Liquid Level Indicator

Yu. K. Petrov

The level indicator is intended mainly for aligning the foundations of large machines. Usually a geodetic level is used for this purpose. The root-mean-square error of measurements with a standard level is ±0.3 mm.

A liquid level indicator can be used where greater measurement accuracy is required. The optics of a standard level do not permit its use in cramped premises and in cases where there is no unobstructed circular view over the measurement area. In such cases the level indicator can considerably simplify the measurement task.

The instrument operates on the principle of communicating vessels. As the working liquid one may use any liquid with a small coefficient of viscosity, for example: water, alcohol, or mercury. The most readily available working liquid is water.

Description of the Instrument

The instrument (Fig. 1) consists of two stands a and b, connected by hoses to cylinder c. A piston is inserted into the cylinder and is rigidly connected with a micrometer screw; the levels during measurements are read from the scales of the micrometer screw. For connection

Fig. 1.

we used two hoses of vacuum rubber with an internal diameter of 6 mm, each 8 meters long. The operating radius of the instrument is 16 m. Vacuum rubber was chosen for reasons of mechanical strength.

Tap water was used as the working liquid. The sufficiently high electrical conductivity of tap water

made it possible for us to create a convenient system for indicating levels by means of headphones, for which a simple electrical circuit was required (Fig. 2). The resistance of the headphones in the circuit is 2200 ohms; the step-down transformer is 220/30 V. The contacts in the standpipes are made of silver wire 1 mm in diameter. This gives good contact, and no drop forms on the point.

If desired, instead of headphones one may use any sensitive pointer-type instrument. The moment at which the point touches the water level can also be determined visually. The point is reflected in the surface of the water, and the visible gap between the point and its reflection is twice the gap between the point and the water level. This latter circumstance increases the accuracy of the visual determination of the moment at which the point touches the liquid level; however, visual observation is undesirable, since it requires at least two operators.

Fig. 2.

The procedure for taking measurements is as follows.

Switches \(P_1\) and \(P_2\) (Fig. 2) are closed, and with the micrometer screw the water level in the standpipes is raised until one of the contacts closes, the moment of closure being noted from the sound signal in the headphones. By means of one of the switches the sound signal is eliminated, and thus the standpipe in which closure has occurred is determined. Next, a reading is taken from the scales of the micrometer screw. Then the piston is advanced further until closure occurs in the second standpipe, and a second reading is taken. The level difference is determined from the difference between the two readings.

Sources of Error

If between standpipes \(a\) and \(b\) there is a temperature difference \(\Theta_1 - \Theta_2\), an error \(\Delta l\) will arise, which can be determined from the formula

\[ \Delta l = [\alpha(\Theta_1 - \Theta_2) + \beta(\Theta_1^2 - \Theta_2^2) + \ldots]l, \tag{1} \]

where \(\alpha, \beta\) are the coefficients of thermal expansion of water,

\(l\) is the height of the liquid in the standpipe and hoses.

In the case when the measurements are carried out in one room, the temperature difference will hardly exceed \(1^\circ\text{C}\), and the error, for a column height \(l = 100\) mm, does not exceed \(\pm 0.01\) mm.

Because of the surface tension of water, the moment of breaking contact when the liquid level is lowered becomes indeterminate. The uncertainty in the breaking of the contacts will cause considerable measurement errors; therefore readings should be taken only

\(k_0\) when the contacts are closed. Before operation, the sharp contacts are wiped with alcohol; otherwise a drop may form on the point, which will lead to a gross measurement error.

One of the sources of error may be the presence of a transient process at the moment of measurement. Every measurement should be started after all transient processes associated with pouring water into the system, moving it, and setting up the stands have completely ended; for our instrument it is sufficient to allow a pause of 3–5 minutes. During the measurements themselves, the influence of transient processes is eliminated.

We used two hoses of the same length; in this case the hydrodynamic resistances in both hoses are the same, and when the micrometer screw is operated the levels in the stands rise in such a way that no level difference is produced, which would be the cause of a transient process.

Two errors associated with the micrometer screw may be mentioned: backlash of the screw and play between the traveling nut of the screw and the piston. We did not take special measures to eliminate the backlash, but paid particular attention to the quality of manufacture of the thread. The clearance between the piston and the nut was made equal to 0.05 mm. Both errors are practically reduced to zero when the screw is run in one direction, as is the case when operating only to close the contacts. The relationship between the piston travel \(l_0\) and the height \(l\) through which the water rises in the stands is expressed by the formula

\[ l = \frac{S_0}{S_1 + S_2}\, l_0, \tag{2} \]

where \(S_0\) is the cross-sectional area of the piston,
\(S_1\) and \(S_2\) are the cross-sectional areas of the glass vessels of the stands.

The effect of the error associated with the screw is proportional to the coefficient on the right-hand side of formula (2); it is therefore advantageous to take \(S_1 + S_2 \gg S_0\).

In our case \(S_1 = S_2 = 25\ \text{cm}^2\), \(S_0 = 4\ \text{cm}^2\). It is obviously necessary to choose tubes with constant cross sections \(S_1\) and \(S_2\). Graduated cylinders and measuring beakers are the most suitable for this purpose.

If it is desired to increase the range of measured heights, the cross-sectional area of the vessels in the stands can be reduced, but this lowers the accuracy of the measurements. We have made a version of the instrument in which \(S_1 = S_2 = S_0 = 4\ \text{cm}^2\); the range of measured heights is 6 cm, and the root-mean-square error of the measurements is \(\pm 0.25\) mm. In testing the instrument, a level difference of 3 mm was measured twenty times over the course of 1 hour 30 minutes. The root-mean-square error of a single measurement, calculated from the results of the twenty measurements, is \(\pm 0.02\) mm.