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Q.

A horizortal-oriented tube AB of length l :2.5 m rotates with a constant angular velocity ω = 5 rad/s about a stationary vertical axis OO' passing through the end A(figure). Initially the tube is filled with an ideal fluid. The end A of the tube is open, the closed end B has a very small orifice. Find the velocity of the fluid (in m/s) relative to the tube when the liquid column length in tube reduces to h=1 m.

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answer is 25.

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Detailed Solution

Using Bernoulli's theorem, we havePB=Patm+12ρv2.....(i) and  PB−Patm=∫l−hl dr⋅ρ⋅ω2x=ρω22l2−(l−h)2PB−Patm=12ρω22l−h2.....(ii) From Eqs. (i) and (ii), 12ρω22l−h2=12ρv2⇒v=ωh2lh−1=5×2.52×2.51−1=25m/s
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A horizortal-oriented tube AB of length l :2.5 m rotates with a constant angular velocity ω = 5 rad/s about a stationary vertical axis OO' passing through the end A(figure). Initially the tube is filled with an ideal fluid. The end A of the tube is open, the closed end B has a very small orifice. Find the velocity of the fluid (in m/s) relative to the tube when the liquid column length in tube reduces to h=1 m.