An airplane wing of (3 mathrm{~m}) chord length moves through still air at (15^{circ} mathrm{C}) and (101.3

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An airplane wing of \(3 \mathrm{~m}\) chord length moves through still air at \(15^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa}\) at a speed of \(320 \mathrm{~km} / \mathrm{h}\). A 1:20 scale model of this wing is placed in a wind tunnel, and dynamic similarity between model and prototype is desired.

(a) What velocity is necessary in a tunnel where the air has the same pressure and temperature as that in flight?

(b) What velocity is necessary in a variable-density wind tunnel where absolute pressure is \(1400 \mathrm{kPa}\) and temperature is \(15^{\circ} \mathrm{C}\) ?

(c) At what speed must the model move through water \(\left(15^{\circ} \mathrm{C}\right)\) for dynamic similarity?

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