Question

Three layers of liquid are flowing over a fixed solid surface as shown below. The correct order of velocity of liquid in these layers is: \includegraphics[]{127.png}

• A. \( V_1>V_2>V_3 \)
• B. \( V_1 = V_2 = V_3 \)
• C. \( V_3>V_2>V_1 \)
• D. \( V_3>V_1>V_2 \)

Hint:

In fluid dynamics, the velocity of a liquid flowing over a solid surface follows \( V_{{top}}>V_{{middle}}>V_{{bottom}} \) due to the no-slip condition.

Answer 1

The Correct Option is C

Step 1: Apply the No-Slip Condition - The layer of liquid in direct contact with the solid surface has zero velocity. - As we move away from the surface, velocity increases. Step 2: Identify Velocity Profile From the diagram:
- Layer 1 (bottom-most, near the solid surface) → Lowest velocity (\( V_1 \)).
- Layer 2 (middle layer) → Higher velocity (\( V_2 \)).
- Layer 3 (top-most, farthest from the surface) → Highest velocity (\( V_3 \)). Step 3: Correct Order of Velocities \[ V_3>V_2>V_1 \] Thus, the correct answer is \( V_3>V_2>V_1 \).