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Fluid Mechanics

Differential Manometer

1.Introduction

  • Differential manometers are used to measure the difference of pressures between two points in a pipe or in two different pipes. There are two types of differential manometers.
            1. U-tube upright differential manometer
            2. U-tube inverted differential manometer
1.2  U-tube Upright Differential Manometer
  • It is used to measure pressure difference at two points in a pipe or between two pipes at different levels.
Case 1 - U-tube upright differential manometer connected at two points in a pipe at same level
  • The construction and arrangement of a manometer connected at two different points, A and B, of a pipe is shown in figure 1

                             Fig.1U-tube upright differential manometer
  
Let,         
ρ1 = density of liquid flowing in the pipeline
ρ2 = density of manometer liquid (assume mercury)
S = Specific gravity of liquid for which pressure has to be determined
S1 = Specific gravity of manometer liquid
hA be the pressure in terms of height of fluid in the pipe at point A
hB be the pressure in terms of height of fluid in the pipe at point B
h is the distance of mercury level in the right limb from the datum line XX
h1 is the height of manometer liquid level in the right limb from the centre of pipe at point B.









Case 2 - U-tube upright differential manometer connected between two pipes at different levels and carrying different fluids

Fig. 2 Vertical differential manometer (pressure difference between two pipes)

Let,         
S1 = Specific gravity of liquid in pipe A
S2 = Specific gravity of liquid in pipe B
S = Specific gravity of manometer liquid
hA be the pressure head in terms of height of fluid in the pipe at point A
hB be the pressure head in terms of height of fluid in the pipe at point B
h is the distance of mercury level in the right limb from the datum line XX
h1 is the height of manometer liquid level in the left limb from the from the datum line XX
h2 is the height of manometer liquid level in the right limb from the from the centre of pipe at point B.








2  U-tube Inverted Differential Manometer
  • In such types of manometers light fluids for e.g.oil is used as manometer fluid.
  • In the previous derivation, the term (hS) is added, but here in the left and right limb equations, it is necessary to subtract (hS) term.


Fig. 3 Inverted differential manometer

Let,         
S1 = Specific gravity of liquid in pipe A
S2 = Specific gravity of liquid in pipe B
S = Specific gravity of manometer liquid
hA be the pressure head in terms of height of fluid in the pipe at point A
hB be the pressure head in terms of height of fluid in the pipe at point B
h is the distance of manometer liquid level in the right limb from the datum line XX
h1 is the height of manometer liquid level in the left limb from the from the datum line XX
h2 is the height of manometer liquid level in the right limb from the from the centre of pipe at point B








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