A car travels at 70 mph to the right assumed nx direction on

A car travels at 70 mph to the right (assumed +nx direction) on a level road on a calm, 80 deg. F day. You may assume the ambient pressure is 14.7 psia.

First, assume the car is moving and the ambient air is stationary.

i) Find the relative air velocity far away from the car.
ii) What is the pressure far away from the car?
iii) Find the absolute air velocity on the front bumper of the car, which is assumed to be a stagnation point in the flow.
iv) Find the relative velocity at this same point on the bumper.
v) Find the total pressure at this same point on the bumper.
vi) Find the static pressure at a location on the top of the car where the local relative air velocity is
100 mph in the nx direction.
vii) Find the local absolute velocity of the air at this same location on the top of the car.

Now, assume the car is stationary in a wind tunnel with 70 mph air (in the nx direction) at the same
conditions given in problem (4) flowing over the car, which faces into the wind. Which answers would change?

Solution

70 mph = 102.67 ft/s
At 80 F for air, density rho = 0.074 lb/ft^3

i)
Relative air velocity far away from the car = 0 (since calm air away from the car is not affected by its motion)

ii)
Pressure far away from the car = 14.7 psia (= atmospheric pressure, since calm air away from the car is not affected by its motion)

iii)
Absolute air velocity at the bumper = 0, since it is a stagnation point.

iv)
Relative velocity at the bumper = -70 mph

v)
Total pressure = P + 1/2*rho*V^2
= 14.7 + 1/2*(0.074/32.2)*102.67^2 /12^2
= 14.784 psia