Question

If \( P_{\text{in}} = 1.2 \, \text{Pa} \) and \( P_{\text{out}} = 1.0 \, \text{Pa} \) are the average pressures at inlet and outlet respectively for a fully-developed flow inside a channel having a height of 50 cm, then the absolute value of average shear stress (in Pa) acting on the walls of the channel of length 5 m is

• A. 0.005
• B. 0.02
• C. 0.01
• D. 0.05

Hint:

In fully-developed flow, the average shear stress can be calculated using the pressure difference, channel length, and channel height.

Answer 1

The Correct Option is C

For a fully-developed flow in a channel, the average shear stress can be calculated using the following formula: \[ \tau_{\text{avg}} = \frac{P_{\text{in}} - P_{\text{out}}}{L} \times \frac{h}{2}, \] where \( P_{\text{in}} \) and \( P_{\text{out}} \) are the inlet and outlet pressures, \( L \) is the length of the channel, and \( h \) is the height of the channel. Substituting the given values: \[ \tau_{\text{avg}} = \frac{1.2 - 1.0}{5} \times \frac{0.5}{2} = \frac{0.2}{5} \times 0.25 = 0.01 \, \text{Pa}. \]

Step 1: Apply the formula.
The formula relates the pressure difference and the dimensions of the channel to calculate the average shear stress.

Step 2: Conclusion.
Thus, the absolute value of the average shear stress is \( 0.01 \, \text{Pa} \).

Final Answer: \text{(C) 0.01}