Question

To estimate aerodynamic loads on an aircraft flying at 100 km/h at standard sea-level conditions, a one-fifth scale model is tested in a variable-density wind tunnel ensuring similarity of inertial and viscous forces. The pressure used in the wind tunnel is 10 times the atmospheric pressure.
Assuming ideal gas law to hold and the same temperature conditions in model and prototype, the velocity needed in the wind tunnel test-section is ______________. 
 

• A. 25 km/h
• B. 50 km/h
• C. 100 km/h
• D. 20 km/h

Hint:

For Reynolds number matching in wind tunnels: increase pressure → reduce required velocity; reduce model size → increase required velocity.

Answer 1

The Correct Option is B

Step 1: Use similarity of Reynolds number and Mach effects.
The question requires similarity of inertial and viscous forces → maintain same Reynolds number. At equal temperatures, density varies directly with pressure using ideal gas law.

Step 2: Pressure ratio.
Wind tunnel pressure = 10 × atmospheric pressure → density becomes 10 times.

Step 3: Velocity scaling.
Model scale = 1/5.
For Reynolds number matching: \[ V_{\text{model}} = \frac{L_{\text{prototype}}}{L_{\text{model}}} \cdot \frac{\rho_{\text{prototype}}}{\rho_{\text{model}}} \cdot V_{\text{prototype}} \] \[ V_{\text{model}} = 5 \times \frac{1}{10} \times 100 = 50\ \text{km/h} \]

Step 4: Conclusion.
Velocity required in the wind tunnel = 50 km/h.

Final Answer: (B) 50 km/h