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Question

Water from a tap emerges vertically downwards with an initial speed of 1.0ms1. The cross-sectional area of the tap is 104m2. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15m below the tap is (g=10ms2)

A
5.0×104m2
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B
1.0×105m2
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C
5.0×105m2
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D
2.0×105m2
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Solution

The correct option is B 5.0×105m2
Volume flow rate =104m3sec
ΔP=ρgh=103kgm3×10m2s×0.15
ΔP=1500Pa
ΔP=12ρ(v22v12)
1500=12×103(v21)
v=2ms
By equation of continuity,
A1v1=A2v2
104×1=A2×2
A2=5×105m2

956986_794446_ans_c6cb5b2e8f6e4437bbd47de2382b1031.PNG

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