A prototype sphere flows through atmospheric air at Vp = 50 m/s (112 mph). We wi

Question

A prototype sphere flows through atmospheric air at Vp = 50 m/s (112 mph). We wish to build a 1:10 scale model in a wind tunnel so that Dm = Dp/10. Assuming the same air density and air viscosity between the model and prototype, i.e., ?m = ?p and ?m = ?p, what does the velocity of the wind tunnel, Vm, have to be to maintain similarity with the prototype? Show your work and how you determined Vm. If you have time, show that if this similar condition is met, then in this case, FD,m = FD,p.

Explanation / Answer

We have Froude Number similarity =>Vm/sqrt(Dm) = Vp/sqrt(Dp) =>Vm = Vp*sqrt(Dm/DP) = 50*sqrt(1/10) = 15.8114 m/s

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