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

Options

A. `gh rho a`
B. `2gh// rho a`
C. `2 rho agh`
D. `rho gh//a`

Answer

C

Explanation

Net force on container -
`F=F_B-F_A = (dp_B)/(dt)-(dp_A)/(dt)`
`= a v_B rhoxx v_B-av_A rho xx v_A`
`a rho(v_B^2-v_A^2)`
According Bernoulli.s Principle -
`P_A+1/2 rho v_A^2-rho gh=P_B+1/2 rho v_B^2`
`implies v_B^2-v_A^2=2gh`
`:. F= - a rho xx 2gh=- 2a rho gh`
(Neglect -ve sign it shows direction only).