A technique for measuring the volume of an incompressible liquid in a rigid tank involves measurement of the total volume of gas in those parts of the tank not occupied by the liquid. The volume of liquid is then computed by subtracting V from the total volume of the tank and the associated plumbing.

The Volume of Gas (including bubbles) in the tank is determined by measuring the small change in pressure that accompanies a small change in volume. The volume of liquid is then computed by subtracting the volume of gas from the total volume of the tank and plumbing.

Unlike liquid-level-measuring techniques, this technique works whether or not a gravitational field is present and is unaffected by the shape of the liquid or tank. Even if bubbles of gas are present in the liquid or if the liquid has broken up into separate globules or pools, the measurement of the total volume of gas is unaffected.

The pressure in the tank is measured while the total volume of the tank is varied by use of a piston or bellows (see figure). It is assumed that the gas is a noncondensible ideal gas, that the alternating compression and decompression of gas is adiabatic, and that the variation in volume is a small fraction of the total volume of gas. Under these assumptions, the total volume (V) of gas in the tank is given by V = – γP(∆V/∆P), where γis the specific heat of the gas at constant pressure ÷ the specific heat of the gas at constant volume, P is the pressure, ∆V is the change in volume, and ∆P is the change in pressure that accompanies the change in volume. In a demonstration of this technique, the volume of water in a 94-liter tank was determined within 1 liter.

This work was done by Frank T. Hartley of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp  under the Mechanics category. NPO-19211


This Brief includes a Technical Support Package (TSP).
Measuring Volume of Incompressible Liquid in a Rigid Tank

(reference NPO-19211) is currently available for download from the TSP library.

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