Question

The area of two holes A and B are $2a$ and $a$ respectively. The holes are at height $\frac{H}{3}$ and $\frac{2H}{3}$ from the surface of water. Find the correct option(s)

• A. the velocity of efflux at hole B is 2 times the velocity of efflux at hole A
• B. the velocity of efflux at hole B is $\sqrt{2}$ time the velocity of efflux at hole A
• C. the discharge is same through both the holes
• D. the discharge through hole A is $\sqrt{2}$ time the discharge through hole B

Answer 1

Answer: (B), (D)

The correct options are
B the discharge through hole A is $\sqrt{2}$ time the discharge through hole B
D the velocity of efflux at hole B is $\sqrt{2}$ time the velocity of efflux at hole A

$V_A={\left(2g\frac{H}{3}\right)}^{\frac{1}{2}}$
$V_B=\left(\frac{4gH}{3}\right)=\sqrt{2}{\left(\frac{2gH}{3}\right)}^{\frac{1}{2}}=\sqrt{2}{V}_A$
$Q_A=V_A\left(2a\right)$
and $Q_B=V_B\left(a\right)=V_A\sqrt{2}\left(a\right)\Rightarrow \frac{Q_A}{Q_B}=\sqrt{2}$