Question

There are two holes, each of cross-sectional area $a$, on the opposite sides of a wide rectangular tank containing a liquid of density $\rho$ . When the liquid flows out of the holes, the net force on the tank is :

( $h$ is the vertical distance between the two holes )

• A. $2a\rho gh$
• B. $4a\rho gh$
• C. $0.5a\rho gh$
• D. $\rho gh$

Answer 1

Answer: (A)

$2a\rho gh$

For 1st hole,
Velocity of water from P = $\sqrt{2gH}=V_1$
Q = AV
Force exerted by water on the tank = $\rho a{V}_1^2$
$=2\rho agH$-----------------(1)
Similarly for 2nd hole,
Velocity= $\sqrt{2g(H+h)}=V_2$
Q = $a{V}_2^2$
From exerted = $2\rho ag(H+h)$---------------(2)
Net force on the tank
$=2\rho ag(H+h)-2\rho ag\left(H\right)$
$=2a\rho gh$