Fluid Mechanics Viscosity Question 281

Question: A cylindrical vessel contains a liquid of density$ \rho $ filled upto a height h. The uper surface of the liquid is in contact with a pistion of mass m and area of cross-section A. A small hole is drilled at the bottom of the vessel. (Neglect the viscous effects) The speed with which the liquid comes out of the hoe is:

Options:

A) $ \sqrt{2}gh $

B) $ \sqrt{2}g\left( h+\frac{m}{\rho A} \right) $

C)$ \sqrt{g\left( h+\frac{m}{\rho A} \right)} $

D) $ \sqrt{g\left( h+\frac{2m}{\rho A} \right)} $

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Answer:

Correct Answer: B

Solution:

[b] $ h\rho g+\frac{mg}{A}=\frac{1}{2}\rho v^{2} $