Question

On a vacation flight, you look out the window of the jet and wonder about the forces exerted on the window. Suppose the air outside the window moves with a speed of approximately 150m/s shortly after takeoff, and that the air inside the plane is at atmospheric pressure.

(A) Find the pressure difference between the inside and outside of the window.

(B) If the window is 25cm by 45cm, find the force exerted on the window by air pressure.

Answer 1

Given that  Speed of air outside is v2 = 150 m/s

inside v1 = 0 m/s

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From Bernoulli's equation ,

        P1 + (1/2)? v₁² + ?gh = P2 + (1/2)? v₂² + ?gh

        ?P = (1/2)? v₂² -  (1/2)? v₁²

              = (1/2)?(v₂² - v₁²)

              = (1/2)(1.29 kg/m³)(150^2 m/s² - 0 m/s² )

              = 14512.5 Pa

              = 14.512 kPa

(b) Upward force exerted on the wing is

A = 25*45 cm^2 = 0.1125 m^2

              F = ?P*A

                 = (14512.5 Pa)(0.1125 m²)

                 = 1632.65 N