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Q.

Water  (ideal fluid) is flowing through a horizontal tube having cross sectional areas of its two ends being A and A'  such that the ratio A/A'  is 5.If the pressure difference of water between the two ends is  3×105Nm−2, the velocity of water with which it enters the tube will be (neglect gravity effects)

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a

5ms−1

b

10ms−1

c

25ms−1

d

5010  ms−1

answer is A.

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Detailed Solution

According to Bernouli’s theoremP1+12ρv12=P2+12ρv22 From equation ,P1−P2=3×105,A1A2=5 According to equation of continuity A1v1=A2v2 Or,   A1A2=v2v1=5⇒v2=5v1From equation (i)P1−P2=12ρ(v22−v12) Or  3×105=12×1000(25v12−v12)⇒600=6v1×4v1 ⇒v12=25     ∴v1=5m/s
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