Answer to Question #130131 in Mechanics | Relativity for Ariyo Emmanuel

Question

The aerodynamic drag of a new sports car is to be predicted at a speed
of 50.0 mi/h at an air temperature of 25 °C. Automotive engineers build
a one-fifth scale model of the car to test in a wind tunnel. It is winter and
the wind tunnel is located in an unheated building; the temperature of
the wind tunnel air is only about 5 °C. Determine how fast the engineers
should run the wind tunnel in order to achieve similarity between the
model and the prototype. Properties of air at 25 °C are density 1.184
kg/m3 and dynamic viscosity is 1.849 * 10-5
, at 5 °C density is 1.269
kg/m3 and dynamic viscosity 1.754 * 10-5.

Answer 1

$$Re_m=\frac{\rho_mV_mL_m}{\mu_m}=Re_p=\frac{\rho_pV_pL_p}{\mu_p}$$

$$V_m=V_p\left(\frac{\mu_m}{\mu_p}\right)\left(\frac{\rho_p}{\rho_m}\right)\left(\frac{L_p}{L_m}\right)\\V_m=50\left(\frac{1.754}{1.849}\right)\left(\frac{1.184}{1.269}\right)\left(5\right)=221\frac{mi}{h}$$