# Fluid mechanics- Dimensional analysis

1. Aug 8, 2012

### andyb1990

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

The drag force F on a car depends upon its speed V, length L, the density ρ of the air
and the dynamic viscosity of the air µ . Show that this statement regarding five
physical quantities can be re-written in terms of two independent non-dimensional
groups. Preferably using the method of sequential elimination of dimensions, find two
appropriate non-dimensional groups

I have got my two non- dimensional groups as (Dρ/µ^2) and (ρVL/µ)

FOR THE SECOND PART (BELOW) I AM UNSURE ON HOW TO ACHIEVE THE AIRSPEED IN THE TUNNEL

A car being developed for the Le Mans 24 Hour Endurance Race is to have a top speed
of 230 mph assuming an air density of 1.2kg/m^3 and dynamic viscosity of 1.9 x 10^-5
Pa.s. Tests carried out on a 1/4-scale model car in a pressurized and cooled wind tunnel
in which the air density is 5kg/m^3 and the dynamic viscosity is 1.1 x 10^-5
Pa.s give a drag force of 469 N. What must be the airspeed in the wind tunnel for dynamic similarity (at top speed for the full-size car)? Calculate the drag force on the full size car
and the power needed to run at top speed.

2. Relevant equations

3. The attempt at a solution

for part a i have the two non dimensional groups shown above and for part (b) I have worked out the drag force using the equation

Df= (ρm/ρf)* (μf/μm)^2 * Dm

(f= full scale, m= model)

It would be of great help if someone could help me understand how to calculate the windspeed and power needed?