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JEE Main 2014 (11 Apr, Shift 1) · Velocity of Efflux (Torricelli)

Velocity of Efflux (Torricelli) question from JEE Main 2014 (11 Apr, Shift 1)

Q28JEE Main 2014 · 11 APR · SHIFT 1Medium

Velocity of Efflux (Torricelli)

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 ms−2{}^{-2} and density of water = 103 kg m−3{}^{-3})

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Answer: (b)

  1. Gauge pressure at the bottom: ρkghk+ρwghw=800(10)(2)+1000(10)(3)=46000 Pa\rho_k g h_k + \rho_w g h_w = 800(10)(2) + 1000(10)(3) = 46000\text{ Pa}
  2. Bernoulli at the hole: 12ρwv2=46000⇒v2=92\frac{1}{2}\rho_w v^2 = 46000 \Rightarrow v^2 = 92
  3. v≈9.6 m/sv \approx 9.6\text{ m/s}
  4. So the answer is (b) 9.6 m s−1^{-1}.
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