Question

Consider a cylindrical tank of radius $1 m$ is filled with water. The top surface of water is at $15 m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5 m$ from the bottom. A force of $5 × 10^5 N$ is applied on the top surface of water using a piston. The speed of efflux from the hole will be:

(Given atmosphere pressure $P_A = 1.01 × 10^5 Pa$, density of water $ρ_w 1000 Kg/m^3$ and gravitational acceleration $g = 10 m/s^2$)

• A. 11.6 m/s
• B. 10.8 m/s
• C. 17.8 m/s
• D. 14.4 m/s

Answer 1

Answer: (C)

17.8 m/s

Answer 2

Apply Bernoulli's theorem between Piston and hole $P_A +ρgℎ = P_0 + \frac{1}{2}ρv_e^2$

Assuming there is no atmospheric pressure on piston

$\frac{5×10^5}{π}+10^3×10×10 = 1.01×10^5+ \frac{1}{2}×10^3 ×v_e^2$

⇒ $v_e = 17.8 m/s$