Page 54 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 3.6

Oil

water

An inverted U tube as shown in the figure above is used to measure the pressure

difference between two points A and B which has water flowing. The difference in level h

= 0.3 m, a = 0.25 m and b = 0.15 m. Calculate the pressure difference PB – PA if the top of
the manometer is filled with oil relative density 0.8.

Solution :

Putting  W = 10 kg / m 3 , b = . 0 15m , a = . 0 25m , h = 3 . 0 m :
3
 = S = 8 . 0 x 10 = 800kg / m
3
3
oil W
In either case, the pressure at X-X will be the same in both limbs, so that

p = p
XX XX

p XX = p −  W ga −  oil gh = p −  W g (b + ) h
A
B
p − p =  g (b+ ) h −  ga  gh
−
B A W W oil
p − p =  g (b+ ) h −  ga  gh
−
B A W W oil
= 9810 . 0 ( 15 + ) 3 . 0 − 9810x . 0 25 − 800x . 9 81x 3 . 0

= 4414 5 . − 2452 5 . − 2354 4 .

2
= − 392 4 . N / m

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