A jet airplane in level flight has a mass of 8.61 10 4 kg, and the two wings hav

Question

A jet airplane in level flight has a mass of 8.61 104 kg, and the two wings have an estimated total area of 94.0 m4.

(a) What is the pressure difference between the lower and upper surfaces of the wings?

(b) If the speed of air under the wings is 229 m/s, what is the speed of the air over the wings? Assume air has a density of 1.29 kg/m3.
m/s

(c Explain why all aircraft have a "ceiling," a maximum operational altitude.

The density of air  ---Select--- (decreases or increases )with increasing height, resulting in a  ---Select--- (greater or smaller) pressure difference. Beyond the maximum operational altitude, the pressure difference can no longer support the aircraft.

Explanation / Answer

m =8.61*10^4 kg, A =94 m^2

d = 1.29 kg/m^3, v1 = 229 m/s

(a) w = mg

pressure = Force/area

Plower -Pupper = mg/A = (8.61*10^4*9.8)/(94)

Pressure difference = 8.976*10^3 Pa

(b) From Bernoulis principle

P1+(1/2)dv1^2 = P2+(1/2)dv2^2

P1 -P2 = (1/2)d(v2^2 -v1^2)

8976 =0.5*1.29(v2^2 - (229*229)

v2 = 257 m/s

(c) As you can see, density plays a very significant role in the lift equations. If density is too low (high altitude) the airplane may not be able to get enough of a pressure difference to offset its weight.

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