GATE 2021 AE – Question 38
To estimate loads on an aircraft flying at 100 km/h at standard sea level, a one-fifth scale model is tested in a variable-density tunnel at ten times atmospheric pressure. Assuming ideal gas, equal temperature and Reynolds similarity, the tunnel speed is
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Correct answer: (B) 50 km/h
Explanation
For a model test to represent the full-scale aircraft, the **Reynolds numbers** must be equal:
$$\frac{\rho_mV_mL_m}{\mu_m}=\frac{\rho_pV_pL_p}{\mu_p}.$$
**Conditions.**
- The temperature is the same, so the viscosity $\mu$ is the same for the model and the prototype.
- The air is an ideal gas at equal temperature, so the density is proportional to the pressure. The model is tested at ten times atmospheric pressure, so $\rho_m=10\rho_p$.
- The model is one-fifth scale, so $L_m=L_p/5$.
**Solve for the tunnel speed:**
$$V_m=V_p\,\frac{\rho_p}{\rho_m}\,\frac{L_p}{L_m}=100\times\frac1{10}\times5=\mathbf{50\ km/h}.$$