Question

Water is poured in a tank through a cylindrical tube of area of cross-section \( A \) and ejecting water at a constant speed 4 m/s. The tank contains a hole of area \( \frac{A}{2} \) at the bottom. The level of water in the tank will not go up beyond

• A. 5.6 m
• B. 4.8 m
• C. 3.2 m
• D. 1.8 m

Hint:

Use the continuity equation and Bernoulli's principle for fluid flow problems to relate the rate of flow entering and exiting the system.

Answer 1

The Correct Option is C

The problem can be solved using the principle of conservation of mass. According to Bernoulli's equation, the rate of flow entering the tank must equal the rate of flow leaving the tank. - The rate of water entering the tank is: \[ Q_{\text{in}} = A \cdot v = A \cdot 4 \] where \( A \) is the cross-sectional area of the tube and \( v = 4 \, \text{m/s} \) is the velocity of water through the tube. - The rate at which water exits the tank is through the hole at the bottom with an area \( \frac{A}{2} \), and the flow speed \( v_2 \) is determined by the height of the water. Since the water is rising at a steady rate, we can calculate the equilibrium point where the outflow matches the inflow. By equating the inflow and outflow, we find that the maximum height of the water will be \( 3.2 \, \text{m} \). Thus, the correct answer is (C).