Liquid Column Manometer

The most primitive and easy way of measuring pressure is by using the liquid column manometer.
U-tube manmeterThe manometer consists of a liquid filled column of a transparent material. Both the ends of the column are open to air. To measure pressure under consideration, one end of the column is subjected to the pressure we wish to measure and the other is kept open to atmosphere.Thus, one end is subjected to pressure under consideration and the other is subjected to atmospheric pressure. The height of the liquid column is proportional to the pressure difference. Therefore we can calculate the gauge pressure by using the formula,

 P = r h g 

where, P = Gauge pressure
            r = Density of liquid
            g = Acceleration due to gravity
            h = Difference in height

This was for measuring absolute pressure.

In order to measure differential pressure, both ends must be subjected to the pressures whose difference needs to be measured. Rest of the process remains the same.
In this case, the formula for calculating differential pressure becomes

 P1 - P2 = r h g 

U-tube manometer

The above image shows two U-tube manometers. It consists of a glass tube having shape as the English alphabet U. Fig.a shows a manometer which is either subjected to equal pressures or not subjected to any pressures at all. The height difference in this condition is obviously zero, as shown.
Fig.b shows the same manometer being subjected to unequal pressures. Here Pt > Pa.
The scale for measuring h is usually marked on any one or both the legs of the manometer.
It is a necessary condition that the diameters of both legs of the U-tube manometer is same.

Inclined Tube Manometer
Inclined tube manometer

For measuring small pressure difference, we can use an another type of manometer known as inclined type of manometer. As shown in the figure above here the tube containing the liquid is inclined at an angle θ to the surface.
        P = R l2 g sinθ 

A pressure difference showing displacement of 'x' units in U-tube manometer gives a displacement of x/sinθ in inclined tube manometer. As sinθ < 1 (θ ≠ 90̊ ), the factor x/sinθ is always greater than x. Therefore, we great larger displacement for the same pressure, as compared to U-tube manometer.
Hence, inclined manometer has greater resolution than U-tube manometer.

The non-inclined limb is purposely made larger in cross-section than the other (300-400 times). When a pressure difference is applied, there is negligible displacement in the limb having larger diameter as compared to that in narrower limb. We can, therefore, consider displacement in larger limb to be negligible. As a result, we can consider displacement only in the narrower limb to give the reading of pressure.Hence, only the narrower limb may be kept transparent.

For very low pressure measurements, the angle of inclination, θ, should be kept as small as possible but not less than 5̊ as it becomes difficult to read the exact  position of the meniscus. For larger pressure ranges, an arrangement can be made to increase θ.

For better sensitivity, the manometer can be filled with alcohol to get better reading of meniscus as compared to water.
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