A frequently quoted rule of thumb in aircraft design is that wings should produc

Question

A frequently quoted rule of thumb in aircraft design is that wings should produce about 1000 N of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.) (a) At takeoff the aircraft travels at 56.0 m/s, so that the air velocity relative to the bottom of the wing is 56.0 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast must it move over the upper surface to create the ideal lift? m/s

(b) How fast must air move over the upper surface at a cruising speed of 240 m/s and at an altitude where air density is one-fourth that at sea level? Note that this is not all of the aircraft's lift--some comes from the body of the plane, some from engine thrust, and so on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the wing creates turbulence. m/s

Explanation / Answer

a)

From Bernoull's equation

P1+(1/2)pV12 =P2+(1/2)pV22

P1-P2 =(1/2)p[V22-V12]

V22-V12=2*dP/p

V2 =sqrt[(2*dP/p) + V12]----------------1

V2=sqrt[(2*1000/1.29)+562]

V2=68.46 m/s

b)

Given

p=1.29/4 =0.3225 Kg/m3

at V1=240 m/s

From 1

V2=sqrt[(2*1000/0.3225)+2402]

V2=252.6 m/s

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