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Question

# A closed tube filled with water is rotating about an axis as shown in figure. The pressure difference PA−PC is

A
12×103 N/m2
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B
24×103 N/m2
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C
6×103 N/m2
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D
20×103 N/m2
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Solution

## The correct option is B −24×103 N/m2Pressure at any point, x distance away from the axis in a rotating fluid is given by: P=P0+12ρω2x2 where, P0→ Pressure at the point on the axis at the same level i.e at point B in this case At point A, PA=P0+12×1000×(2)2×22 ∵ω=2 rad/s, ρ=1000 kg/m3, x=2 m ⇒PA=P0+8×103 ...(1) Similarly at point C, PC=P0+12×1000×22×42 ∵x=4 m PC=P0+32×103 ...(2) On subtracting Eq.(2) from Eq.(1) PA−PC=−24×103 N/m2 The pressure difference between point A and C is negative, hence PC>PA.

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