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5.9, 2.6.3 Single Column Manometer. Single column manometer is a modified form of a U-tube, manometer in which a reservoir, having a large cross-sectional area (about 100 times) as compared to, the area of the tube is connected to one of the limbs (say left limb) of the manometer as shown in Fig. 2.15., Due to large cross-sectional area of the reservoir, for any variation in pressure, the change in the liquid, level in the reservoir will be very small which may be neglected and hence the pressure is given by the, height of liquid in the other limb. The other limb may be vertical or inclined. Thus there are two types, of single column manometer as, 1. Vertical Single Column Manometer., 2. Inclined Single Column Manometer., , I. Vertical Single Column Manometer, 2.15 shows the vertical single column manometer. Let X-X be the datum line in the reservoir, and in the right limb of the manometer, when it is not connected to the pipe. When the manometer is, , Fig.

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Pressure and its Measurement 49, to, , c o n n e c t e d, , the pipe,, will rise, , due to, in the, , downward and, Ah =Fall.of heavy, Let, , high pressure at A, the heavy liquid in the reservoir will be pushed, right limb., , liquid in reservoir, in, h =Rise of heavy liquid right limb, h Height of centre of pipe above X-X, DA, , =, , 2, , Pressure at A, which is to be measured, A, , A = Cross-sectional area of the reservoir, , RESERVOIR 1x, , a = Cross-sectional area of the right limb, , Sp. gr. of liquid in pipe, S=Sp. gr. of heavy liquid in reservoir and right limb, P Density of liquid in pipe, , S, , =, , Ah, , Fig. 2.15 Vertical single column, manometer., , Density of liquid in reservoir, , p, , Fall of heavy liquid in reservoir will cause a rise of heavy liquid level in the right limb., A, , X, , Ah, , =, , a x, , h^2, , Ah X h, , .(i), , A, Now consider the datum line Y-Y, , as, , shown in, , Fig., , 2.15. Then pressure in the, , right limb, , above Y-Y., , P2 X 8 x (Ah + h2), Pressure in the left limb above Y-Y = P, , these pressures,, , Equating, , we, , X g X (Ah + h;) + PA, , have, , P2X8 X (Ah + h,) = P Xg x (Ah + h,) +pA, PAP28 (Ah + ha) - Pi8(Ah + h,), Or, , = Ahlpz8-P18] +h2P28- h1P18, Ah= X h, , But from equation (i),, , PA, AS the, , area A is, , very, , large, , as, , Pigl, Ip:8A, , +, , h2P28-, , to a, hence ratio, , compared, , a, , A, , hiP18, , ...(2.9), , becomes very small and can be, , neglected., Then P, , = hP28 - h;P18, , ...(2.10), is known, , From equation (2.10), it is clear that as h, and hence by knowing h, or rise of heavy liquid in the, ght hmb, the pressure at A can be calculated., 2. Inclined, Column Manometer, , Single, , ., , h, , ah, , shows the inclined single column manomg This2.16manometer, is more sensitive. Due to inclina-, , the distance moved by the heavy liquid in the right, limb will be, , more., , Fig., , 2.16, , Inclined single column, manometer.

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50, , Fluid Mechanics, L, , Let, , =, , Length of heavy liquid, , Inclination, , h, From, , =, , in, , moved, , right limb from X-X, , of right limb with horizontal, , Vertical rise of heavy, , X-X, liquid in right limb from, , =, , LX sin 0, , at A is, , equation (2.10), the pressure, , PAhP28-h1P18., Substituting the value of h2, we get, PA, , of, , .(2.11), , x p28 - hP18, , a liquid of sp. gr. 0.9, connected 1to a pipe containing, is, single, is 100 times the area, area ofthe reservoir, the, the, in, if, pipe, Find, the, pressure, shown in Fig. 2. 17., is 13.6., The specific gravity of mercury, 2.17., in, shown, Fig., manometer, the, reading, , Problem 2.14, as, , Sin, , column, , A, , manometer, , the tube for, , Solution. Given:, S =0.9, , Sp. gr. of liquid in pipe., , P, , Density, Sp. gr. of heavy liquid,, , S, , Density, , P2, , 900 kg/m*, = 13.6, , 40, , 13.6x 1000, , 20 cm, , A = 100, , Area of reservoir, , Area of right limb, , h, , Height of liquid,, , 20, , =, , cm, , =0.2, , m, , Fig. 2.17, , Rise of mercury in right limb,, , h2, , 40, , =, , PA, , Let, , Using equation (2.9),, , we, , 100, 0.4, , 100, , x 0.4[13.6 x, [133416, , 533.664, , 1000, , 8829], , 53366.4, , =0.4 m, , Pressure in pipe, , get, PA, , F, , cm, , +, , x, , 9.81, , 53366.4, , 1765.8, , A, , halP28 Pi8] + h>P28 -h,P18, , 900, , -, , x, , 9.81], , +0.4, , x, , 13.6, , x, , 1000 x 9.81, , 1765.8, , N/m =52134 N/m =5.21 N/cm., , Ans., , -, , 0.2, , x, , 900, , x, , 9.81