Question

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Net force (reaction) $=F=F_B-F_A=\frac{d{p}_s}{dt}-\frac{d{p}_A}{dt}$

$=a{v}_B\rho \times v_B-a{v}_A\rho \times v_A\therefore F=a\rho (v_B^2-v_A^2)\cdots \left(i\right)$

According to Bernoulli's theorem

$P_A+\frac{1}{2}\rho v_A^2+\rho gh=p_B+\frac{1}{2}\rho v_B^2+0\Rightarrow \frac{1}{2}\rho (v_B^2-v_A^2)=\rho gh\Rightarrow v_B^2-v_A^2=2gh$

From equation (i), $F=2a\rho gh$