Halliday, Resnick & Walker — Fluids: Problem Problem_82

Race car down force. Modern race cars come with a variety of airfoils to help hold them on the track, especially in flat turns where the cars tend to slide out of the turn. Another technique involves channeling air through an opening in the front of the car, down under the car’s body, and then out behind the car. The air effectively flows through a pipe that is narrow in one section (the space below the car). Suppose the front opening has area \(A_f = 0.75 \text{ m}^2\) and the space between the track and the bottom of the car has an area of \(A_b = 0.15 \text{ m}^2\). If the car is moving at speed \(v = 240 \text{ km/h}\) and the pressure above the car is 1.0 atm, approximately what is the pressure difference (in atmospheres) between the top and bottom of the car, pushing down on the car?