# Similitude, Dimensional analysis for fluid mech.

1. Nov 3, 2013

### hqjb

1. The problem statement, all variables and given/known data

The aerodynamic drag of a new sports car is to be predicted at a
speed of 100 km/hr at air temperature of 25°C. Automotive engineers
build a ¼ scale model of the car to test in a wind tunnel, where the air
temperature is 10°C. A drag balance is used to measure the drag, and
the moving belt is used to simulate the moving ground. Determine the
speed of the wind tunnel that the engineers must run in order to achieve
similarity between the model and prototype. (Note: the temperature in
this case only affects the properties of fluid only).

$V_m = ?$
$V_p = 100km/h$
$T_m = 10°C$
$T_p = 25°C$
$L_p/L_m = 4$

2. Relevant equations

$\frac{D}{\rho V^2L^2} = (\frac{\rho VL}{\mu},\frac{V}{\sqrt{gL}}, r/L)$

3. The attempt at a solution

$(\frac{\rho VL}{\mu})_p = (\frac{\rho VL}{\mu})_m$

and I use property tables to find the ρ and μ for the given temperatures...
I end up getting V_m = 400km/h when the answer is 365km/hr

Thanks!