter the injector, the connection of the branch with the main line is necessarily made lateral; in addition, it may prove useful to install a steam dryer or a water separator on this branch. To regulate the quantity of incoming steam, a valve is placed immediately before the injector; the inflow of water is regulated by the position of the nozzles.

When it is necessary to feed the boiler at a time when the engine is not running, a small pipe for live steam is arranged from the steam space of the boiler. It is necessary that this steam, supplied to the apparatus below the steam valve of the branch, should lose its elasticity on the way and enter the nozzle with a pressure close to that of the exhaust steam.

Schäffer and Budenberg build and supply injectors of exactly this type; they manufacture them in 9 sizes, with a capacity from 240 to 7200 liters per minute.

If the back pressure exceeds 5–5½ atmospheres, then, to strengthen the action of the jet of exhaust steam, an additional jet of live steam is supplied, producing an impact on the mixture already in the depth of the condensing nozzle.* An injector of this type is shown in Fig. 50; an injector of the Holden and Brooke works, likewise operating with exhaust steam, is indicated in Fig. 51. Its action is clear without special explanations; at pressures higher than 5 atm., as with other injectors, an additional jet of live steam is supplied.

It is interesting to point out here the peculiar installation of such injectors on mine hoisting engines. In their periodic operation, the desire to utilize the heat of the exhaust steam encountered the difficulty that it was necessary either to put up with losses of water when it flowed in openly through the discharge pipe, or else each time the engine stopped to shut off its inflow.

* In the same way, an additional nozzle for live steam is installed in the case where it is desired to obtain a suction action. In this case a throttle valve is placed in the steam chamber of the injector, by which the quantity of incoming exhaust steam is regulated. When starting the suction injector, first the air cock on the feed pipe is opened, and then the exhaust and live steam are admitted; the pipe for water from the reservoir situated below remains open all the time. The Schäffer & Budenberg works make injectors of this type in 8 sizes, with a water delivery from 600 to 7200 liters per minute; the back pressure may reach 11 atmospheres; at pressures up to 5 atm. and with a non-suction injector, the temperature of the water may be 32° C.; at higher pressures it must be cold. The temperature of the water entering the boiler reaches 80–85° C. The consumption of live steam amounts to 1/3 of the consumption of exhaust steam.

Holden and Brooke, for such machines, provide Johnson’s automatic control valve, shown in Fig. 52.

It is placed on the water-supply pipe. The valve is opened by the pressure of steam on a piston in the head, the steam being led by a small pipe from the slide-valve chest. As long as the machine is operating and live steam is present, the valve remains open for water; when the machine stops, the spring above the piston lowers the valve disk onto the seat, and the inflow of water ceases.

Suction Injectors

As was already indicated above, these injectors must have regulation of the issuing steam jet, so that at the beginning of operation the vacuum necessary for lifting the water may be obtained in the condensing nozzle; it is likewise necessary to regulate the quantity of water entering the nozzle. The latter may be done either by hand or automatically. Regulation is necessary in order to ensure proper operation of the apparatus under variable steam pressures and feed-water temperatures. The means by which this is achieved will be seen from the description of the various injectors of this type.

Figs. 53 and 54 show Giffard injectors in their modern form, manufactured by the firm of Schaeffer and Budenberg for vertical and horizontal arrangements. The receiving and condensing nozzles are screwed together, inserted into the body, and occupy a definite position, bearing against the guide of the check valve placed behind the receiving nozzle. The head with the spindle is screwed on with bolts; such an arrangement facilitates setting the apparatus in accordance with the circumstances, owing to the possibility of shifting the upper part on the bolts in any direction.

The steam jet is regulated by a spindle; it is of two kinds. In the first, the spindle is solid and has at the top a disk, which serves to shut off the admission of steam; at the lower end there is a conical tail, the position of which in the nozzle determines a greater or lesser area of passage for the steam jet. A spindle of the second kind is shown on a larger scale in Fig. 55; here at its lower end there are transverse and axial openings, through which, at the start, when putting into operation, a fine jet of steam flows out, producing suction. To stop the admission of steam, a special valve is placed on the steam pipe. The shifting of the spindle is effected, in vertical injectors, by a handwheel on a screw; in horizontal ones, either by the same method or by a simple lever; in the latter, instead of

of the check valve, pressed by the steam pressure against the receiving nozzle, the feed valve is screwed in. The clearance remaining between the receiving and condensing nozzles falls near the opening for the delivery pipe. The latter must have an area considerably larger than the opening through which the steam jet producing the preliminary rarefaction is admitted; otherwise there will be throttling, and the steam will pass along the water pipe into the reservoir.

These injectors can operate with steam pressures from 3 to 9 atm.; with nozzles of a special profile, and at higher pressures; the temperature of the feed water may be up to 30° R. Their capacity varies, depending on size, from 240 to 9000 liters per hour.

The original Giffard injector, besides the spindle, had a movable steam nozzle; for tightness, the body had a stuffing box; in practice it proved very difficult in this case to keep the joint tight so that there would be no leakage of steam either into the atmosphere or into the injector, which disturbed the action of the apparatus. Therefore, such regulation of the steam is now not used; the steam nozzle is made fixed, while either all the others, or only the condensing nozzle, can be moved.

The shortcomings of stuffing boxes with movable steam nozzles are ingeniously eliminated in the American “Metropolitan” injector, shown in Fig. 56. By turning handle K, the inflow of a small jet of steam is opened, which produces the suction of water; upon further rotation the full cross-section of the nozzle is opened for it. If the steam pressure is very high, or the suction lift is great, the usual passage for water between the nozzles is insufficient; then, with further rotation of the handle in the same direction, the steam nozzle S will also be set in motion, its extreme position being determined by the clamp fitted on it. At low steam pressure, the handle is turned in the opposite direction, and the nozzle assumes the corresponding position under the influence of the steam pressure acting on its enlarged part, in which the spindle is placed. Here an especially careful fitting of the nozzle and its guides is required, so that there is no leakage of steam into the condensing chamber, since this reduces not only the suction capability but also the capacity.

In Fig. 57 is shown Sellers’s self-regulating injector, very convenient for cleaning, inspection, and repair of its parts. By turning handle H through a small angle backward, the outlet of steam jets through the spindle is opened, by which rarefaction is produced in the condensing nozzle; the valve K, located behind the receiving nozzle, on the overflow pipe must be open. When water appears through it,

the handle is moved back through its full travel and the drain opening is closed.

Thereafter the operation of the injector proceeds with automatic regulation of the quantity of incoming water when the pressure, suction head, or temperature of the water changes. This is achieved by the fact that the coupled condensation and receiving nozzles are movable together and change their position relative to the fixed steam nozzle. The front part of the first nozzle is made in the form of a piston fitted to a bronze bushing, which serves as its cylinder. At the place where the condensation nozzle passes into the receiving nozzle, openings are made through which excess water flows out, not into the drain opening, but into a special chamber. If, after starting, too much water enters, it fills this chamber, exerts pressure on the reverse side of the piston, and brings both nozzles closer to the steam nozzle; the inflow of water decreases. If, on the other hand, there is too little water, then the nozzles are pushed back by the increased pressure on the front side of the piston and open a larger area for the flowing water. The same action occurs when the suction head is increased or decreased, and when the temperature of the incoming water is increased or decreased. Suppose, for example, that the water temperature rises. The former quantity of it is insufficient for condensing the steam, and therefore the pressure on the front part of the piston increases, which will move the nozzles backward, and the inflow of water will increase. If, however, the water temperature falls, then, conversely, the more intensive condensation of steam will reduce the pressure on the front side of the piston, and the nozzles will approach the steam nozzle. To reduce the capacity of the injector, the position of the spindle relative to the steam nozzle is changed, thereby increasing or decreasing the amount of steam flowing through the main nozzle; the condensation and receiving nozzles again automatically take up a fully definite position corresponding to the quantity of water required for condensation. So long as the moving parts are in good order and are not clogged by deposits of scale, dirt, etc., the self-regulation of the apparatus is quite reliable. To make the injector insensitive to shocks and jolts, an air chamber E is provided, connected with the suction pipe; by the elasticity of the air in this chamber the shocks and jolts of the suction pipe are absorbed.

There are then injectors with multiple admission of water into the condensation nozzle; in this case the latter consists of a series of separate short nozzles placed one after another. This method of introducing water will be encountered by us in the types described below, and we shall now turn to restarting injectors, i.e. those which are themselves capable of beginning operation again if, for any reason, it has been interrupted.

One of the chief causes of failure of ordinary injectors is the penetration of air and the cessation of water suction; in order to restore the action of the apparatus, it is necessary to start it again. With restarting injectors there is no need for this; while it is working one may, for example, take the suction pipe out of the water and then lower it again into the reservoir; the injector again easily raises it and continues to feed the boiler with water.

In Fig. 58 is shown the Schaeffer and Budenberg “Perfect” restarting injector. The regulation of the steam is performed by a spindle entering the steam nozzle. The condensing nozzle has the form already familiar to us, as in injectors working with exhaust steam. Its parts, fitted tightly one to another, are bored as a single whole, so that when closed an exact cone is obtained. Rising under the pressure of the steam, the movable part of the nozzle gives the steam a wide passage to the outside, not allowing it to be detained in front of the condensing nozzle, to increase the counter-pressure before it, and to impede the inflow of water. It then escapes through the test opening, the cross-section of which is considerably larger than that of the steam nozzle; when the injector is in operation, the condensing nozzle presents a closed cone. If, for some reason, the inflow of water and its supply for feeding should cease, the issuing jet of steam throws back the movable part of this nozzle; the steam, finding a free outlet to the atmosphere, readily produces suction again, and the action of the injector is automatically restored. The condensing and receiving nozzles, with two different positions of the movable part, are shown separately in Fig. 59. As is evident from the drawing, the upper part of the condensing nozzle is independent of the middle part entering it. Thus, with the half closed, the continuity of the jet is ensured during its passage through the nozzle; for good action of the injector the nozzle must be made with particular care, so that there is no leakage of air. Restarting injectors are especially suitable for locomotives; besides their insensitivity to shaking and shocks, they lose almost no water through the overflow opening. The starting of the Perfect injector is carried out in the following manner. The extreme positions of the handle are indicated by dotted lines. Steam from the boiler is led through an opening in the head, where there is a guide for the spindle connected with the shut-off valve. On the axis of the handle there is eccentrically mounted a finger \(F\), which enters the corresponding slot of an appendage connected with the spindle. Owing to this, when the handle is turned the spindle receives a progressive axial motion, opening the discharge of steam. On the outside of the handle there is an indicator moving over an arc attached to the body, on which the steam pressures are indicated. When turning the handle, the indicator must be set against the division corresponding to the pressure, corresponding to

to the steam pressure in the boiler, and the injector begins to deliver water. These injectors are made in 14 sizes, with a delivery from 240 to 22500 liters per hour, assuming the pressure to be \(5 \frac{1}{2}\) atm., the water temperature \(15^\circ\), and the suction height 2 meters. They operate within pressure limits from 3 to 11 atmospheres; at lower pressures it is necessary to regulate the inflow of water. The opening of the delivery pipe \(L\) is closed by a check valve upon which, in addition to atmospheric pressure, a weak spiral spring also acts. In injectors intended for locomotives, several overflow openings are made, for greater freedom in choosing the place of installation and the position of the overflow opening. In the following tables some data are given concerning the working conditions of these injectors.

Steam pressure in atmospheres.	\(2 \frac{1}{4}—2 \frac{1}{2}\)	3	\(3 \frac{1}{2}—4\)	5	6	7	8	9	10	11
Greatest possible suction height ..........	2	3	4	5	6	6	6	6	6	—

With inflowing water, or with a suction height of 1 meter, the temperature of the feed water may be:

Pressure in atmosph.	\(3 \frac{1}{2}—4\)	\(4 \frac{1}{2}—6 \frac{1}{2}\)	7	8	9	10	11
Temperature..........	58—62	55—65	54	50	45—48	40—43	38—40

At 7 atm. pressure and 2—3 meters of suction, the water temperature may be 45—50°, and at 4—5 meters—35—40°.

The hotter the water, the smaller the quantity of it that can be delivered for feeding. At the greatest permissible temperature it amounts to \(\frac{4}{5}\) of the quantity of water delivered when its temperature is \(15^\circ\).

In Fig. 60 is shown the restarting injector of Holden and Brooke. Its distinction is that the condensation nozzle is divided; the gap between its parts leads into a special chamber, closed by a valve, while the overflow opening has a direct connection with atmospheric air. The valve seat is movable, so that the injector can be set in any position, provided only that the valve closes freely under the influence of its own weight. The second special feature of this injector is that the inflow of steam and of water is regulated simultaneously. The upper part of the steam nozzle is made cylindrical, and moves along

in the axial direction, without rotating in its guide. In this part there are slots for the admission of steam, which then enters the nozzle when the spindle in the nozzle is open. By means of this spindle the quantity of entering steam is regulated, and its access is completely shut off. The upper part of the nozzle and the spindle have an operating screw thread; so that the nozzle should not rotate, there is a pin inserted into the corresponding recess in the body; against longitudinal displacement the spindle itself is held by a ring. Owing to the large pitch of the screw thread, to open the nozzle fully only a small turn of the handle is required. As it descends, the steam nozzle opens a larger passage for the steam and, at the same time, approaching the condensing nozzle, reduces the cross-section for the inflowing water. Thus, at high steam pressures a reduction of the inlet area for steam is associated with an increase of the inlet area for water, and conversely at low steam pressures. The pointer located at the end of the handle makes it possible to set, according to the scale marked on the nut, the inflow of steam and water corresponding to the available pressure.

Starting and regulation are very simple; since the moving parts are situated in the steam space, scale, silt, and dirt from the water have no effect on the mobility of the steam nozzle. The injector is very easily taken apart for cleaning, which can be carried out under steam if special valves are provided on the steam and delivery pipes. Fig. 61 shows the same injector for horizontal installation directly on the firebox wall of a locomotive boiler.

Fig. 62 shows a later type of the same “Sirius” injector of the Holden & Brooke works. On the spindle there is a bracket, through the opening of which passes the stem P of a valve located in the water chamber. When the handle is turned and the spindle is raised, the bracket is simultaneously raised, and with it the valve admitting water. In starting, the spindle of the steam nozzle is raised somewhat; through the opening in its tip, and through a small steam nozzle arranged axially in it, a jet of steam flows out, drawing in water through the simultaneously slightly opened valve. By further turning the handle, the proper ratio is established between the quantity of inflowing water and of issuing steam. The water valve is made with two disks, the lower one passing freely through the seat. The lower the steam pressure, the larger the nozzle cross-section must be in order to pass the quantity of steam required for forcing water into the boiler; the inflow of water must also be reduced, owing to the small live force of the steam jet. This is achieved by the lower disk of the water valve. In order to obtain tight closure of the steam nozzle and of the water chamber independently of one another,

from each other; only the lifting of the valve is effected together with the lifting of the spindle; it is lowered and pressed to the seat under the action of a special spring.

Fig. 63 shows an injector of the Siemens and Halske works. It also belongs to the restarting type, owing to the large area of the overflow opening. Its peculiarity is that the forced seating of the feed valve is carried out simultaneously with the stoppage of the injector.

The remaining details, as well as the method of starting, are clear without explanation. The works gives the following standards for operation.

Injector No.	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Liters per minute at 5 atm. pressure and 2 meters suction height.	5	10	15	25	37.5	50	65	80	100	125	150	175	200	225	250	300	350	400	450	500

With a greater suction height, hotter water (above 25° C.), and lower pressure, the quantity of water delivered is \(^{2}/_{3}\) of that indicated.

Pressure in atm.	3	4	5	6	7	8	9	10	11	12
Highest temperature possible at 1 meter suction.	60	58	56	54	52	48	46	42	40	38
Greatest suction height at 25°.	4½	6	6	6	6	6	6	6	6	6

If the injector operates with an inflow, the water may have a temperature 5–6° higher.

Fig. 64 shows the Gresham and Graven injector, very widespread on English railways, of the vertical type, attached to the front wall of the firebox on a single flange. Through the lower opening in it, closed by valve F, and channel M, steam passes to the steam nozzle A. By screw L one can tightly close the opening for the feed water in case repairs under steam are necessary. The latter is easy to do if the nut above the cone of the receiving nozzle D is removed; each nozzle is unscrewed one after another from the corresponding seats in the body. By handle O the inflow of water is regulated; handle N serves to heat the water in case of an excess of steam. The peculiarity of the injector is in the arrangement that makes it restarting. In the lower part of the receiving nozzle a small cone is inserted

C, which can move in the axial direction; to center it, this motion is guided by four ribs on its surface.

In the drawing, cone C is shown in the position which it occupies during the suction period; steam flows out through the gap between the condensing nozzle and the movable cone C into space H, and also through the end of this cone along the slot between it and the receiving nozzle. When water enters the chamber, part of the steam condenses, a vacuum is formed in nozzle B, and the movable cone descends until its flange comes into contact with it. In this position it is held by atmospheric pressure, forming, together with nozzle B, a long common condensing nozzle. The injector works dry, since there is no loss of water through the overflow opening; moreover, as is evident from the drawing, pipes are entirely absent. Injectors of the same type are also made for horizontal installation.

Fig. 65 shows Friedmann’s restarting injector. The steam nozzle is made double; such an arrangement is intended to facilitate the suction of water into the injector.

When the lever is moved to the left, the valve adjacent to the steam nozzle opens it for the admission of steam. Part of it passes through the annular gap between the nozzles, producing a vacuum in the condensing nozzle; the other part flows through the longer second nozzle into the depth of the first. During operation, the first nozzle, after raising the water, transfers it to the second, where the jet receives from the impact the necessary kinetic energy.

To facilitate the exit of the steam and make back pressure from the suction side impossible, the condensing nozzle has, for this purpose, openings in two places. The injector has a box communicating through the overflow opening with the atmosphere; the outlet opening for steam in this box is closed by a valve. Friedmann’s new injectors, in addition, have the following further feature. Near the water chamber a cock d is installed, which generally serves to regulate the quantity of water; it is arranged so that through it communication can be established between the suction pipe C and channel e. A check valve g closes the passage from this channel to the internal chamber of the injector. If communication is established by cock d, then at high steam pressures it becomes possible for the injector to suck in an additional quantity of water, entering through the same slots into the condensing nozzle, through which the excess steam is discharged during starting. At this time the check valve g prevents the escape of steam and its penetration into the suction pipe.

Friedmann injectors are manufactured for deliveries from 1080 to 13800 liters per hour (at a working pressure of 10 atm.). At 5–7 atm. the water

can have a temperature up to 60°, while at higher temperatures heating occurs with losses through the overflow opening.

Friedmann’s modification of the injector is the widespread one on American Monitor locomotives, shown in Fig. 66. The arrangement of the condensing nozzle is the same; the special feature is the installation of a separate steam nozzle—an ejector. By turning handle A, steam is admitted through this auxiliary nozzle. Since the ejector is placed at the overflow opening, the jet of steam and the air entrained by it very easily find an outlet from the chamber, whereby a strong rarefaction is quickly attained in the condensing nozzle. As soon as water appears, handle B opens the main steam nozzle and the delivery of water to the boiler is established; with a proper inflow of water and steam, only steam flows out through the overflow pipe, which indicates that feeding has begun; the ejector is then closed. If the steam pressure is low, then after the main nozzle is opened water continues to pass through the overflow pipe; in that case, by means of handle C its inflow is regulated until once again only steam issues. The injector makes it possible to regulate the feed in accordance with the steam consumption, permitting, within considerable limits, a change in capacity at different pressures.

A more recent design of the same injector is shown in Fig. 67. There is no special ejector here; for drawing in the water there is a spindle-nozzle, set in motion by a lever or by a handwheel, if the spindle has a thread. By first moving the handle aside, the admission of steam into the inner nozzle is opened; this produces the rarefaction in the condensing nozzle. When water appears through the overflow opening, by further moving the handle the main nozzle is opened, and water begins to enter the boiler. The inflow of water is regulated by a valve on the suction pipe. The steam nozzle of the new injector has a larger cross-section, which was done chiefly to increase the capacity of the injector at low steam pressures; at high pressures, the quantity of steam is determined by the corresponding position of the spindle within it.

These injectors are manufactured in 9 sizes (Nos. 4–12), with a water delivery from 2000 to 15000 liters per hour at a working steam pressure of about 10 atm. and a water temperature of 15–20° C.

The Penberthy injector, manufactured by the firm Dreyer, Rosenkranz, Droop, is shown in Fig. 68; it is very common on American locomotives. The outlet for the excess quantity of steam during the period of suction of water from the condensing nozzle is arranged at the end of the latter, through the clearance between it and the receiving nozzle. Between these nozzles there is a freely moving disk valve T, which, under the action of its own weight, bears against the receiving nozzle; this posi-

…during starting; when the water enters the condensing nozzle and the jet passes along the receiving nozzle, part of the water drains into the chamber surrounding the nozzle, and by the pressure of this water the disk valve is raised upward and then serves as an extension of the condensing nozzle. In the event of an interruption of the jet in the suction pipe, the valve assumes its initial position; the steam passes through the clearance into the drain chamber, and from there, through the drain opening closed by valve P, is discharged to the atmosphere.

All these restarting injectors can also operate with water supplied to them under pressure; in this case it is necessary to install on the water-supply pipe a valve or cock by which the inflow would be regulated during operation and stopped when the injector is shut down. In many of the injectors described above, such valves for regulation have been indicated. If the injector is used to heat water, then the valve of the delivery pipe is closed tightly either by a screw or by a special eccentric pressure device, as in Friedmann’s injector.

The ability of injectors to self-prime is especially valuable for the boilers of locomotives and steamships, where their pipes are subject to shocks and vibrations, and the water level in the reservoir to fluctuations caused by them. If, owing to this, the jet in the suction pipe is broken or air enters it, the injector stops working, but immediately begins suction again by itself, and its action is restored. With simple suction injectors, in the event of such an interruption, the device would have to be started again. Their ease of operation favors their wide distribution also in factory boilers.

It has already been indicated above that the limiting back pressure for injectors operating with wet steam is about 5 atm. With considerable back pressure, the admission, indicated above, of an additional jet of live steam is sometimes insufficient, and the injector assumes a special form.

Fig. 69 shows the Davies and Metcalf injector for locomotives, belonging to the type of double or compound injectors. The injector consists of two parts. The first is an injector of the same factory for wet steam, with a split condensing nozzle. On the branch pipe connecting the injector with the wet-steam line there is a throttle valve, by which the injector is isolated from the steam line. On the injector side, near this valve, there is an opening for live steam, with which the injector operates while the locomotive is standing. The water inflow has a regulator in the form of a valve. From the steam line of the second injector, operating with live steam, there runs a connecting tube, which supplies the same live steam to the nozzle for wet steam. Between both injectors there is a check valve, which closes…

on the side of the injector, of high pressure. Each has a drain opening, closed by valves, as may be seen from the drawings of the sections in the plane passing through the axes of these drain openings. In the low-pressure injector this opening is closed by a suspended valve, pressed against the seat by its own weight and by the pressure of the atmospheric air; in the high-pressure injector it is closed by a special device ensuring the forced seating of the valve. On the spindle of the valve, placed in the drain opening, there is a piston, above which is a diaphragm clamped between the cover and the body.

At the top of the cover there is an opening through which, by means of a connecting tube, the space beneath it communicates with the delivery chamber of the injector below the non-return feed valve. So long as there is no delivery, the drain opening may be open; but when feed has become established, when the pressure in the delivery box increases, the diaphragm, pressing on the piston, presses the valve tightly against the seat. The injectors are very easily dismantled for inspection and for cleaning the nozzles. The device described above proved necessary for the following reasons. The first injector, of low pressure, delivers water to the second with an excess pressure above atmospheric; in the condensing nozzle of the second injector and in its delivery chamber there is, consequently, an excess of pressure, owing to which the valve of the drain opening would always be open and would lose water. On starting, this excess pressure is transmitted by the connecting tube to the diaphragm and by it to the piston. Since the area of the latter is smaller than the area of the valve, at equal pressure the valve has a moderate lift for the passage of water and steam. But when feed is established, the pressure in the delivery box becomes higher than the pressure in the condensing nozzle, and the valve is pressed tightly against the seat. This arrangement, eliminating the loss of water, at the same time gives the injector the ability automatically to resume operation in the event of a possible interruption of the jet.

Instead of a diaphragm, the same works installs, for this purpose, the device shown in Fig. 70. Here a lever rests on the spindle of the valve of the drain opening; the other end of the lever lies in a slot of a small metal rod; this rod moves in a cylinder, and its lower end plays the role of a piston. The pressure of the delivery box, acting upon it, is transmitted by the lever to the valve of the drain opening and thereby produces its forced seating. This completely eliminates the need to repair or replace the rubber diaphragm, which may deteriorate at the high temperature of the water. Starting the injector is carried out in the following manner. First of all

water is admitted and the inflow of steam into the high-pressure injector is opened, after which this injector begins to operate; only then is the inflow of live steam opened. To cleanse it of oil, an oil separator, Metcalf’s patent, is installed on the branch leading to the injector; it automatically discharges the condensation water and oil to the outside.

The oil separator is shown separately in Fig. 71, and Fig. 72 shows the general arrangement of the injector on a locomotive; they are usually installed only on one side of it, while the other injector is installed of the ordinary type.

In locomotives equipped with them there is almost always an excess of steam, owing to the heating of the water by live steam; the saving of fuel amounts to about 10% per train-mile.

The temperature of the feed water reaches 125–130° C., which, of course, apart from the saving of coal, results in a considerable preservation of the boiler itself, owing to the absence of cooling of its walls by water. These injectors draw water at a temperature up to 27° C.; at higher temperatures the water must flow by gravity. Another injector of the same type, by the firm Holden and Brooke, is shown in Fig. 73. To start the injector, the handle of the high-pressure injector is raised; steam enters a special chamber and through a bypass pipe goes to the low-pressure injector; the passage into the nozzle remains closed, owing to the spindle. When water appears at the overflow pipe, by a further movement of the handle the inflow of steam into the nozzle of the second injector is opened, and then delivery is established. After this, by the corresponding position of the throttle valve on the live-steam line, the proper inflow of it to the injector is established.

The effort to attain the greatest suction lift and the desire to deliver the hottest possible water led to the construction of double injectors. The first such injector was made by Körting. The obstacles that exist in single injectors are as follows. The water in the interval between the steam and condensation nozzles, if the injector operates with an open overflow, cannot be above 100°, and, conversely, must be below this temperature so that there is no reverse evaporation. One or the other temperature depends on the degree of perfection of steam condensation in the nozzle; when a non-return valve is installed in the overflow orifice, as is the case in most restarting injectors, the temperature may be somewhat higher than in the former case, and the pressure in the interval may correspond to the steam pressure at this temperature; but in any case this pressure cannot be higher than atmospheric pressure, while approaching it considerably. If, instead of a non-return valve in the overflow orifice, a weighted valve were installed (the load from the spring is very small in restarting injectors, and what is meant here is ...).

not on it), then by this means it would be possible to raise both the pressure in the interval and the temperature of the water; but with such a valve it would be necessary, during starting, to lift it, otherwise the injector could not begin to work.

These obstacles have been eliminated by installing two injectors, of which the first, having raised the water under a small pressure of up to 2–2.5 atmospheres, delivers it to the second, which sends it onward, at the velocity required for overcoming the resistances, into its receiving nozzle.

Körting’s double injector is shown in Fig. 74. The left-hand part plays the role of the low-pressure injector, the right-hand part that of the high-pressure injector. The nozzle of the first has very small dimensions, so that, with the small quantity of steam issuing, one can dispense with slots or other devices on the condensing nozzle that are needed for removing it. By turning handle A, fixed immovably on the shaft, the eccentrically mounted washer b and lever c are set in motion. Rod d thereby receives an upward motion, and with it also rod e. On the crosspiece attached to the shaft to it are suspended valves f and g; since the area of valve g is greater than that of valve f, the latter opens first; the jet of steam produces a rarefaction, and when the water has risen to the injector, the mixture of steam and water appears through the overflow opening D. With cock D, upon further motion of handle A, channel h is closed; the water now goes through channel E, through the second injector and channel i. Turning the handle farther, whereby cock D at the same time closes channel i, brings the guide spindle of valve f to the dead position, while valve g opens the inlet for steam into the second injector. The jet of this steam imparts to the water energy sufficient for lifting valve H; the water enters for feeding. The processes described follow one another so rapidly that starting the injector is accomplished by a continuous slow rotation of handle A to the corresponding position.

Körting injectors, together with feed-water heaters using exhaust steam, are employed on German railways. They may be vertical or horizontal. The data on their operation are as follows. At 7 atm. working pressure and with inflow of cold water, they deliver: injectors with a cast-iron body (16 sizes), from 1,560 to 29,600 liters; bronze injectors (14 sizes), from 570 to 19,200 liters. When drawing in water, at lower steam pressure, and with heated water, their capacity decreases to \(^{2}/_{3}\).

The greatest suction height for cold water reaches 6.5 meters; the greatest temperature of the water flowing to the injector may be 70°.

The following table gives information on the commercial injectors of this factory. They operate:

at a working steam pressure of	2	3	4–8	9–10	11–12	atm.
they take cold water in suction at	2.5	5	6	5	4	m.
they force hot incoming water	54°	60°	65°	64°	62°	C.
they draw it from 2 meters at	50°	58°	60°	57°	54°	C.

In Fig. 75 is shown a modified form of the same injector, manufactured by Schutte in America. The starting operation is in no way different from that already described above; the valve of the overflow opening is closed simultaneously with the motion of the handle, owing to its connection with the rod that grips the handle on the spindle of this valve. The quantity of water supplied is regulated by a cock on the suction pipe; in a later construction, for regulating the suction water, a spindle-nozzle is inserted in the nozzle of the first injector, its position being changed by a special handle.

In Fig. 76 is presented the “Metropolitan” injector, very widespread on locomotives in America. The distinctive feature of its construction is the automatic action of the overflow-opening valve and the regulation of steam for both injectors by a single valve D. The regulator shown in the drawing for the first injector is used exclusively for locomotive injectors; it can also be used for regulating the quantity of water entering the boiler in factory boilers operating with a variable consumption of steam.

This regulation takes place as follows. Between the condensing and receiving nozzles of the first injector there is a slot g: when the quantity of steam in the steam nozzle is reduced, not all the incoming water can pass into the receiving nozzle, and therefore part of it will overflow through opening g into the supply chamber. When the steam jet is intensified, the deficiency of water entering through the condensing nozzle is made up by its inflow through this same slot. To start the injector, by deflecting handle A the annular valve mounted on rod D is opened; a small quantity of steam passes through the slots of valve b into chamber c, and from it into chamber d and the steam nozzle of the first injector. When the raised water, having filled space H and lifted valve e, appears through cock f of the overflow pipe, handle A is moved to its extreme position. This opens the steam inlet to the nozzle of the second injector and simultaneously closes the valve of the overflow opening; the increased pressure of the delivery chamber also closes valve e. These injectors are manufactured by Hayden and Derby, in New York. According to the factory’s data, they begin to operate at a steam pressure of 1.75 atm. and without any special regulation

they continue feeding up to a pressure of 18 atm. With a steam pressure of 6.5 atm. the injectors take water at a temperature of 63–65° C.; when the steam pressure is increased, the temperature of the water must be that indicated in the table:

Steam pressure	8.25 atm.	10 atm.	11.5 atm.	13 atm.
Temperature	61°	57°	54°	51° C.

In general, in the design of double injectors, for the sake of simplicity in operating them, the aim is that with one handle it should be possible to set the correct opening of both steam valves and the closing of the valve of the overflow opening. This problem is solved very simply in the injector of the Hannoversche Centralheizungs- und Apparate-Bau-Anstalt, shown in Fig. 77. The axis of the overflow cock A passes through the center of the apparatus between the nozzles of the injectors; at its end a screw thread is made, the nut of which has two shoulders b, b, entering the corresponding recesses on valves d and e.

While valve d is open, e still remains closed, since shoulder b has in it a small lost motion. Feeding by the first injector, the water passes through the condensing nozzle B and by channel f flows outward through the cock; by further turning the handle the cock A is closed, the water is now led to the second injector; simultaneously with this the second steam valve e opens, and feeding of the boiler begins.

These injectors are made in 14 sizes with water delivery from 470 to 15900 liters per hour at 7 atm. pressure, 2 meters suction lift, and 25° water temperature.

An increase in suction lift and in the temperature of the water, and a decrease in steam pressure, reduce the stated capacity.

To the same type of double injectors also belongs the “Belfield” injector, indicated in Fig. 78. The sharp difference from those described above is that both nozzles are arranged on one axis. When the handle is turned, the inlet of steam into the spindle nozzle is opened first; water is sucked in and, passing through the nozzles, issues from the overflow opening. By a further turn of the handle the inflow of steam into the main nozzle is opened; the spindle remains inside it, so that the water is acted upon both by the central jet of steam issuing from it and by the jet of steam issuing through the annular gap. Simultaneously with this, the steam passes through the grooves visible in the drawing into the channel and to the second row of nozzles. By means of a rod and crank, at the same time a tight seating on the saddle of the overflow-opening valve is also produced; by the nut on the stem the moment of this closing can be regulated depending on the opening of the ports for the inflow of steam. By this means it is possible to attain quite satisfactorily the smallest capacity of the apparatus, and to vary it

in general within sufficiently wide limits. These injectors are manufactured in 8 sizes, with a capacity from 1130 to 12790 liters per hour, at a steam pressure of 8 atm. and a suction height of 1.5 mtr.

Fig. 79 shows the American “Buffalo” injector. Turning the handle first opens the admission of steam to the first injector, and, with further movement of it, to the second as well. The overflow opening closes automatically when the pressure in the delivery chamber of the second injector increases; when it is stopped, however, it opens.

Fig. 80 shows the double “Albion” injector, in which the first injector is completely separate from the second. The purpose of this is to deliver hot water when its level in the reservoir is low, when it is difficult to produce suction.

The first injector is immersed in the water, and its steam pipe, in order to eliminate condensation, has an outer casing made of another pipe; in the gap between the pipes there remains an insulating layer of air. There is one steam valve for admitting steam to both injectors; the valve is hollow, with openings around its circumference, through which the steam enters inside it. When the handle is turned, first of all the inner spindle is moved away from valve a at the end; the steam passes through opening b to the lower injector; when water appears at the overflow opening of the upper injector, further movement of the handle opens the large valve, whereby the inner valve a engages the corresponding projection inside it. The steam now enters the nozzle of the second injector and produces the forcing of water into the boiler. Two fingers c,c, attached to the steam valve, engage, when moving to the right, the steam nozzle of the second injector, move it away, and thereby increase the passage for water to the high-pressure injector. The initial setting therefore corresponds to the smallest capacity of the apparatus. For simultaneous servicing of both injectors, the closing of the overflow opening is arranged as follows. The receiving nozzle of the second injector is movable, and at the end nearest the steam jet it has an expansion; the condensing nozzle consists of two parts: the first is fixed and has, on the side of the receiving nozzle, the same expansion as the latter. The movable part of the condensing nozzle can move within these expanded ends, being guided by ribs which center all three parts.

When water is delivered upward by the first injector, it first pushes both movable nozzles away and then separates them. For the exit of the water, a sufficiently wide passage area opens toward the overflow opening. Now, by turning the handle, steam is admitted into the upper injector; the jet of water is established in it and, by pressure on the opposite sides of the nozzles, forces them to move toward the

steam. The jet of water is completely isolated from the atmosphere, and therefore its temperature may be considerably higher than 100°.

In addition to those described here, there is a whole series of other injectors, differing from one another in minor details; their consideration would add nothing new to an acquaintance with the types of injectors.

Materials for injectors, machining of their parts, repair, wear; rules for installation and maintenance.

The materials used for injectors are cast iron, gun bronze, ordinary bronze, and brass. The first is used exclusively for making the body of the injector, while the nozzles are always made of bronze or of alloys close to it in quality. For the more expensive and responsible parts an alloy of greater hardness is used; for wearing parts that are easily replaced, a softer material is employed. For example, it is advantageous to make cocks and valves of softer bronze, in order to spare the valve seat or the body of the cock, etc., from rapid wear.

A mixture of copper and tin, forming alloys in various proportions by weight, yields bronze—a material very widespread in mechanical engineering. For ordinary machine parts, an alloy of the following composition is quite satisfactory:

80% copper, up to 18% tin, about 2% zinc, and 0.5% lead.

For injector parts the following alloy is recommended:

88% copper, 10% tin, about 2% zinc, and 0.5% lead.

Depending on the purpose of the alloy, manganese, antimony, or phosphorus are added; iron and silicon are harmful to the quality of the alloy. The density and hardness of the alloy depend on the percentage content of tin. The qualities of the alloy differ from the qualities of its constituent parts; its density is greater than the mean density of the constituent metals; the alloy is less subject to oxidation and is harder. Its melting temperature is lower than that of copper and higher than that of tin. It is very important not to lose sight of this circumstance when casting, since the homogeneity of the material in the article depends on it. The casting of parts should be performed as rapidly as possible, and the casting should be cooled as quickly as possible, in order to prevent the phenomenon of liquation. Likewise, when making the alloy, the copper should be melted quickly, and the tin, when mixed with it, should be kept immersed in the mass of copper in order to avoid the formation of its oxide. The presence of oxide is harmful and disadvantageous because it gives the material excessive hardness; when machining the article it is troublesome to keep the tool and cutters sharp, and during work itself

there will be noticed uneven wear of the part, owing to the presence on the surface of places of differing hardness. Oxide so greatly hampers the machining of parts that at times individual parts, as inconvenient and unsuitable for machining, have to be consigned to the foundry scrap.

The addition of 2% zinc, which plays the role of a deoxidizer, has a beneficial effect on the alloy, restoring its purity and making it somewhat harder; phosphorus acts in the same way as zinc.

The best way to machine nozzles is by drilling; if the nozzle is bored or sawn out, then traces and grooves from tearing of the metal remain on its walls. These roughnesses present great resistance to the moving jets of steam and water. Therefore the nozzles must be well ground. This is especially necessary for the condensation nozzle and for the receiving nozzle in its front part up to the receiving mouth and in the mouth itself. In the first case there is a considerable impact effect; in the second, in the throat, the liquid passes with the greatest velocity. In general, the machining of parts requires very skillful and patient work, which, in connection with the necessity of an experimental search for the best nozzle profiles, concentrates the manufacture of injectors in the hands of special factories equipped with special machines and the most suitable tools for this purpose. The cutting or drilling speed is taken as 70–80 revolutions per minute *).

Wear of injectors is expressed in the abrasion and eating away of the inner surfaces of the nozzles. It depends chiefly on sand, dirt, and the amount of salts dissolved in the water. The condensation nozzle is the first to be subject to wear; if the jets of steam and water are well centered, there will be only uniform abrasion of the surface; but if the water is broken up by the steam jet and thrown toward the walls, then characteristic hollows and pits may appear at the places of impact. Then, from the same causes, the wear of the receiving nozzle also depends. It proceeds especially rapidly in the throat of the nozzle, increasing its diameter; while in the widened part, under the action of splashes issuing from the condensation nozzle, grooves and depressions may likewise form. The uniformity of wear is directly dependent on the degree of perfection of the casting and on the homogeneity of the material throughout the whole part: soft places will be worn away sooner than hard ones, which may completely spoil the correctness of the profile outline and impair the action of the apparatus.

The repair of these nozzles consists in removing these damaged places by boring or drilling out and by new grinding of the sur—

) More detailed information on materials may be found in Revue chemin de fer*, 1897, January 20, pp. 391–411.

surfaces. At the same time, of course, the dimensions of the nozzles change, and after repair the injector’s operation will proceed under conditions different from those of a new one. Knowledge of these new conditions is very necessary for the reliability and safety of the boiler, and therefore the apparatus must first be tested; a separate chapter is devoted to the methods of this testing. Instead of repair, worn parts may be replaced with spare ones, the cost of which is approximately about \(1/5\) of the cost of the injector itself.

Apart from repair, the injector requires careful supervision of the cleanliness of its parts, especially those among them which have certain moving parts. Inspection, of course, is possible only if this was not omitted already in the design; therefore, in choosing an injector, the most serious attention should be paid to accessibility and ease of cleaning. Along with eliminating defects noticed in the apparatus, one should also determine their cause and take measures to create more favorable conditions for the operation of the apparatus. If the cause lies in an abundant content of mud and sand in the water, then one should not even stop short of the expense of installing settling tanks and purification, for the condition of an injector working with such water indicates, in part, what may also be expected in the boiler itself. France, for example, uses water purification on its railway lines; this has had a noticeable effect on increasing the service life both of injectors and of the boilers themselves. In exactly the same way, purification has also been introduced on the Baden railways at the stations Lauda, Heidelberg, and Osterburken*). With slight fouling, cleaning is easily carried out by immersing the removed nozzles in hydrochloric acid.

The first attempts to use the injector for feeding factory boilers were unsuccessful and confirmed its reputation as an unreliable and capricious apparatus; but with the passage of time, when the original type had been modified and considerably improved, it also found very wide application for these boilers. If even now troubles occur with it, they can be eliminated very quickly, since their causes can easily be discovered.

*) More detailed information on the subjects considered here may be found in the following journals.

Revue Industrielle 1900, 31, 490. Avaries dans les tuyaux des injecteurs.

Organ 1902, 233—235. Wasserreinigungsanlage des badischen Eisenbahn.

Zheleznodor. delo 1903, p. 311. Distilled water in the service of locomotives.

Practical Engineer 1903, II, 307. A new injector for bad feed water.

” ” 1905, p. 442. Cleaning an injector by chemical means.

Failure of the injector in operation may depend on the eccentric position of the nozzle—a defect of the factory that has released such an instrument onto the market; however, with the testing of every injector now common at factories engaged in manufacturing injectors, this defect is almost eliminated;

on the narrowing of the passage cross-sections by rings pressed inward when cold; to eliminate this, it is recommended to install metal gaskets (for example, conical bronze rings fitted by grinding, as in Fig. 79, copper rings in grooves centering the parts being joined, etc.);

on leakage of the injector body or of the suction pipe; this is remedied by installing the corresponding gaskets or packings;

on narrowing of the cross-sections of the nozzle by deposition of scale on its walls; this is remedied by cleaning;

on the presence of large resistances due to abrupt changes in the cross-section of channels and pipes carrying water, and due to excessively sharp bends; this is remedied by a corresponding alteration of the water conduit.

The causes of failure may sometimes be an excessively great height of water in the delivery pipe, the inertia of which the newly delivered water is unable to overcome because of its low velocity; this is remedied by raising the injector itself closer to the water level in the boiler; or excessively hot water, which the injector cannot suck in; this is remedied either by rearranging it so that the water flows to the injector, or by diluting it with cold water.

In locomotive injectors, the cause of failure may be freezing of water in low-lying water pipes; this is remedied by installing blow-off and drain cocks in the appropriate places.

Failure of the injector may also depend on the following causes. Leakage of the steam valve, and, as a consequence, heating of the whole instrument and of the suction pipe. During operation this is easily remedied by cooling with water; but when the boiler is stopped, it is necessary to lap the valve and the seat until they fit tightly and hermetically.

Leakage is easy to detect both from the thermal condition of the instrument and by observing the overflow pipe; if it exists, then with the steam valve closed the outflow of a weak jet of steam will be noticeable. In this case the failure depends on an insufficiently high vacuum caused by the high temperature of the instrument.

Leakage of the suction pipe; this defect is easy to detect if the valve of the overflow opening is closed and the steam valve is opened. Steam will pass through the suction pipe into the reservoir; if there are leaks, then also through them at the same time.

Leakage of the feed valves on the boiler. In this case, as in the first, heating of the apparatus occurs.

Sometimes the injector takes in water, but works irregularly, in spurts, or with continuous discharge without delivery through the discharge pipe. The cause of this may be the less considerable permeability of the suction pipe; the presence of air in the water manifests itself by rupture of the jet in the nozzles, but its quantity is not so considerable as to make suction altogether impossible;

clogging of the suction pipe, or insufficient area of the openings in the strainer placed on it to prevent such clogging. The strainer must be installed with such calculation that the total area of the openings is 2–2½ times greater than the area of the pipe itself; clogging is removed by blowing through the suction pipe, for which steam must be admitted into the apparatus with the outlet valve closed;

improper action of the feed valve on the boiler (tilting, etc.); this is remedied by cleaning and grinding-in.

Corresponding to these causes of failure in operation, and in order to avoid such failure, the following rules for mounting injectors may be recommended.

Pipelines should be run without sharp bends, with a small number of smooth turns, and without abrupt changes in cross-section. Usually the pipes are installed of the same diameter as the outlets from the injector on the corresponding flanges. Their size is sometimes indicated in manufacturers’ price lists. To determine them by calculation, one should assume in the suction and discharge pipes of single injectors a velocity of flow from 0.8 to 1.7 metr., and for double injectors from 0.8 to 2.3 metr. The higher the No. of the injector, the greater the velocity that may be taken as the basis of the calculation. The steam pipe of the injector is made of the same diameter as for water; with live steam, the size of the pipe is determined by its volume and velocity. After assembling all the pipes, they must be carefully cleaned; for this purpose the pipes are first tapped through with a hammer and then blown strongly with steam. Old pipes covered with rust should not be used, since its presence will immediately affect the condition of the nozzle surfaces; this is one of the reasons why copper pipes are preferably used on locomotives. The steam pipe for the injector should be taken from the boiler independently of the other steam lines. Its beginning on the boiler should be arranged so that the driest steam is directed to the injector; it is advantageous to insulate it to reduce condensation. A special shut-off valve should be placed between the boiler and the injector.

The joints of the suction pipe must be made with the greatest care to ensure their tightness; if the injector is placed away from the reservoir of water, the suction pipe should be laid with a continuous rise toward it.

To prevent clogging, it is useful to place a screen at its end. For better observation of the operation, long pipes should not be placed at the overflow opening; if it is necessary to drain away the water, then for this purpose, under the short nipples of the overflow pipe, it is advantageous to place a funnel through which the outflowing water can be led away.

Testing of the Injector

In 1904, at the congress of engineers and delegates of the International Union of Associations for the Supervision of Steam Boilers in Barmen-Elberfeld, Mr. Kapio presented a report on the steam consumption and the efficiency coefficient of an injector.*)

This report was intended to answer the question posed by the Union: whether reliable experimental data exist for estimating the steam consumption in an injector, and what the principal results of these experiments are in the above-mentioned respect. It turned out that the question of steam consumption, and of the mechanical and thermal efficiency coefficient, had not been developed practically at all; only on the initiative of two societies—the Alsatian and the Swiss—had experiments been carried out, whose chief purpose was to compare the injector with the feed pump. The latter society published the results of tests indicating that the thermal efficiency coefficient of the injector is, in round numbers, 81%, and that of the pump 48%.

Zeuner, in his book Grundzüge der mechanischen Wärmetheorie (second ed., 1866), mentions experiments carried out by him, but these have not been published to this day and at the present time have only historical significance, since they were performed with steam whose pressure was 3.3 atm.

To clarify the matter, Mr. Kapio carried out independent experiments, the results of which enabled him to determine the mechanical efficiency coefficient at 2% (two), and the thermal coefficient at 96%.

Apart from the experimental investigations mentioned above in the description of nozzles, there is no information in the European literature on experimental testing of injectors.

American journals are richer in information on this subject; unfortunately, I was unable to obtain Cassier’s Magazine,**) in which a summary of experiments with injectors in America is given.

) Protocoll der 33 Delegierten- und Ingenieur-Versammlung des Internationalen Verbandes der Dampfkessel-Ueberwachungs-Vereine, p. 182. See also Zeitschr. des Bayerischen Revisions-Vereines*, 1904, p. 147.

**) Febr. 1892.

In the American Machinist for 1896 (pp. 105, 288) there are data on the testing of an injector and on measuring its power in the case of its drawing in water and of its inflow under pressure.

The steam pressure was 4.9 atm.; the suction height 0.6 mtr.; the pressure under which the water flowed to the injector, 1.8 atm. Wakeman found that in the second case the injector delivered 22% more water than in the first, including the steam consumed.

Several notes based on test data are found in the journal of the Franklin Institute; one of the latest articles, presenting a summary of the results of testing a Sellers injector, is cited below *).

Thus, the question of steam consumption remains entirely unclear. It is true that the injector does not belong among devices that “devour heat,” in view of the high value of its thermal efficiency, but there can be no doubt that the steam consumption in it is large in comparison with the work produced.

With respect to any heat engine, at the present time we have sufficiently definite and reliable data that may be used as the basis for comparing the perfection of one or another of them, both when choosing one for an installation and when testing in order to improve the economy of the working process. And only with respect to injectors have we no information at all about the steam consumption in one system or another, being guided in the choice only by tables of capacity offered in factory price lists **).

It is true that every injector, before being put on the market, is subjected to testing at the factory; in this respect specialized factories do not stint on the expense of equipping test stations. But the tables printed in price lists give average values, and for each injector there may be deviations in one direction or another. Moreover, the device itself is so delicate and sensitive that checking its power and its working capacity under various conditions after a certain interval of time has elapsed following installation is not superfluous; there may also be grounds for this depending on the local conditions of a given case. For example, the tables give the suction height and the temperature of the water; when installing on site it may prove necessary, while preserving the suction height according to the tables, to assign the injector—

*) Journal of the Franklin Institute, October, 1906.

**) I personally have never, even in works devoting some space to the question of injectors, encountered a definite indication that such-and-such an injector consumes \(a\) kg of steam while delivering \(b\) kg of water for each kg. Only general figures are given: at low steam pressure, 18–20 kg of water per 1 kg of steam are required, and at high pressure from 9 to 12 kg.

the [instrument] by some distance to the side. Without doubt, the length of the suction pipe and changes in the direction of motion that may occur will not fail to influence the quantity of water delivered.

Likewise, the dryness of the steam is not everywhere the same: in one boiler it is greater, in another less; and the moisture content of the steam, being reflected in the velocity of its jet in the nozzle, will also influence the delivery of water by the instrument.

The necessity of periodic testing of injectors appears most urgent when they are used on a locomotive. The engine driver must know the suitability of the apparatus for work under given conditions and its ability to perform that work, especially if the injector has been subjected to cleaning and repair.

The purpose of the present chapter will be to acquaint the reader with methods for testing injectors and to outline those problems which should form the subject of such tests.

The subjects for testing may be the following questions.

1) To study the influence of steam pressure on the mechanical coefficient of useful effect, on the thermal coefficient, and on the power of the injector.

The test must be carried out at various steam pressures; for exact investigations it will be necessary to change the working pressure in the boiler itself, and not by throttling the steam or lowering its pressure in the expansion valve. In that case, as is known, the steam becomes superheated; this will be reflected in its motion in the nozzle and in the power of the injector.

The test must be conducted in series. Each series must include the results of at least five experiments at one and the same steam pressure, delivery pressure (equal to it), suction height, and temperature of the suction water. In each subsequent series only the pressure of the working steam and the counter-pressure (equal to it) should change; the suction height and the temperature of the suction water should remain unchanged for all series.

The test must give the maximum and minimum of the water delivered and its temperature in either case. The results obtained should then be plotted on a diagram and the whole course of the change represented graphically. In Fig. 81 is shown a diagram compiled from the results of a test performed with a Sellers injector at the Franklin Institute.

Along the axis of abscissas are laid off the pressures of the working steam, varying from 0.14 to 22.75 atm.; along the axis of ordinates, the liters of water delivered per hour. The circles placed on the curves indicate the observed data. The diagram already represents a summary of the test by individual

series; the numbers placed on the curves indicate the temperature of the water being drawn in. As may be seen, it was 10, 18, 27, 35, 43, 51, and 60° C.

From the diagram it is very easy to find the capacity that the injector can deliver under given conditions. For example, at 10.5 atm. working pressure and a feed-water temperature of 27° C., the maximum delivery will be about 14,000 liters per hour, the minimum 6,400 liters. The delivery of feed water, consequently, can be varied under these conditions by 7,600 liters; it can be regulated within 45.7% of the maximum capacity. This means that if, in selecting the injector, we took it of such a size that in an hour it would deliver twice the quantity of steam consumed by the boiler, then the injector, working at minimum delivery, would feed the boiler almost continuously; in this case, of course, a uniform and regular consumption of steam from the boiler is assumed.

Secondly, from the diagram it is easy to find the critical, so to speak, temperature of the suction water for a given steam pressure. By this name we shall understand that temperature at which there is no full delivery of water into the boiler; part of it is lost through the overflow opening, and this loss cannot be eliminated.

The essence of the phenomenon consists in the fact that a considerable part of the steam flowing out through the nozzle cannot be condensed by the water; this steam increases the volume of the water, which, at the given velocity, cannot all pass through the mouth of the receiving nozzle. If the water delivery were increased in some way, its velocity would be insufficient to give the jet the force necessary to overcome the pressure on the valve.

In this case there would likewise inevitably be a loss through the overflow opening. The presence of steam, in a considerable quantity uncondensed, affects the rarefaction of the condensing nozzle, whereby the possibility of increasing the inflow of water is removed.

From the diagram it is seen that at a steam pressure of 12.25 atm. the temperature of the suction water of 43° C. will be critical.

At this moment, as is not difficult to understand, the maximum delivery is equal to the minimum; the intersection of both curves indicates the limiting pressure. For example, at a temperature of 51° C., the limiting pressure will be approximately 6 atmospheres.

The critical temperatures can be plotted separately in a special diagram (Fig. 82). Here the corresponding water temperatures are laid off along the ordinates, and the steam pressures along the abscissas.

The solid line connects the observed (small circles) temperatures at different pressures; under these conditions excess water runs off through the overflow opening; the dash-dotted line indicates the curve of temperatures at which the injector is capable of self-suction (ex-

the tested injector belonged to the type of restarting injectors). If the overflow opening was closed hermetically,* then the temperature of the water being sucked in could be somewhat raised; the curve of these temperatures is shown by the dotted line. From the diagrams we note that for a pressure of 10.5 atm. the critical temperature is 47°; self-suction is still possible at a temperature of 55° C.; with the overflow closed the critical temperature is 65.5° C.

In the diagram (Fig. 83) curves are constructed which, for various pressures and temperatures, give the ratio of the minimum delivery to the maximum; these ratios are multiplied by 100, so that the upper horizontal line corresponds to the ratio 1, i.e. the maximum is equal to the minimum. This, as we have just seen, at a given steam pressure occurs at the critical temperature of the water being sucked in. Consequently, the beginning of the curves corresponding to a known temperature on this line gives the limiting steam pressure.

From the diagram it is seen that, at a water temperature of 35° C., the limiting steam pressure is equal to 16 atm.; at a steam pressure of 14 atm., it is possible to regulate the water delivery down to 72% of the greatest capacity; at a pressure of 6 atm. the greatest regulation at this temperature is attained, to 46% of the greatest capacity. The lower the water temperature, the wider the limits for varying the capacity.

In the diagram (Fig. 84), along the axes of ordinates are laid off, in kg, the quantities of water delivered by one kg of steam. The test was made with a water temperature of 18° C. As was indicated earlier, with an increase in steam pressure the quantity of delivered water decreases, owing to the strongly increasing expenditure of steam through the nozzle.

The tested injector had the main nozzle in the form of a converging cone. It would be very interesting to have such a diagram for an injector with a diverging cone, in order to see the law of variation of the quantity of water delivered by 1 kg of steam as a function of pressure, and to compare the test results with one another.

From the diagram it is seen that at 5.25 atm. 1 kg of steam delivers 17 kg of water, at 10.5 atm. 13 kg of water, and at 21 atm. 7 kg.

From the foregoing it is seen how clearly the picture of the injector’s operation under various conditions is represented when using the method of graphical representation of the results found by experiment.

2) One may set as the problem the study of the influence of the temperature of the water being sucked in on the coefficient of useful action and on the capacity of the injector.

These tests should also be conducted in series, with 5 experiments in each. Constant in each series should be all conditions, except

* Forced seating of the valve of the overflow opening, as in Friedmann’s injector.

of the temperature of the water being sucked in; in each experiment the steam pressure, the delivery pressure (equal to it), the suction lift, and the temperature must be constant. The experiment must determine the maximum and minimum quantity of water delivered. If the results are represented graphically, one should obtain curves closing on the ordinate corresponding to the critical temperature for the given pressure.

The diagram (Fig. 85) shows such curves for the same injector. From these curves it is seen that, as the temperature increases, the maximum capacity of the injector decreases, while the minimum increases; i.e., both tend toward equality, which is reached at the critical temperature.

The decrease of the maximum is explained by the fact that, as the temperature of the water increases, the percentage not condensed in the steam jet will increase; but up to a certain limit it will be able to pass through the mouth of the receiving nozzle, so long as this increase in volume is compensated by an increase in the final velocity of the jet after impact; the latter will depend on the decrease of the mass of inflowing water, as is seen from the equation for the quantity of motion:

\[ w + mu = (1 + m)\,u_1 . \]

When \(m\) decreases, and with \(w\) and \(u\) unchanged on the left-hand side, in order to preserve equality \(u_1\) on the right-hand side must increase.

The decrease in inflow will depend on the rise of pressure in the condensing nozzle, owing to the higher temperature of the inflowing water.

The increase of the minimum, however, will depend on the necessity of supplying, for successful condensation of the steam, a larger quantity of heated water.

3) One may set the task of investigating the influence of delivery pressure on the capacity of the injector and on its coefficient of efficiency.

These tests are likewise divided into series of 3 experiments in each. In each series, except for the delivery pressure, all conditions must remain unchanged, i.e. the pressure of the working steam, the suction lift, and the temperature of the water being sucked in; in each experiment all four remain unchanged.

The test must show how, at a given working steam pressure, the capacity changes if the back pressure increases; thereby the highest possible delivery pressure and its ratio to the working steam pressure are determined.

4) One may set the task of determining that temperature of the water at which, at a given steam pressure, the injector can begin operation and, by raising it, determine that at which it ceases to deliver water.

It is a known fact that, for an injector that has begun to force water, the level of the latter may be lowered during operation in comparison with that at which it can begin to work; the same is true when the temperature is changed, when the water level remains unchanged.

The test must establish these limiting temperatures for various steam pressures.

5) One may set the aim of determining the amount of water lost through the overflow opening during the period of starting the injector and stopping it, in non-suction injectors. Such a test is of interest for locomotive injectors, for purposes of comparing them with one another, since the unnecessary loss of water from the tender when starting up in motion reduces the time between two stops required for replenishing it.

6) Finally, a subject for study may be the determination of the conditions for the automatic resumption of the injector’s action, i.e. its ability to take up water again in the event of a break in its jet for any reason; for example, in a suction injector in service on a locomotive, while running and under shaking, the end of the suction pipe may at times become exposed, owing to oscillation of the water level in the tender.

To start Restarter injectors, as is evident from their description, it is necessary slowly to move the lever or handle controlling the admission of steam; when its operation has become established, the lift-valve opening remains closed. If the water level is lowered so much that the end of the suction pipe is exposed, the delivery ceases; the steam and air escape either through the lift pipe, in the full volume of both, or else, besides this, rush also into the suction pipe, which will occur if the cross-sectional area of the overflow opening is insufficient. If the water level rises again and covers the end of the pipe, then in the first case the injector will take up water, while in the second it will be necessary to start it again.

In addition, a whole series of tests of the injector may be made with regard to its ability to perform work under known conditions. One may, for example, observe how a certain number of turns of the delivery pipe affects its capacity at a given back pressure, or the latter at a definite capacity; one may subject the suction pipe, for example, to shocks and impacts that may cause a break in the jet, and determine the sensitivity of the instrument to them; one may observe how, at the limiting temperature of the water, heating of the injector body and suction pipe affects it (with leaky steam valves); one may investigate within what limits of variation of the working steam pressure and back pressure (equal to it) no kind of [continued]

adjustment of either the steam or the water, so that there would be no losses through the overflow opening, etc.

For the records made during the test readings, a special form should be prepared according to the appended Form No. 1, in the columns of which the results of the observations are entered; it is useful, moreover, to furnish such a form with a sketch and description indicating the general arrangement of all the appliances and devices that were present during the experiment.

To fill out such a form, pressure gauges and thermometers must be placed in the corresponding locations; the measuring instruments must be checked beforehand. To check a pressure gauge, in the absence of a special apparatus with a dead-weight load or one operated by an oil press, such a check may be made by comparing its readings with those of a well-calibrated control pressure gauge. As for thermometers, they should be checked against a standard one at every five degrees, by immersing them in oil heated to a known temperature, and from the results of the comparison a table of corrections should be compiled.

For measuring the water it is necessary to have a pair of tanks, placed on scales or calibrated; one of them must serve as a reservoir for the water delivered by the injector, the other must contain the water taken in by it during operation. From the difference in weight between the water delivered by the injector and that taken in by it, the quantity of steam consumed during the test is determined.

A more detailed description of the arrangement of the pipes and the installation of the measuring instruments is given below.

From the data of the above-mentioned form one can judge the steam consumption by the injector and the work performed by it; for this ultimate purpose of the test it is even possible to dispense with these tanks, as may be seen from the following example.

Let \(h_s\) be the suction height in metres;

\(h_d\) — the height corresponding to the delivery pressure.

Their sum \(h_s+h_d\) gives the total height of lift of the water.

If \(P\) represents the weight of the water consumed, in kgr., per minute, and \(m\) the weight of the steam in the same time, then the lifting work will be

\[ P \cdot (h_s+h_d)\ \text{kgr.-mtr. per minute} \]

or

\[ \frac{P \cdot (h_s+h_d)}{75 \cdot 60}\ \text{horse-power}. \]

Since the steam consumption per hour is \(60m\), then per one horsepower there is consumed

\[ \frac{60m \cdot 75 \cdot 60}{P(h_s+h_d)} \]

Form No. 1.

Injector Test.

Time and place of the test ............................................................................................................

Experimenter ..............................................................................................................................

Purpose of the test ......................................................................................................................

......................................................................................................................................................

Firm that manufactured the injector ...................................................................... Injector No. ..................

and its class ..................................................................................................................................

(suction or non-suction, single, double).

Diameters of the steam nozzle ........................................ mixing ............................................

receiving .................... suction pipe ........................ discharge ....................................

steam .................... outlet ....................................

Barometer pressure ....................................; room temperature ....................................

Test No.	Duration of test, in minutes.	Steam pressure by manometer \(p_1=\)	Dryness of steam \(x_1\)	Suction height of water \(h_s\) (meters).	Temperature of suction water \(t_a\) (°C).	Delivery pressure by manometer \(p_2=\)	Temperature of delivery water \(t_c\) (°C).	Weight of water supplied to the injector \(w_s\), kg.	Weight of water delivered by the injector \(w_a\), kg.	Remarks.

or

\[ \frac{270.000}{h_s+h_d}\cdot \frac{m}{P}\ \text{kg of steam per h.p.} \]

The ratio \(\frac{P}{m}\) may be found either by weighing the water, or calculated from the observed temperatures.

Since the dryness of the steam is assumed known, the heat of \(m\) kg of steam will be

\[ m(q+rx); \]

the heat of the water before delivery is \(Pt_a\); if its temperature upon delivery is \(t_e\), then we have the equality:

\[ m(q+rx-t_e)=P(t_e-t_a) \]

and

\[ \frac{m}{P}=\frac{t_e-t_a}{q+rx-t_e}. \]

The steam consumption per horsepower will therefore be

\[ \frac{270.000\,(t_e-t_a)}{(h_s+h_d)(q+rx-t_e)}\ \text{kg per h.p.} \]

The thermal efficiency is determined in the following manner.

External work of lifting is equal to . . . \(P(h_s+h_d)+m.h_d=L.\)

Kinetic energy of the jet*) . . . . . . \(\dfrac{P+m}{2g}\,v^2=K.\)

Energy in the form of heat received by the water . . . . \(P(t_e-t_a)=M.\)

If we express them in heat units, then we shall have

\[ AL,\quad AK\quad \text{and}\quad M. \]

Thus the sum \(AL+AK+M\) represents for us the thermal energy found by us in the raised water.

The heat of the steam expended on this work is

\[ m(q+rx) \]

The thermal efficiency will be

\[ \eta_{\text{therm.}}=\frac{AL+AK+M}{m(q+rx)} \]

Attention should be paid to the term \(M\) of the numerator, which we introduce here because the water returns this heat to the boiler; if

*) \(v\)—velocity in the delivery pipe.
\[ v=\frac{V\ \text{cu. m.}\ 10000}{\text{duration of the test}\times 60\times \text{area of the pipe in cm.}} \]
\(V\)—volume of water delivered by the injector.

if the injector were operating as an ordinary pump for raising water and the heat could not be utilized, then the thermal efficiency would be

\[ \frac{AL+AK}{m(q+rx)} \]

Since the weight of all the water accounted for per 1 kg of steam will be known from weighing or calculation, it will also be possible to find the mechanical efficiency.

The velocity of the steam, depending on the form of the nozzle, will be found; \(w_1\) is known.

The velocity of the jet at the mouth of the receiving nozzle is found in the following manner. In one minute \((P+m)\) kg of water are delivered, which, if \(\gamma_e\) is its specific weight, gives

\[ \frac{P+m}{\gamma_e} \]

cubic meters; if the area of the mouth of the receiving nozzle is \(\omega\) square meters, then the velocity of the jet will be

\[ u=\frac{P+m}{60.\omega.\gamma_e} \]

As for the velocity with which the water enters the injector, it may be determined by the following calculation.

If the area of the annular gap between the nozzles is \(\omega_1\) square meters, the velocity of flow \(u_2\) will be

\[ \frac{P}{60.\omega_1.\gamma_a}=u_2 . \]

To determine the mechanical efficiency, we have equality of the amounts of energy before impact and after impact.

\[ \eta_{\text{mech.}}\left[\frac{m}{60}\cdot\frac{w_1^2}{2g}+\frac{P}{60}\cdot\frac{u_2^2}{2g}\right] = \frac{P+m}{60}\cdot\frac{u^2}{2g} \]

or

\[ \eta_{\text{mech.}}= \frac{(P+m).u^2}{mw_1^2+Pu_2^2}. \]

The method of testing indicated above is very simple and uncomplicated both in the execution and conduct of the experiment and observations, and in the preparation for it; but, of course, it is not exact and is suitable only for rough determinations, for purposes of practical comparison of the advantage of one injector or another. For testing according to the program outlined above, it will be more expedient to arrange the experiment itself.

First of all, as has already been indicated, the test must be carried out in series; the duration of each test in such a series will depend on the capacity of the measuring tanks. The results of the observations of each

the given experiment, conducted under exactly identical conditions, must be immediately compared with the observations of previous experiments; in the event of a sharply expressed difference, which may depend either on errors in the observations or on deviations from the conditions normal for the given experiment that had not been noticed beforehand, the test must be repeated; in deriving average data, such observations should not be included in the calculation. It is necessary, of course, before undertaking a repeated test, to analyze thoroughly the causes that may have affected the uniformity of the observations, and to eliminate them.

For the records it will be necessary to prepare blank forms of the second appended form *).

The steam and delivery pressures, as well as the temperatures of the water sucked in and delivered, etc., must be entered according to readings taken at definite intervals of time. It is quite sufficient to make such readings every two minutes.

From the entries on such a blank, the test report is compiled according to the appended form No. 3.

The ultimate purpose of the report should be the determination of the thermal and mechanical efficiencies, \(\eta_t\) and \(\eta_m\), of the useful action; of the consumption of dry steam \(\alpha\) per one horsepower per hour; of the impact coefficient \(\psi\); and of the coefficient of perfection of condensation \(\varepsilon\); \(\varepsilon^2\)—at the same time the density of the jet of mixture will be determined as it passes through the interval between the nozzles.

It will be possible to compute, from the velocity determined by the formula for the outflow of steam, the quantity of it theoretically consumed by the nozzle, and to compare it with that quantity of steam which is determined by weighing the delivered water; this will make it possible to judge the influence of the cold water on the condensation of the steam inside the nozzle.

As for the actual arrangement of the injectors for the test, this may be done according to the following diagrams (Fig. 86).

A tank with cold water (1), with graduated glass tubes for reading the quantity of water, is placed at a certain elevation; instead of graduating the glass tubes, which must be done at a known water temperature, it is better to fill the tank with weighed water, for which purpose a tub or a small-capacity tank of galvanized iron (3), with a drain cock (4), is set on the scale platform (2). Water is brought to this tank by a pipe (5), having a branch (5a) to the reservoir (7), from which the injector (12) takes water during the test. The temperature of the feed water is measured by a thermometer (11), the bulb of which is immersed in the stream of flowing water. For the readings it is necessary to have a thermometer with degree divisions of \(1/10\) within the limits from

*) An approximate filling-in with observation data is indicated.

Form No. 2.

Injector Test.

Time and place of the test ____________

Purpose of the test ____________

Experimenter _____________

Injector No. ______,

(factory or name of the injector) No. ______, (suction, non-suction, simple or double)

Diameter of the steam nozzle ___ length ___

(cylindrical; with converging or diverging orifice)

______ cross-sectional area ______

(at the discharge orifice)

______ nozzle orifice area ______

(at the discharge orifice)

(converging or diverging cone; length of the diverging part ______

area of the outlet section ______ profile: rectilinear cone or traced along curves.)

Diameter of the condensing nozzle ___ length _____

(outlet)

______ cross-sectional area ______

Diameter of the annular gap ___ area _______

Diameter of the throat of the receiving nozzle ____

area of the throat _____________

(outlet)

Diameter and angle of the receiving nozzle _______

length of the diverging part ___ area of the throat _____

area of the outlet section ___________

Outline of the nozzle and of the outlet of the suction ________

steam ____ delivery ______ pipes

Room temperature ___ Height of the barometer _____

Corresponding boiling temperature of water _______

Readings in order	1.	2.	3.	4.	5.	6.	7.	8.	Average	Notes
Time of beginning of the test	12 h								12 h 15 m
Steam pressure at the injector, in kg/cm²	4,5	4,4	4,4	4,5	....	....	....	....
Delivery pressure, in kg/cm²	4,5	4,5	4,5	4,5	..	....	....	....
Vacuum in the nozzle, in mm of mercury column	160 mm	..	162	....	160	....	....	....
Suction lift, in meters	2,2	2,2	2,3	2,3	2,2	....	....	....
Temperature of the water drawn in, in °C	15°	....	....	....	....	....	....	....
Temperature of the delivered water, in °C	60°	60°	61°	61°	60°	....	....	....
Time of completion of the test	—	—	—	—	—	—	—	12 h 15 m
Duration of the test	15 minutes	15 minutes	15 minutes	15 minutes	15 minutes	15 minutes	15 minutes	15 minutes	15 minutes

	During the test	Per minute	Per hour
Quantity of water taken by the injector, in kg	900	60	3600
Quantity of water delivered by the injector	954	63,6	3816
Steam consumption	54	3,6	216

0° to 100° C.; although in most cases it will not be necessary to use water above 50–55°, it is nevertheless necessary to have just such a thermometer, in order to avoid damaging it in the event of the injector’s stopping; the zero of the scale should be set by \(^{m}/_{m}\) at 40–50 from the reservoir with mercury, so as to have a free portion of the capillary, necessary for inserting the thermometer.

As regards the installation of the thermometers, this can easily be done by means of gas tubes screwed into the pipe and provided with a small stuffing box with a tightening nut. The steam is supplied by pipe (9), which has a shut-off valve; between it and the injector a pressure gauge (10) is placed for observing the steam pressure. The steam pipe must be well insulated against heat losses in order to avoid premature condensation of the steam; if the steam line is long, it will be useful to place, before the injector, a reliably operating steam dryer. By shutting it off in two successive experiments, it will be possible to trace the influence of preliminary condensation of the steam on the temperature of the delivered water and on its quantity.

The injector (12) is set at a definite height above the reservoir (7); thus the suction height will be given, if the level of the water in the reservoir is kept constant. Taking water through pipe (8), the injector delivers it into the delivery pipe (18). On it there is likewise placed accurately a thermometer (14) for measuring the temperature of the delivered water and a pressure gauge (15) for observing the pressure at which delivery takes place.

To increase and, in general, to vary the pressure against which the injector works, a cock or valve (16) is placed on pipe (18); by closing it, back pressure is created at the injector’s check valve. At some distance beyond this valve a three-way cock (17) is placed.

The water delivered by the injector enters the second tank (19), which may be graduated for determining the quantity of water delivered, or, better, its quantity is again determined by weighing; for this purpose, near tank (19), a tub (20) is placed on the platform of scales (21).

During the test, in addition to weighing the feed water, it will consequently be necessary to take readings on two thermometers and two pressure gauges; to determine the vacuum in the suction pipe, a mercury vacuum gauge may be connected to it.

Before beginning the experiment, the reservoir (7) is filled with water of the proper temperature; the tank (19) is emptied, and into (1) a certain quantity of water is poured.

Having opened the inflow of steam to the injector, it is put into operation. The steam valve must be opened to full travel, so that there does not occur—

Form No. 3.

REPORT OF AN INJECTOR TEST.

Time and place of test..................................................................................................................

Experimenter.................................................................................................................................

Purpose of test..............................................................................................................................

Injector................................................................ No. ................., ..............................................
(Factory or name of injector).                      (Suction, non-suction, simple, double).

Diameter of steam nozzle .................. cross-sectional area .................. length ..................
Diameter of condensing nozzle .................. outlet area .................. length ..................
Diameter of receiving nozzle .................. throat area .................. outlet area ..................
length of nozzle ..................

Diameter of pipes {
 steam ........................................
 suction ......................................
 delivery .....................................
 overflow opening ..........................
} Areas {
 ........................................
 ........................................
 ........................................
 ........................................
}

Room temperature .................................... Barometer height ....................................
Corresponding boiling \(t\) ....................................

The report must include a description of the nozzles.

No.		Designation	Test data	Formula for calculation	Remarks
1	Average steam pressure by manometer in kg/cm² .....	\(p_0\)
2	Average delivery pressure in kg/cm² ........	\(p_1\)
3	Delivery pressure in mtr. of water column .......	\(h_d\)
4	Suction height in mtr.	\(h_s\)
5	Temperature of the suction water (C.) ...............	\(t_a\)
6	Temperature of the delivered water (C.) ..............	\(t_e\)
7	Quantity of water taken by the injector in kgr. per hour ....................	\(P_1\)
8	Quantity of water delivered by the injector in kgr. per hour ................	\(P_2\)

No.		Designation	Test data	Formula for calculation	Notes
9	Quantity of water delivered by the injector per hour, in cubic meters..............	\(V\)		\(V=P_2:\gamma_e\)	\(\gamma_e\)—density of water corresponding to temperature \(t_e\).
10	Dryness of steam..............	\(x\)			If not determined directly, take \(0.98\).
11	Quantity of wet steam consumed, in kg per hour........	\(D\)		\(D=P_2-P_1.\)
12	Quantity of dry steam consumed per hour, in kg...........	\(D_1\)		\(D_1=x.D.\)
13	Quantity of water delivered by the injector per 1 kg of wet steam....	\(Q\)		\(Q=P_1:D.\)
14	Quantity of water delivered by the injector per 1 kg of dry steam........	\(Q_1\)		\(Q_1=P_1:D_1\)
15	Velocity of water in the delivery pipe, in meters per sec............	\(u_0\)		\(u_0=\dfrac{25.V}{9\times \text{area in sq. cm.}}\)
16	Heat expended on lifting the water, in calories.	\(W_1\)		\(W_1=\dfrac{P_1(hd+h_s)+Dh_d}{427}\)	\(427\)—mechanical equivalent of heat.
17	Heat for heating the water.	\(W_2\)		\(W_2=P_1(t_e-t_a).\)	More exactly, replace the temperature difference by the corresponding quantity of heat \(Q_a\) and \(Q_e\)
18	Heat equivalent to the kinetic energy of the water..	\(W_3\)		\(W_3=P_2\dfrac{u_0^2}{2g}\cdot\dfrac{1}{427}\)
19	Total expenditure of heat energy, in calories per hour..............	\(W\)		\(W=W_1+W_2+W_3\)
20	Heat delivered by the dry steam........	\(E\)		\(E=D_1(\lambda-q_e).\)	\(\lambda\)—latent heat of vaporization.
21	Thermal coefficient of useful action....	\(\eta_t\)		\(\eta_t=\dfrac{W}{E}\)

No.	Quantity	Designation	Experimental data	Formula for calculation	Notes
22	Mechanical efficiency coefficient	$\eta_m$		$\eta_m=\dfrac{W_1+W_3}{L}$
23	Work of the injector in horsepower	$L$		$L=\dfrac{P_1(h_d+h_s)+Dh_d}{75\cdot3600}$
24	Consumption of dry steam per 1 horsepower per hour	$a$		$a=\dfrac{D_1}{L}$
25	Steam pressure at the outlet section of the steam nozzle	$p'$		$p'=0.57p_0$	For a converging conical nozzle; for a diverging nozzle, at the throat section.
26	Velocity of steam outflow	$w_1$		Page 15, formula 9.	$p_2=p'$ for a converging nozzle. $p_2=$ pressure at the end of the nozzle for a diverging conical nozzle.
27	Quantity of dry steam per hour in cubic meters	$v$		$v=D_1\times$ volume of $1$ kg of steam.
28	Quantity of motion of 1 kg of steam	$m_1$		$m_1=\dfrac{w_1}{g-9.81}$
29	Velocity of water at entry into the condensation nozzle	$w_2$		$w_2=\dfrac{P_1\cdot25}{9\times\gamma_a\times\omega\;(\mathrm{cmtr})}$	$\omega=$ area of the annular gap between the nozzles in sq. cm. $\gamma_a=$ initial temperature of the water.
30	Quantity of motion of $Q$ kg of water	$m_2$		$m_2=\dfrac{w_2\cdot Q}{g}$
31	Exit velocity from the condensation nozzle	$w_3$		$w_3=\dfrac{25V}{9\times\omega_1(\mathrm{cmtr})}$	$\omega_1=$ area of the outlet section of the condensation nozzle in sq. cm.
32	Quantity of motion of the mixture after impact	$m_3$		$m_3=\dfrac{w_3}{g}(1+Q)$
33	Impact coefficient	$\mu$		$\mu=\dfrac{m_3}{m_1+m_2}$
34	Outflow velocity corresponding to the head $h_d$	$w_d$		$w_d=\sqrt{2gh_d}$
35	Quantity of water flowing out per second through the mouth of the receiving nozzle, in kg	$Q'$		$Q'=w_d\omega_2\cdot\gamma_d$	$\omega_2=$ area of the mouth of the receiving nozzle. $\gamma_d=$ density of water at pressure $p_0$.
36	Coefficient of perfection of condensation	$\varepsilon$		$\varepsilon=\dfrac{P_2}{3600\cdot Q'}$

which directs the steam jet; the three-way cock (17) must be in such a position that the water taken up by the injector is discharged somewhere to the side; in exactly the same way the water flowing down the discharge pipe (13) is also led away.

The consumption of water is replenished into the reservoir (7) through the branch (5a), its inflow being regulated by a cock; at the same time, by closing the valve or cock (16), the pressure in the delivery pipe is raised to the desired height (for example, \(1/2\,p\), \(p\), \(1.2\,p\), etc., where \(p\) is the steam pressure according to the pressure gauge at the injector); by regulating the inflow of steam, the operation of the injector is now adjusted so that it delivers water at the given pressure without loss through the overflow opening. When this has been achieved, the inflow of water through pipe (5a) is stopped, and at the same time the cock (17) is quickly turned, directing the water into the tank (19), and the time is noted; immediately thereafter the reservoir (7) is fed from the tank (1) through the pipe (6), and readings are taken from the pressure gauges and thermometers. The duration of the experiment will depend on the capacity of the injector and the volume of the measuring tanks; the test is ended by simply stopping the injector.

When the injector has taken up the water and begins to raise the delivery pressure, part of the water may appear through the overflow pipe; gradually increasing the inflow of steam, we bring its quantity to such a ratio with the incoming water that all of it is directed into the delivery pipe. This moment is easily recognized by the sound: if too much steam enters, the injector works noisily, while with the proper ratio between the quantities of steam and water its operation proceeds almost noiselessly. Only with a poorly fitted valve of the overflow opening is a whistle heard from the air being drawn in through the pipe.

In this case the operation of the injector will correspond to normal conditions; the quantity of water delivered by it and its temperature will have values lying between the maximum and the minimum of both.

If the spindle or valve of the injector is opened to full stroke and the water flowing to it is sufficient for condensation of the steam, we obtain the maximum delivery; to determine the minimum it will be necessary to set the cock for regulating the water on the suction pipe; the temperature in this case will be the highest.

The disadvantage of an installation according to this scheme consists in the fact that the pointer of the pressure gauge of the delivery pipe is subject to oscillations, which at times attain a very large amplitude.

This makes it difficult to read its indications and may be the cause of large inaccuracies, whereas one of the principal conditions for testing injectors—

—obtaining by means of readings from measuring instruments more accurate data for further calculations.

The influence of the above-mentioned shortcoming can be reduced by placing, between the injector and the cock or valve, an air bell of sufficient dimensions, or by transmitting the pressure to the manometer through an intermediate, heavier liquid, for example, mercury.

Instead of a cock, by the partial closing of which the pressure in the delivery pipe is raised, one may use a safety lever valve; depending on the weight of the load and its position on the lever, it will be possible to obtain the desired pressure in the pipe.

With an arrangement according to this scheme, it is best to force the water directly into the same boiler from which the working steam is taken, or into another one if the delivery pressure must be different from the pressure of the working steam. In this case, of course, only the water taken in by the injector can be weighed; the amount of steam expended must be calculated from observations of the temperatures in the suction and delivery pipes.

For injectors of a large number this method will also be inconvenient in that the water level in the boiler will rise considerably, while feeding it with a large quantity of only slightly heated water will be accompanied by a drop in pressure in it, i.e. by a reduction of the back pressure against which the injector is to be tested.

A more satisfactory arrangement is the installation of the injector according to the second scheme, shown in Fig. 87.

Here tank (1) serves as a reserve reservoir for heated water; from tank (10), buried in the ground, the injector takes water during the experiment, the suction height depending on the height of the water level in this tank; for almost all injectors it will be sufficient to have this tank with a height of 5 mtr. The water level is maintained during the experiment by continuously replenishing the amount drawn from it from tank (7), placed on the weighing platform; the capacity of this tank, 700 kgr. of water, will be sufficient for the operation of injectors up to No. 7 for 10–15 minutes. The testing of injectors may be carried out with cold or hot water.

In the first case tank (10) is filled with water from the water supply through line (3); at the same time, with the aid of cock (5), tank (7) is filled and weighed. During the entire preparatory period for setting up the injector operation, water is replenished from the water supply, and its quantity, in order to keep the level constant, is regulated by valve (6). When the readings begin, cock (6) is quickly closed, and the reservoir is replenished with weighed water from tank (7).

The temperature of the water is measured by a thermometer placed on the suction pipe; the rarefaction in it is determined by means of a mercury vacuum gauge (11).

Steam is supplied to the injector through pipe (23), which has a stop valve and a pressure gauge (12) for measuring its pressure before the injector. The temperature of the delivered water is measured by thermometer (14); (15) is a three-way cock; (16) is the feed check valve. It is connected to reservoir (17), 0.6–0.7 meter in diameter and about 2 meters high; the reservoir must be calculated for a pressure of 18–20 atmospheres; the pressure in it is measured by pressure gauge (21), and the water-gauge glass (18) indicates the water level in it. On the side opposite (16) a safety lever valve (19) is attached to the reservoir, beneath the end of whose pipe is placed tank (20), situated on the scales platform. Valve and pipe (24) connect the space of this reservoir with the steam-pipe line; the steam may be taken either from the same boiler from which it is taken for the injector—the normal conditions for operation of the apparatus—or from another boiler with higher pressure, in case the greatest back pressure at which the injector can operate is to be determined.

Cock (15) serves here chiefly to fill tank (1) with hot water, where it is diluted with water from the water-supply line (2) to the desired temperature. Having first removed the remaining water from (10) by means of a jet elevator or by some other method, this reservoir is filled with this heated water through pipes (4) and (8). The quantity of water consumed during the test is in this case determined from glass (25), graduated respectively by volume or by weight; tank (7) serves as a spare reservoir for the same heated water before the readings are begun. If the temperature of this water is so high that the injector refuses to take it up, then it is brought to it under pressure through line (4,4).

In this case a special small barrel is placed under the injector overflow pipe for the water lost during starting; the quantity of this water is then excluded from the indicated reading on the glass scale.

The convenience of an installation of this kind consists in the fact that the operation of the apparatus, with respect to constancy of the back pressure on the feed valve, proceeds under more favorable conditions. The installation of reservoir (17) eliminates the shortcomings of delivering water directly into the boiler, but at the same time excludes the possibility of determining the quantity of steam expended by the weight of the water delivered and taken by the injector, since the former will also depend on the quantity of steam condensing in the boiler.

Weighing the water will give satisfactory results only when the boiler is filled with compressed air; in this case, by setting the load on the lever of the valve accordingly, it will be possible to achieve a continuous discharge of water through it at an almost constant delivery pressure.

The same valve may also be used when testing injectors of larger sizes. The quantity of water taken up by the injector (at (7) for 700 kgr.) will be determined by the scale of the gauge glass, the quantity of steam by the temperatures, while the discharge of water through the valve will be needed to eliminate excessively rapid filling of the boiler (17) with water and, consequently, to increase the duration of the test.

Very good results in reports can be obtained by using, in the installation according to the first scheme, instead of the cock (16), for increasing the pressure in the delivery pipe, a specially designed valve, shown in Fig. 88.

This is a modified feed valve, in which the stem a, firmly connected with the disk of the valve, has at its other end a piston of the same cross-sectional area. The piston is well fitted to cylinder c, and, for tightness, two ordinary cut split rings are inserted in it. In the upper part of the cylinder there is an opening d, to which a branch from the steam pipe must be connected; the steam must be taken after the valve of the steam pipe (9) to the injector, so that its pressure will be the same as that of the steam working in the latter.

If the former cock (16) is left after such a valve, then by partly closing it the delivery pressure can be raised; the same can be achieved by placing in chamber c of the proposed valve a spiral spring, the tension of which is produced and regulated by advancing bolt f with a lock nut. In all other respects the arrangement of the installation remains unchanged.

Fig. 35.

Fig. 36.

Fig. 37.

Fig. 38.

Fig. 39.

Fig. 42.

Fig. 43.

Fig. 44.

Fig. 40.

Fig. 41.

Fig. 45.

Fig. 46.

Visible letter labels in the drawing: \(W\), \(w\), \(S\), \(P\), \(h\).

Fig. 47.

Fig. 48.

Visible letter labels in the drawing: \(a\), \(b\), \(c\), \(d\), \(e\), \(g\), \(x\), \(y\), \(z\).

Fig. 49.

Fig. 50.

Fig. 51.

Fig. 52.

Fig. 53.

Fig. 54.

Fig. 55.

Fig. 56.

Fig. 57.

Fig. 58.

Fig. 59.

Fig. 60.

Fig. 61.

Fig. 62.

Fig. 63.

Fig. 64.

Fig. 64 bis.

Fig. 65.

Fig. 66.

Fig. 67.

Fig. 68.

Fig. 69.

Fig. 70.

Fig. 71.

Fig. 72.

Fig. 73.

Fig. 74.

Fig. 75.

Fig. 76.

Fig. 77.

Fig. 78.

Fig. 79.

Fig. 80.

Fig. 81.

Quantity of water in cubic feet.

Steam pressure in atmospheres.

Fig. 82.

Final temperature of the water.

Steam pressure in atmospheres.

Fig. 83.

Fig. 84.

Fig. 85.

Diagram axes:

• Vertical axis: Amount of supplied water in liters per hour.
• Horizontal axis: Initial water temperature.

Diagram of the setup of an injector for testing.

Fig. 86.

Fig. 88.

Diagram of the setup of an injector for testing.

Fig. 87.