Question

A cylindrical vessel contains a liquid of density $\rho$ up to height $h$. The liquid is closed by a piston of mass $m$ and area of cross section $A$. There is a small hole at the bottom of the vessel. The speed $v$ with which the liquid comes out of the hole is

• A. $\sqrt{2gh}$
• B. $\sqrt{2(gh+\frac{mg}{\rho A})}$
• C. $\sqrt{2(gh+\frac{mg}{A})}$
• D. $\sqrt{2gh+\left(\frac{mg}{A}\right)}$

Answer 1

The correct option is B $\sqrt{2(gh+\frac{mg}{\rho A})}$

Applying bernaulis theorem on the bottom of the piston and orifice

$(P_0+\frac{mg}{A})+O+O=P_0+\rho gh+\frac{1}{2}{\rho V}^2$

$\Rightarrow V=\sqrt{2(gh+\frac{mg}{\rho A})}$