Physics - Fluid Question with Solution | TestHub

Total pressure at the bottom of the tank is given by:

$P_{\text{total}}=P_{\text{atm}}+\rho gh$

Given $P_{\text{total}}=4H$ and $P_{\text{atm}}=H$:

$4H=H+\rho gh$

$\rho gh=3H$

$gh=\frac{3H}{\rho }$

According to Torricelli's law, the velocity of efflux $v$ from a hole at the bottom of the tank is:

$v=\sqrt{2gh}$

Substituting the value of $gh$:

$v=\sqrt{2\left(\frac{3H}{\rho }\right)}=\sqrt{(}\frac{6H}{\rho })$

Answer: $\sqrt{\frac{6\mathrm{H}}{\rho }}$