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A fully loaded Boeing aircraft has a mas...

A fully loaded Boeing aircraft has a mass of `3.3xx10^(5)kg`. Its total wing area is `500m^(2)`. It is in level flight with a speed of 960 kg/h. (a) estimate the pressure difference between the lower and upper surfaces of the wings (b) estimates the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface. [the density of air is `rho=1.2kgm^(-3)`].

Text Solution

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(a) The weight of the Boeing aircraft is balanced by the upward force due to the pressure difference
`DeltaPxxA=3.3xx10^(5)kgxx9.8`
`DeltaP=(3.3xx10^(5)kgxx9.8ms^(-2))//500m^(2)`
`=6.5xx10^(3)Nm^(-2)`
(b) We ignore the small height difference between the top and bottom sides in Eq. The pressure difference between them is then
`Delta=(rho)/(2)(v_(2)^(2)-v_(1)^(2))`
Where `v_(2)` is the speed of air over the upper surface and `v_(1)` is the speed under the bottom surface.
`(v_(2)-v_(1))=(2Deltarho)/(rho(v_(2)+v_(1)))`
Taking the average speed
`v_(av)=(v_(2)+v_(1))//2=960km//h=267ms^(-1)`, we have
`(v_(2)-v_(1))//v_(av)=(DeltaP)/(rhov_(av)^(2))~~0.08`
The speed above the wing needs to be only 8% higher than that below.
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