Question

A flat plate of 0.15 m\(^2\) is pulled at 20 cm/s relative to another plate, fixed at a distance of 0.02 cm from it with a fluid having \( \mu = 0.0014 \, \text{Ns/m}^2 \) separating them. The power required to maintain the motion is ...........

• A. 0.014 W
• B. 0.021 W
• C. 0.035 W
• D. 0.042 W

Hint:

Use Newton's law of viscosity to relate force and velocity gradient when dealing with fluid layers.

Answer 1

The Correct Option is D

Given:
Area \( A = 0.15 \, \text{m}^2 \)
Velocity \( V = 20 \, \text{cm/s} = 0.2 \, \text{m/s} \)
Separation \( y = 0.02 \, \text{cm} = 0.0002 \, \text{m} \)
Viscosity \( \mu = 0.0014 \, \text{Ns/m}^2 \)
Shear force \( F = \mu \cdot A \cdot \frac{V}{y} \)
\[ F = 0.0014 \cdot 0.15 \cdot \frac{0.2}{0.0002} = 0.0014 \cdot 0.15 \cdot 1000 = 0.21 \, \text{N} \]
Power \( P = F \cdot V = 0.21 \cdot 0.2 = 0.042 \, \text{W} \)
\[ \boxed{P = 0.042 \, \text{W}} \]