MEASUREMENT OF PRESSURE IN A FLUID

The simplest method of measuring the pressure of a fluid in a pipe is to use a piezometer ("pressure measuring") tube. This is a tube, containing the fluid under pressure, in which the fluid is allowed to rise to a height that corresponds to the excess of the pressure of the fluid over its surroundings. In most cases the surroundings are ambient air as shown in Fig. 4.1(a).

The pressure of the fluid in the pipe is measured by allowing the fluid to rise in the vertical tube until it reaches equilibrium with the surrounding air pressure, the height to which it rises is the pressure head existing in the pipe. This tube is called the manometer tube. The height (head) can be related to the pressure in the pipe by use of eqn. (3.3) and so we have:              P = Z1r1g where P is the pressure, Z1 is the height to which the fluid rises in the tube, r1 is the density of the fluid and g the acceleration due to gravity. Figure 4.1. Pressure measurements in pipes. A development of the piezometer is the U-tube, in which another fluid is introduced which must be immiscible with the fluid whose pressure is being measured. The fluid at the unknown pressure is connected to one arm of the manometer tube and this pressure then causes the measuring fluid to be displaced as shown in Fig. 4.1(b). The unknown pressure is then equal to the difference between the levels of the measuring fluid in the two arms of the U-tube, Z3. The differential pressure is given directly as a head of the measuring fluid and this can be converted to a head of the fluid in the system, or to a pressure difference, by eqn. (3.3). EXAMPLE 4.1. Pressure in a vacuum evaporator The pressure in a vacuum evaporator was measured by using a U-tube containing mercury. It was found to be less than atmospheric pressure by 25 cm of mercury. Calculate the extent by which the pressure in the evaporator is below atmospheric pressure (i.e. the vacuum in the evaporator) in kPa, and also the absolute pressure in the evaporator. The atmospheric pressure is 75.4 cm of mercury and the specific gravity of mercury is 13.6, and the density of water is 1000 kg m-3. We have P = Zrg                  =  25 x 10-2 x 13.6 x 1000 x 9.81                  =  33.4 kPa Therefore the pressure in the evaporator is 33.4 kPa below atmospheric pressure and this is the vacuum in the evaporator. For atmospheric pressure:                       P = Zrg               P = 75.4 x 10-2 x 13.6 x 1000 x 9.81                  = 100.6 kPa Therefore the absolute pressure in the evaporator                  =  100.6 - 33.4                  =  67.2 kPa Although manometer tubes are used quite extensively to measure pressures, the most common pressure-measuring instrument is the Bourdon-tube pressure gauge. In this, use is made of the fact that a coiled tube tends to straighten itself when subjected to internal pressure and the degree of straightening is directly related to the difference between the pressure inside the tube and the pressure outside it. In practice, the inside of the tube is generally connected to the unknown system and the outside is generally in air at atmospheric pressure. The tube is connected by a rack and pinion system to a pointer, which can then reflect the extent of the straightening of the tube. The pointer can be calibrated to read pressure directly. A similar principle is used with a bellows gauge where unknown pressure, in a closed bellows, acts against a spring and the extent of expansion of the bellows against the spring gives a measure of the pressure. Bellows-type gauges sometimes use the bellows itself as the spring.