Page 47 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 1

A U-tube manometer similar to that shown below is used to measure the gauge pressure

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3
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of water (mass density ρ = 1000 kg /m ). If the density of mercury is 13.6 × 10 kg /m ,
calculate the gauge pressure at A if h1 = 0.45 m and h2 = 0.7 m above BC.

Solution :

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Considering  hg = 13 6 .  10 kg / m ,  W = 0 . 1  10 kg / m , h = . 0 45 m h = 7 . 0 m
,
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1
the pressure at left-hand limb;
p = Pressure, p at A + Pressure due to depth, h of water
A
1
B
= p +  W h
1
A
= p +  W gh
A
1

the pressure at right-hand limb;

p = Pressure p at D + Pressure due to depth h of mercury
C
2
D
p = 0 + hg h = 0 +  hg gh
C
2
2
Since p = p …………… p +  W gh =  hg gh
C
B
2
1
A
p =  Hg gh −  w gh 13 = 6 . 10  . 9 81 7 . 0 − 0 . 1  10  . 9 81 . 0 45
3
3
1
A
2
2
3
2
= 88976 7 . N / m = 88 . 97  10 N / m

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