Fluid Mechanics Applications/A40: Pressure measurement

Introduction

Pressure means force per unit area exerted by a fluid on the surface of the container. Absolute pressure means the fluid pressure above the reference value of a perfect vacuum or the absolute zero pressure. Gauge pressure represents the value of pressure above the reference value of atmospheric pressure. The techniques for pressure measurement are quite varied, depending on whether the pressure is moderate, very high or very low or also whether it is static or dynamic.

Low pressure measurement(Range <0.1 torr)

McLeod Gauge

This is used between 0.01 and 0.001 microns and is modified mercury manometer. It operates on the principle of compressing a known volume of low pressure gas to a higher pressure and measuring the resulting volume change. the unknown pressure source is connected to the gauge and the mercury level is adjusted so that the pressure source fills the bulb B and capillary C. then mercury is forced to reservoir A up in the bulb and reference column R. when the level reaches the cutoff point F,a known volume of gas is trapped in the bulk and capillary. the volume remaining in the capillary is read directly from the scale and the difference in heights y is a measure of the pressure p. using Boyles law, If

p=unknown pressure
A=capillary area
V_c=volume of gas in capillary =Ay
P_c=pressure of gas in the capillary C after compression
V_F=volume of capillary and bulb till F

then,

                    p=P_cV_c/V_F

where y=p_c-p

                    p=Ay²/(V_F-Ay)

Pirani Gauge

It consist of a platinum filament enclosed in a chamber. The wire forms an arm of a wheatstone bridge. The temperature of the wire, for a given magnitude of current, depends on the rate of heat dissipation, which in turn depends on the conductivity of the surrounding medium and hence its pressure.Thus, with change in pressure of the medium, the temperature and resistance of the wire changes, which can be measured by Wheatstone bridge.

Ionisation Gauge

This is used for measurement of very low pressures, of the order of 1 micron and below. the gauge consists of a triode vacuum tube.the heated cathode emits electrons that are accelerated by positively charged grid.As the electrons move towards the grid, they ionize the gas molecules through the collisions.the plate is maintained at a negative potential so that positive ions collect there, producing a plate current i₁.the electrons and negative ions collected by the grid, producing grid current i₂.it is found that the pressure of gas is given by '

                                 p=i₁/ki₂

k=sensitivity of gage.

Knudsen gauge

in this type of gauge,the gas chamber contains fixed plates F1 & F2 heated to and maintained at temperature T.near these plates is a restrained movable vane V,such as the gap between the vane & the fixed plates is less than the mean free path of the gas whose pressure is to be measured.the vane is at gas temperature T₀. The gas molecules rebound from plates F1 & F2 with greater momentum than from V,thus imparting a net force to V which may be measured by measuring the angular displacement of mirror M.it is found that

                                                      p=KF/((T/T₀)-1)^1/2

where p is gas pressure,F the force and K is a constant.

Moderate pressure measurement

There are two types of devices,which can be used for this.

Manometers
Others using elastic elements.

Manometers

Manometers are used for measuring static pressure. a simple U-tube manometer uses water, mercury or any other suitable fluid.the difference in levels h between the two limbs is an indication of the pressure difference (p1-p2) between the two limbs.if one of the pressures applied to limb 1.

                                       h=(p1-p2)/ρg

ρ being the mass density of the liquid used in the manometer.

We can use one more convenient device to use is the cistern or well type manometer. In this type the well area is large compared to that of the tube.thus only a single leg reading may be noted and the change in level in the wall may be ignored.If p1 & p2 are absolute pressures applied .force equilibrium gives:

                                                p1A-p2A=Ahρg

ρ being mass density of the liquid.

                                                p1-p2/ρg =h

if p2 is atmospheric,h is a measure of the gage pressure applied at the well.

An inclined type manometer is another device, which is sensitive and convenient to use.in such a manometer the length l along the inclined tube is read as a measure of the pressure difference(p1-p2)and l is given as:

                                                h1+h2=p1-p2/ρg
                                                  
                                                A1h1=A2l
                                                
                                                 h2=lsinθ

                                                p1-p2=ρglsinθ=ρgh2

Bourdon tube

Elastic elements, when subjected to pressure, deforms.the deformation, when measured, gives an indication of the pressure. Bourdon gage is commonly used for measuring pressure .this consists a bourdon tube.the cross-section of the tube, due to pressure, tends to round out.the tube uncoils since the inner and outer arc lengths remain approximately equal to the original ones.the motion of the end of the tube is amplified and indicated by a pointer moving on a calibrated scale.

High pressure measurement

For pressure above 1000 atm, special techniques have to be used.One such technique is based on the electrical resistance change of a Manganin or gold-chrome wire, with hydrostatic pressure, due to bulk compression effect. Usually, the coil is enclosed in a flexible bellows filled with kerosene, for transmitting the pressure to measured to the coil.the change in the resistance of the wire between A & B is measured by wheatstone bridge etc...