Question

The area of two holes $A$ and $B$ are $2a$ and $a$, respectively. The holes are at height $\left(H/3\right)$ and $\left(2H/3\right)$ from the surface of water. Find the correct options(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 $\sqrt{2}$ times the velocity of efflux at hole $A$.
• C. The discharge is same through both the holes.
• D. The discharge through hole $A$ is $\sqrt{2}$ times the discharge through hole $B$.

Answer 1

Answer: (B), (D)

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

We know,
$V_A=(2g\frac{H}{3}{)}^{1/2}$
$V_B=(\frac{4gH}{3}{)}^{1/2}=\sqrt{2}(2g\frac{H}{3}{)}^{1/2}=\sqrt{2}{V}_A$

$Q_A=V_A\left(2a\right)$
and $Q_B=V_B\left(a\right)=V_A\sqrt{2}\left(a\right)$
$\Rightarrow \frac{Q_A}{Q_B}=\sqrt{2}$