GATE 2024 AE – Question 65
It is desired to estimate the aerodynamic drag, D, on a car traveling at a speed of 30 m/s. A one-third scale model of the car is tested in a wind-tunnel following the principles of dynamic similarity. The drag on the scaled model is measured to be $D_m$. The ratio $D/D_m$ is _________ (rounded off to 1 decimal place).
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Correct answer: 1.0 to 1.0
Explanation
Dynamic similarity needs the same Reynolds number, $\frac{\rho VL}{\mu}$. In the same fluid the model speed is $V_m = 3V = 90$ m/s. The drag is $D = C_D\frac{1}{2}\rho V^2L^2$ with the same $C_D$, so $\frac{D}{D_m} = \left(\frac{V}{V_m}\right)^2\left(\frac{L}{L_m}\right)^2 = \frac{1}{9} \times 9 = 1.0$.
Official GATE 2024 answer key: https://gate2026.iitg.ac.in/doc/download/2024/AEFinalAnswerKey.pdf