Answer to Question #211456 in Mechanics | Relativity for Aba

Question

The aerodynamic drag of a new sports truck is to be predicted at a speed of 50.0 km/h at an air temperature of 25°C. Automotive engineers build a one-sixth 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 10°C. Determine how fast the engineers should run the wind tunnel in order to achieve similarity between the model and the prototype, if the drag sensor read 80 N fine the drag force exerted on prototype. Properties for air at atmospheric pressure and T= 25 ºC, ρ=1.184kg/cm3 and μ=1.849*10^-5kg/m.s, similarity at T=10 ºC, ρ=1.22 kg/cm3 and μ=1.792*10^-5kg/m.s.

Answer 1

Solution:-

$V_p=50km/h$

$$\mu_m=1.792\times10^{-5}kg/m.s;\mu_p=1.849\times10^{-5}kg/m s$$

$$\rho_p =1.184kg/cm^3,\rho_m=1.22kg/m^3$$

$V_m=V_p\frac{\mu_m}{\mu_p}\times\frac{\rho_p}{\rho_m}\times\frac{L_p}{L_m}$

$V_m=50\times \frac{1.792\times10^{-5}}{1.849\times10^{-5}}\times\frac{1.184}{1.22}\times 6$

$V_m=282km/h$