Question

You are to conduct a wind tunnel testing of a new football design. It is known that you need to maintain Reynold’s number, Re, and Strovhal Number, St, similarity for the testing. Based on a standard college quarterback, prototype velocity, V = 40mph and rotation, ω = 300rpm. The prototype football has a diameter of D=7inches. Due to instrumentation requirements, the model used in the wind tunnel must be twice as big as the prototype. Dmodel=14inches.

a) Determine the required model freestream velocity in ft/s.

b) Determine the model angular velocity in rpm.

Strovhal number, St=(ωD/V) Reynolds number, Re=(VD/νfluid), you can assume air properties are the same for the prototype and for the wind tunnel air.

Answer 1

Using the formula for Reynold's number,

$\small V_{1}D_{1}=V_{2}D_{2}$

$\small 40\times 7=V_{2}\times 14$

$\small V_{2}=20mph = 0.018 ft/s$

Now using Strovhal number,

$\small \frac{\omega _{1}D_{1}}{V_{1}} = \frac{\omega _{2}D_{2}}{V_{2}}$

$\small \frac{300\times 7}{40} = \frac{\omega _{2}\times 14}{20}$

$\small \omega _{2}=75rpm$