Discussion
A one-eighth scale model of a car is to be tested in a wind tunnel. If the air velocity over the car is 16 m/s, what should be the air velocity (in m/s) in the wind tunnel in order to achieve similarity between the model and the prototype?
Answer: D
The tunnel speed should be 128 m/s.
For flow around a car the governing similarity parameter is the Reynolds number. With the same fluid, air, in the tunnel, \(\nu\) is unchanged, so
\[ \begin{aligned} V_m L_m &= V_p L_p \\ V_m &= 16 \times \frac{L_p}{L_m} = 16 \times 8 = 128\ \text{m/s} \end{aligned} \]
16 m/s would keep the speed but not the Reynolds number, and 2 m/s scales the speed down instead of up. 64 m/s would match Reynolds number only for a quarter-scale model. (At 128 m/s compressibility starts to matter, which is why real tunnel tests often relax full Reynolds matching.)
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