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) is:

(Given : $A_2=A_4=2A_3$ and $A_2,A_3,A_4<<A_1$ ; 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

Answer: (D)

$P_0-3\rho gh$

Velocity of efflux at section (4 or D) is $v_4=\sqrt{2gh}$

Applying equation of continuity between section(3) and (4)

$A_3{v}_3=A_4{v}_4=2A_3{v}_4$

$\therefore v_3=2v_4$

Applying Bernoulli's equation between section (3 or C) and (4 or D)

$P_3+\frac{1}{2}{v}_3^2=P_4+\frac{1}{2}{v}_4^2=P_0+\frac{1}{2}{v}_4^2$

$\therefore P_3+\frac{1}{2}\rho (2v_4{)}^2=P_0+\frac{1}{2}\rho v_4^2$

$\therefore P_3=P_0-\frac{1}{2}\times 3\rho \times {\sqrt{2gh}}^2$

$\therefore P_3=P_0-3\rho gh$