Question

The fluid dynamic characteristics of an airplane flying 240 mph at 10,000 ft are to be investigated with the aid of a 1 : 26 scale model. If the model tests are to be performed in a wind tunnel using standard air, what is the required air velocity in the wind tunnel? Is this a realistic velocity?

Answer 1

Answer:

3750 mph

Explanation:

From the dynamic similarity principle

R_E(model)= R_E

$\frac{V_{model}\rho_{model}l_{model}}{\mu_{model}} =\frac{V\rho l}{\mu}$

we can express the fluid velocity as

$V_{model}=\frac{\mu_{model}\rho V}{\mu \rho_{model}}\times\frac{l}{l_{model}}$

Now, from the table we can obtain the values of density and viscosity of at at 1000 ft altitude, and also values of dynamic viscosity and density of air at normal conditions and substitute them in previous equation.

$V_{model}=\frac{3.74\times10^{-7}(1.756)(240)(20)}{3.534\times10^{-7}(2.38\times10^{-3})}$

calculating we get

V_{model}= 3750 mph