Custom Search

Measurement of Pressure

The pressure of a fluid (gas or liquid) is defined as the force it exerts in a direction perpendicular to a surface of unit area. A differentiation is to be made between absolute pressure which is measured with respect to zero (absolute vacuum), and gauge pressure which is the amount by which the pressure exceeds the atmospheric pressure. Hence: gauge pressure + atmospheric pressure = absolute pressure. This relationship is further clarified where the pressure to be measured is higher and lower than the atmospheric pressure respectively.

The simplest form of pressure gauge is the U-tube manometer (Fig.2). It may either have both arms open to the atmosphere (a) or one sealed arm (b) in which there exists a vacuum (Torricellian vacuum) over the sealing liquid. With type (a) one arm is connected to the pressure P1 to be measured and the other arm is in communication with the pressure of the atmosphere (the reference pressure Pb).

The difference in level H is a measure of the difference in pressure P1 – Pb; i.e., H represents the gauge pressure (as defined above) measured, for example in millimeters or inches of sealing-liquid column. If the sealing liquid is water then H will represent the pressure in units mm or inches of water column (or water gauge).

If the sealing liquid has a specific gravity g, then H can be converted to water gauge by multiplying it by g,: hence: P1-P6 = Hg, (w.g.). The U-tube manometer open at both ends can be employed as a differential gauge for measuring difference between two pressures P1 and P2 as for example in Fig.2c, where an inverted U tube is used to measure the pressure difference P1-P2 in millimeters or inches of the liquid to which the two arms of the gauge are connected, the sealing medium being a gas in this case.

The ring-balance pressure gauge (Fig.3), comprising a pivotably mounted annular tube containing a partition and a sealing liquid, may be regarded as a combination of U-tube gauge and balance. It is particularly used for measuring small different pressures. Thus the pressure difference P1-P2 acting on the partition produces a rotating movement which causes the partition to swing through an angle a in relation to the vertical, so that a state of equilibrium is established when the turning moment Mp = (P1-P2) AR is equal to the counteracting moment MG = G sin a.a, Where A is the cross-sectional area and R is the mean radius of the annular tube, while G is a known weight and a is its distance to the center. The differential pressure P1-P2 can be calculated from the condition Mp=Mg.

An important and commonly used instrument is the Bourdon-tube pressure gauge (or spring-tube pressure gauge Fig.4) in which pressure measurement is based on the deformation of an elastic measuring element (in this case a curved tube) by the pressure to be measured. The deformation is indicated by a pointer on a dial calibrated to give pressure readings. The tube, which is of circular or oval cross-sectional shape, is closed at one end, and the pressure to be measured is applied to other end, causing the radius of curvature of the tube to increase (i.e., the tube tends to straighten itself out, as shown dotted in the right-hand diagram of Fig.4).

In the diaphragm-pressure gauge (Fig.5) the elastic element is a stiff metallic diaphragm held between two flanges; pressure is applied to the underside of the diaphragm, and the movement of the latter is transmitted to a pointer. In the capsule-type pressure gauge (Fig.6) the elastic element is a capsule to the interior of which the pressure is admitted. The piston-type pressure gauge (Fig.7) is a so-called dead-weight apparatus in which the pressure to be measured is balanced by adjustment of the weight G placed on the piston. This is a very accurate type of gauge, usually employed for the calibration and testing of other gauges.

Figs. 1,2 and 3 show examples of pressure gauges employed in level measuring and indicating devices. In the arrangement illustrated in Fig.1 the hydrostatic pressure of the liquid, or its level, is indicated by the gauge – a mercury-float pressure gauge – illustrated in Fig.4. This device is essentially a U-tube gauge with mercury as the sealing liquid.

The variable pressure of the liquid in the tank (in which the level is to be measured) is applied to the “positive” pressure-measuring chamber, and the “negative” chamber is connected to the atmospheric pressure. The movements of the float on the mercury are proportional to the variations in the level of the liquid in the tank and are transmitted through a rack-and-pinion mechanism to a pointer.

Another system is shown in Fig.2: gas, (air, nitrogen, carbon dioxide) under pressure is introduced into the pipes so that bubbles constantly emerge from the mouth of the pipe immersed in the liquid. The gas is kept flowing at a constant rate by means of a metering device and acquires a pressure corresponding to the liquid level in the tank at any particular moment.

This pressure is transmitted to the float pressure gauge. If the liquid in the tank is under more than atmospheric pressure, as in Fig.3, the pressured acquired by the gas in the pipes corresponds to the liquid level plus the pressure of the saturated vapor over the liquid. The vapor pressure must be compensated; it is applied to the “negative” chamber of the float pressure gauge, so that the latter indicates only the liquid pressure or the depth of the liquid in the tank.

When a fluid flows through a constriction (orifice, diaphragm, nozzle) in a pipe-line, the difference in pressure between two points which are respectively located immediately before and after the constriction provides a measure of the rate of flow. More particularly, the flow rate is proportional to the square root of this pressure difference.

The flow rate can thus be measured by means of a pressure gauge – of the type shown in Fig.4, for e.g. whose scale is appropriately divided to give direct flow-rate readings (in ft 3/sec.,m3/min., etc.). By appropriate design of the parts containing the sealing liquid, it is possible to ensure that the float movement is proportional to the square root of the pressure difference, so that the scale can be provided with a linear division (Fig.5). Fig.6 shows a rate-of-flow measuring system comprising a float pressure gauge of this type and a U-tube gauge for checking the float pressure gauge.