In practice, pressure is always measured by the determination of a pressure difference. If the difference is that between the pressure of the fluid in question and that of a vacuum then the result is known as the absolute pressure of the fluid. More usually, the difference determined is that between the pressure of the fluid concerned and the pressure of the surrounding atmosphere. This is the difference normally recorded by pressure gauges and so is known as gauge pressure. If the pressure of the fluid is below that of the atmosphere it is termed vacuum or suction. (The term high vacuum refers to a low value of the absolute pressure.) The absolute pressure is always positive but gauge pressures are positive if they are greater than atmospheric and negative if less than atmospheric.
Most of the properties of a gas are functions of its absolute pressure and consequently values of the absolute pressure are usually required in problems concerning gases. Frequently it is the gauge pressure that is measured and the atmospheric pressure must be added to this to give the value of the absolute pressure. The properties of liquids are little affected by pressure and the pressure of a liquid is therefore usually expressed as a gauge value. The absolute pressure of a liquid may be of concern when the liquid is on the point of vaporizing.
Barometer
If the pressure of a liquid is only slightly greater than that of the atmosphere, a simple way of measuring it is to determine the height of the free surface in a piezometer tube. (The diameter of the tube must be large enough for the effect of surface tension to be negligible.) If such a piezometer tube of sufficient length were closed at the top and the space above the liquid surface were a perfect vacuum the height of the column would then correspond to the absolute pressure of the liquid at the base. This principle is used in the mercury barometer. Mercury is employed because its density is sufficiently high for a fairly short column to be obtained and also because it has, at normal temperatures, a very small vapour pressure. A perfect vacuum at the top of the tube is not in practice possible; even when no air is present the space is occupied by vapour given off from the surface of the liquid. The mercury barometer was invented in 1643 by the Italian Evangelista Torricelli and the near vacuum above the mercury is often known as the Torricellian vacuum. All air and other foreign matter is removed from the mercury and a glass tube full of it is then inverted with its open end submerged in pure mercury.
The various devices adopted for measuring fluid pressure may be broadly classified under the following two heads.
1) Manometers
2) Mechanical Gauges
Manometers
Manometers are those pressure measuring devices which are based on the principle of balancing the column of liquid (whose pressure is to be found) by the same or another column of liquid. The manometers may be classified as
a) Simple Manometers
b) Differential Manometers
Simple Manometers are those which measure pressure at a point in a fluid contained in a pipe or a vessel. On the other hand differential manometers measure the difference of pressure between any two points in a fluid contained in a pipe or a vessel. In general a simple manometer consists of a glass tube having one of its ends connected to the gauge point where the pressure is to be measured and the other remains open to atmosphere. Some of the common types of simple manometers are given below.
i) Piezometer
ii) U-tube Manometer
iii) Single Column Manometer
i) Piezometer
Piezometer is the simplest form of manometer which can be used for measuring moderate pressures of liquids. It consists of a glass tube (Fig. 1) inserted in the wall of a pipe or a vessel, containing a liquid whose pressure is to be measured. The tube extends vertically upward to such a height that liquid can freely rise in it without overflowing. The pressure at any point in the liquid is indicated by the height of the liquid in the tube above that point, which can be read on the scale attached to it. Thus, if ‘w’ is the specific weight of the liquid, then the pressure at point m in Fig. 1 is pm = whm. In other words, ‘hm’ is the pressure head at ‘m’. Piezometers measure gauge pressure only, since the surface of the liquid in the tube is subjected to atmospheric pressure.
Fig. 1 Piezometer
From the foregoing principles of pressure in homogeneous liquid at rest, it is obvious that the location of the point of insertion of a piezometer makes no difference. Hence piezometers may be inserted either in the top or the side or the bottom of the container, but the liquid will rise to the same level in the three tubes.
Negative gauge pressures (or pressures less than atmospheric) can be measured by means of the piezometer. It is evident that if the pressure in the container is less than the atmosphere no column of liquid will rise in the ordinary piezometer. But if the top of the tube is bent downward and its lower end dipped into a vessel containing water (or some other suitable liquid), the atmospheric pressure will cause a column of the liquid to rise to a height ‘h’ in the tube, from which the magnitude of the pressure of the liquid in the container can be obtained.
Neglecting the weight of the air caught in the portion of the tube, the pressure on the free surface in the container is the same as that at free surface in the tube and the equation may be expressed as
p = –wh,
where ‘w’ is the specific weight of the liquid used in the vessel. Conversely ‘–h’ is the pressure head at the free surface in the container.
Piezometers are also used to measure pressure heads in pipes where the liquid is in motion. Such tubes should enter the pipe in a direction at right angles to the direction of flow and the connecting end should be flush with the inner surface of the pipe. All burrs and surface roughness near the hole must be removed and it is better to round the edge of the hole slightly. Also, the hole should be small, preferably not larger than 3 mm. In order to prevent the capillary action from affecting the height of the column of liquid in a piezometer, the glass tube having an internal diameter less than 12 mm should not be used. Moreover, for precise work at low heads the tubes having an internal diameter of 25 mm may be used.
ii) U-tube Manometer
Piezometers cannot be used when large pressures in the lighter liquids are to be measured, since this would require very long tubes, which cannot be handled conveniently. Furthermore gas pressures cannot be measured by means of piezometers because a gas forms no free atmospheric surface. These limitations imposed on the use of piezometers may be overcome by the use of U-tube manometers. A U-tube manometer consists of a glass tube bent in U-shape, one end of which is connected to the gauge point and the other end remains open to the atmosphere (Fig. 2). The tube contains a liquid of specific gravity greater than that of the fluid of which the pressure is to be measured.
Fig. 2 U-tube Manometer
Sometimes more than one liquid may also be used in the manometer. The liquids used in the manometers should be such that they do not get mixed with the fluids of which the pressures are to be measured. Some of the liquids that are frequently used in the manometers are mercury, oil, salt solution, carbon disulphide, carbon tetrachloride, bromoform and alcohol. Water may also be used as a manometric liquid when the pressures of gases or certain coloured liquids (which are immiscible with water) are to be measured. The choice of the manometric liquid, depends on the range of pressure to be measured. For low pressure range, liquids of lower specific gravities are used and for high pressure range, generally mercury is employed.
When one of the limbs of the U-tube manometer is connected to the gauge point, the fluid from the container or pipe A will enter the connected limb of the manometer, thereby causing the manometric liquid to raise in the open limb as shown in Fig. 2. An air relief valve V is usually provided at the top of the connecting tube which permits the expulsion of all air from the portion A’B and its place taken by the fluid in A. This is essential because the presence of even a small air bubble in the portion A’B would result in an inaccurate pressure measurement.
iii) Single Column Manometer
The U-tube manometers described above usually require readings of fluid levels at two or more points, since a change in pressure causes a rise of liquid in one limb of the manometer and a drop in the other. This difficulty may however be overcome by using single column manometers. A single column manometer is a modified form of a U-tube manometer in which a shallow reservoir having a large cross-sectional area (about 100 times) as compared to the area of the tube is introduced into one limb of the manometer, as shown in Fig. 3. For any variation in pressure, the change in the liquid level in the reservoir will be so small that it may be neglected and the pressure is indicated approximately by the height of the liquid in the other limb. As such only one reading in the narrow limb of the manometer need be taken for all pressure measurements.
Fig. 3 Single Column Manometer
The narrow limb of the manometer may be vertical or it may be inclined. The inclined type is useful for the measurement of small pressures. Since no reading is required to be taken for the level of liquid in the reservoir, it need not be made of transparent material. If the pressure at A in the container is negative, the manometric liquid surface in the reservoir will be raised by a certain distance and consequently there will be drop in the liquid surface in the tube. Again by adopting the same procedure the gage equations for the negative pressure measurement can also be obtained.
Differential Manometers
For measuring the difference of pressure between any two points in a pipeline or in two pipes or containers, a differential manometer is employed. In general a differential manometer consists of a bent glass tube, the two ends of which are connected to each of the two gauge points between which the pressure difference is required to be measured. Some of the common types of differential manometers are as noted below.
i) Two–Piezometer Manometer
ii) Inverted U-Tube Manometer
iii) U- Tube Differential Manometer
iv) Micromanometer
i) Two-Piezometer Manometer
As the name suggests this manometer consists of two separate piezometers which are inserted at the two gauge points between which the difference of pressure is required to be measured. The difference in the levels of the liquid raised in the two tubes will denote the pressure difference between the two points. Evidently this method is useful only if the pressure at each of the two points is small. Moreover it cannot be used to measure the pressure difference in gases, for which the other types of differential manometers described below may be employed.
ii) Inverted U-tube Manometer
It consists of a glass tube bent in U-shape and held inverted as shown in Fig. 4. Thus it is as if two piezometers described above are connected with each other at top. When the two ends of the manometer are connected to the points between which the pressure difference is required to be measured, the liquid under pressure will enter the two limbs of the manometer, thereby causing the air within the manometer to get compressed. The presence of the compressed air results in restricting the heights of the columns of liquids raised in the two limbs of the manometer. An air cock as shown in Fig. 4, is usually provided at the top of the inverted U tube which facilitates the raising of the liquid columns to suitable level in both the limbs by driving out a portion of the compressed air. It also permits the expulsion of air bubbles which might have been entrapped somewhere in the pipeline. If pA and pB are the pressure intensities at points A and B between which the inverted U-tube manometer is connected, then corresponding to these pressure intensities the liquid will rise above points A and B upto C and D in the two limbs of the manometer as shown in Fig. 4.
Fig. 4 Inverted U-tube Manometer
iii) U-Tube Differential Manometer
It consists of glass tube bent in U-shape, the two ends of which are connected to the two gauge points between which the pressure difference is required to be measured. Fig. 5 shows such an arrangement for measuring the pressure difference between any two points A and B. The lower part of the manometer contains a manometric liquid which is heavier than the liquid for which the pressure difference is to be measured and is immiscible with it.
Fig. 5 U-Tube Differential Manometer
iv) Micromanometers
For the measurement of very small pressure differences or for the measurement of pressure differences with very high precision, special forms of manometers called micromanometers are used. A wide variety of micromanometers have been developed, which either magnify the readings or permit the readings to be observed with greater accuracy. One simple type of micromanometer consists of a glass U-tube, provided with two transparent basins of wider sections at the top of the two limbs, as shown in Fig. 6. The manometer contains two manometric liquids of different specific gravities and immiscible with each other and with the fluid for which the pressure difference is to be measured.
Fig. 6 Micromanometer
Before the manometer is connected to the pressure points A and B, both the limbs are subjected to the same pressure. As such the heavier manometric liquid of specific gravity S1 will occupy the level DD’ and the lighter manometric liquid of specific gravity S2 will occupy the level CC’. When the manometer is connected to the pressure points A and B where the pressure intensities are pA and pB respectively, such that pA > pB then the level of the lighter manometric liquid will fall in the left basin and rise in the right basin by the same amount Δy. Similarly the level of the heavier manometric liquid will fall in the left limb to point E and rise in the right limb to point F.
Bourdon Gauge
Where high precision is not required a pressure difference may be indicated by the deformation of an elastic solid. For example, in an engine indicator, the pressure to be measured acts at one side of a small piston, the other side being subject to atmospheric pressure. The difference between these pressures is then indicated by the movement of the piston against the resistance of a calibrated spring. The principle of the aneroid barometer may also be adapted for the measurement of pressures other than atmospheric. A curved tube of elliptical cross-section is closed at one end; this end is free to move, but the other end – through which the fluid enters – is rigidly fixed to the frame as shown in Fig. 5. When the pressure inside the tube exceeds that outside (which is usually atmospheric) the cross-section tends to become circular, thus causing the tube to uncurl slightly.
The movement of the free end of the tube is transmitted by a suitable mechanical linkage to a pointer moving over a scale. Zero reading is obtained when the pressure inside the tube equals the local atmospheric pressure. By using tubes of appropriate stiffness, gauges for a wide range of pressures may be made. If, a pressure higher than the intended maximum is applied to the tube, even only momentarily, the tube may be strained beyond its elastic limit and the calibration invalidated. All gauges depending on the elastic properties of a solid require calibration. For small pressures this may be done by using a column of mercury; for higher pressures the standard, calibrating, pressure is produced by weights of known magnitude exerting a downward force on a piston of known area.
Fig. 6 Bourdon Gauge
