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Question

Water flows through a horizontal tube as shown in the figure. If the difference of heights of water column in the vertical tubes is 15 cm, and the areas of cross-section at A and B are 4 cm2 and 2 cm2 respectively, find the rate of flow of water across any section. (Take g=10 m/s2)


A
4×104 m3/s
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B
3×104 m3/s
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C
2×104 m3/s
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D
None of these
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Solution

The correct option is A 4×104 m3/s
Using continuity equation

VAaA=VB×aB

VBVA=aAaB ......(1)

Using Bernoulli’s equation between A and B

12ρV2A+ρgzA+PA=12ρV2B+ρgzB+PB

As both A and B are at same level

zA=zB

12ρV2A+PA=12ρV2B+PB

PAPB=12×ρ(V2BV2A)

ρgΔh=12ρ{(VBVA)21}V2A

From equation (1),

ρgΔh=12ρ{(aAaB)21}V2A

2×10×(15×102)=(4×1042×104)21V2A

VA=1 m/s

Rate of flow =VAaA=1×(4×104)

=4×104 m3/s

Hence, option (A) is correct.
Shortcut:
Q=aAaBa2Aa2B2gh

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