Question

Water is flowing steadily in a river. A and B are the two layers of water at heights $40 \text{ cm}$ and $90 \text{ cm}$ from the bottom. The velocity of the layer A is $12 \text{ cm/s}$. The velocity of the layer B is

• A. $15 \text{ cm/s}$
• B. $21 \text{ cm/s}$
• C. $27 \text{ cm/s}$
• D. $36 \text{ cm/s}$

Hint:

Velocity gradient ($dv/dy$) is constant for ideal steady river flow.

Answer 1

The Correct Option is C

Step 1: Concept
For streamline flow in a river, velocity increases linearly with distance from the stationary bottom ($v \propto y$).

Step 2: Meaning
$v_1/y_1 = v_2/y_2$.

Step 3: Analysis
$12 / 40 = v_B / 90 \implies v_B = (12 \times 90) / 40 = 1080 / 40 = 27$.

Step 4: Conclusion
The velocity of layer B is $27 \text{ cm/s}$. Final Answer: (C)