Page 51 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 1

A U tube manometer measures the pressure difference between two points A and B in a

liquid. The U tube contains mercury. Calculate the difference in pressure if h = 2.0 m, h2 =
0.35 m and h1 = 0.5 m. The liquid at A and B is oil ( s = 0.85 ) and the specific gravity of

mercury is 13.6.

Solution :

Since C and D are at the same level in the same liquid at rest

Pressure p at C = Pressure p at D
C
D

For the left hand limb, p = p +  oil h
A
C
For the right hand limb, p = p +  oil h +  hg h
B
2
D
1
Since, p = p D
C

p +  h = p +  h +  h
A oil B oil 2 hg 1

Pressure difference, p − p
A
B

p − p =  h +  h −  h
B
hg
A
1
2
oil
oil
= . 0 85 (9810 )( 35.0 ) 13+ 6 . (9810 )( ) 05.0 − . 85 (9810 )( 0.2 )

52949= . 47 N / m = 52 . 949 kN / m
2
2

40