Physics - Fluid Question with Solution | TestHub

Velocity of efflux from hole P at depth $2h$ is $v_P=\sqrt{2g(2h)}=2\sqrt{gh}$

Velocity of efflux from hole Q at depth $8h$ is $v_Q=\sqrt{2g(8h)}=4\sqrt{gh}$

Area of square hole P is $A_P=a^2$

Area of circular hole Q is $A_Q=\pi r^2$

Since the volume of water flowing out per second is the same for both holes:

$A_P{v}_P=A_Q{v}_Q$

$a^2(2\sqrt{gh})=(\pi r^2)(4\sqrt{gh})$

$a^2=2\pi r^2$

$a=r\sqrt{2\pi }$

Answer: $r\sqrt{2\pi }$