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
h_A be the pressure in terms of height of fluid in the pipe at point A
h_B 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
h_A be the pressure head in terms of height of fluid in the pipe at point A
h_B 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
h_A be the pressure head in terms of height of fluid in the pipe at point A
h_B 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