An airplane has a mass of 2.4×10 6 kg , and the air flows past the lower surface

Question

An airplane has a mass of 2.4×106 kg , and the air flows past the lower surface of the wings at 80 m/s .

Part A

If the wings have a surface area of 1500 m2 , how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

Express your answer to two significant figures and include the appropriate units.

An airplane has a mass of 2.4×106 kg , and the air flows past the lower surface of the wings at 80 m/s .

Part A

If the wings have a surface area of 1500 m2 , how fast must the air flow over the upper surface of the wing if the plane is to stay in the air?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The wing must provide lift equal to the weight of the airplane for it to remain in the air.

So

F = m*g = 2.4*10^6kg*9.8m/s^2 = 2.352*10^7N

This lift is acquired by the difference in pressure above and below the wing
From Bernoulli we know dynamic pressure force = 1/2*rho*v^2*A

Hence,

1/2*rho*A*v(upper)^2 - 1/2*rho*A*v(lower)^2 = 2.352*10^7N

rho =1.2kg/m^3

v(upper) = sqrt(2/(rho*A)*2.352*10^7 + v(lower)^2) = sqrt(2/(1.2*1500)*2.352*10^7 + 80^2) = 180.4m/s

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