Page 50 - ebook fluid mechanics_finalize

FLUID MECHANICS

b. Differential U-Tube Manometer

It is a device used for measuring the difference of pressures, between two points in

a pipe, or in two different pipes. A differential manometer consists of a U-tube, containing

a heavy liquid with two ends connected to two different points. We are required to find

the difference of pressure at these two points, as shown in Figure 3.11. A differential
manometer is connected to two different points A and B.

Figure 3.11 : Differential Manometer

Pressure p at C = Pressure p at D
C
D
Pressure in the left-hand limb above the datum line

p = p at A +Pressure due to depth h of fluid P
A
C
p = p +  P h ; p = p +  P gh
A
C
A
C
Pressure in the right-hand limb above the datum line

p = p at B + Pressure due to depth h of fluid Q + Pressure due to depth h of
2
B
D
1
fluid P
p = p +  Q h +  P h = p +  Q gh +  P gh
2
1
B
2
B
D
1
Since, p = p p +  P gh = p +  Q gh +  P gh
C
D
B
A
2
1

p − p =  gh +  gh −  gh
A B Q 1 P 2 P

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