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MHT CET 2025 (5 May, Shift 2) · Velocity of Efflux (Torricelli)

Velocity of Efflux (Torricelli) question from MHT CET 2025 (5 May, Shift 2)

Q5MHT CET 2025 · 5 MAY · SHIFT 2Difficult

Velocity of Efflux (Torricelli)

A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' aa ' and hole ' QQ ' is a circle of radius ' rr '. The water flowing out per second from both the holes is same, then side ' aa ' of hole ' PP ' is

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Answer: (b)

  1. Volume flow rate Q=(area)×vQ = (\text{area}) \times v with efflux speed v=2gdv = \sqrt{2gd} at depth dd.
  2. Equal flow: a22g(2h)=πr22g(8h)a^2\sqrt{2g(2h)} = \pi r^2\sqrt{2g(8h)}
  3. a2=πr28h2h=2πr2a^2 = \pi r^2\sqrt{\frac{8h}{2h}} = 2\pi r^2
  4. So the answer is (b) a=r2πa = r\sqrt{2\pi}.
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