Fluid Mechanics

JEE Main level, single correct, medium

84 of 192

Question 84 of 192

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.80.8 ). The height of water is 3 m3 \mathrm{~m} and that of kerosene 2 m2 \mathrm{~m}. When the hole is opened the velocity of fluid coming out from it is nearly: (take g=10 ms−2\mathrm{g}=10 \mathrm{~ms}^{-2} and density of water =103 kg m−3)\left.=10^3 \mathrm{~kg} \mathrm{~m}^{-3}\right)

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Answer: (B) 9.6 ms−19.6 \mathrm{~ms}^{-1}

h1ρ1g+h2ρ2g=12ρ1v2⇒1000×10×3+800×10×2=12×1000×v2⇒v2=2×460001000⇒v=92=9.6 m/s\begin{aligned} &h_1 \rho_1 g+h_2 \rho_2 g=\frac{1}{2} \rho_1 \mathrm{v}^2 \\ &\Rightarrow 1000 \times 10 \times 3+800 \times 10 \times 2 \\ &=\frac{1}{2} \times 1000 \times \mathrm{v}^2 \\ &\Rightarrow \mathrm{v}^2=2 \times \frac{46000}{1000} \\ &\Rightarrow \mathrm{v}=\sqrt{92}=9.6 \mathrm{~m} / \mathrm{s} \end{aligned}

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