Question

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 $ m^2 $. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 $ m/s^2 $)

• A. 3 m/s
• B. 5 m/s
• C. 2 m/s
• D. 4 m/s

Hint:

Use Bernoulli's equation to relate the pressure, velocity, and height at two points in a fluid flow. Consider the pressure due to the applied load and the hydrostatic pressure.

Answer 1

The Correct Option is D

Apply Bernoulli equation between points 1 and 2. 

\( P_1 + \frac{1}{2} \rho v_1^2 + \rho g h = P_2 + \frac{1}{2} \rho v_2^2 + 0 \) 

\( P_0 + \frac{mg}{A} + \rho g \frac{70}{100} = P_0 + \frac{1}{2} \rho v_2^2 \) \( \frac{5000}{0.5} + 10^3 \times 10 \times \frac{70}{100} = \frac{1}{2} \times 10^3 v_2^2 \) \( 10^4 + 10^3 \times 7 = \frac{10^3}{2} v_2^2 \) \( v_2^2 = 16 \) \( v_2 = 4 m/s \) 

As the tank area is large \( v_1 \) is negligible compared to \( v_2 \).