Question

A large tank is filled with water (density $\rho$), upto height $h$. Water is coming out from section (4). Fluid pressure at section (3) at the instant shown is (Given : Area $A_2=A_4=2A_3$ and $A_2,A_3,A_4$ are very small as compared to $A_1$; atmospheric pressure $=P_0$. Assume water to be non-viscous and incompressible)

• A. $P_0+\rho gh$
• B. $P_0-\rho gh$
• C. $P_0-2\rho gh$
• D. $P_0-3\rho gh$

Answer 1

The correct option is D $P_0-3\rho gh$

Velocity of efflux can be calculated for section (4) as it is exposed to atmospheric pressure. By applying Bernoulli's equation on same level, we can find velocity of efflux.
Velocity of efflux at section (4) is $v=\sqrt{2gh}$
$A_3{v}_3=A_4{v}_4$ (continuity equation)
$\Rightarrow v_3=2v_4$
Applying Bernoulli's equation between section (3) and (4)
$P_3+\frac{1}{2}\rho v_3^2=P_4+\frac{1}{2}\rho v_4^2$
$\Rightarrow P_3+\frac{1}{2}\rho (2\sqrt{2gh}{)}^2=P_0+\frac{1}{2}\rho (\sqrt{2gh}{)}^2$
$\Rightarrow P_3=P_0-3\rho gh.$