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 96.km//h. (a)Estimate the pressure difference between the lower and upper surfaces of the wings . (b) Estimate the fractional increase in thespeed of the air on the upper surface of the wing relative to the lower surface. (The density of air is rho=1.2kgm^(-3))(g=9.8ms^(-2))

A fully loaded boeing aircraft has a mass of 3.3xx10^(5)kg . Its total

1.	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 96.km//h. (a)Estimate the pressure difference between the lower and upper surfaces of the wings . (b) Estimate the fractional increase in thespeed of the air on the upper surface of the wing relative to the lower surface. (The density of air is rho=1.2kgm^(-3))(g=9.8ms^(-2))
Answer» <P> Solution :The weight of the boeing aircraft is balanced by the upward force DUE to the pressure difference `=DeltaPxxA` `mg=DeltaPxxA` `thereforeDeltaP=(mg)/(A)` `=(3.3xx10^(5)xx9.8)/(500)` `0.06468xx10^(5)` `therefore` Pressure difference `=6468Nm^(-2)` (b)From Bernoulli.s equation, `P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))+rhog(h_(2)-h_(1))` Neglecting `h_(2)-h_(1)` for its small value, `thereforeP_(1)-P_(2)=(1)/(2)(rho(v_(2)^(2)-v_(1)^(2))` `therefore(2DeltaP)/(rho)=(v_(2)-v_(1))(v_(2)+v_(1))` `thereforev_(2)-v_(1)=(2DeltaP)/(rho(v_(2)+v_(1))=(DeltaP)/(rho((v_(2)+v_(1))/(2)))`...(1) Now average speed`ltvgt=(v_(1)+v_(2))/(2)` `=(960xx1000)/(3600)` `=266.6ms^(-1)` `thereforev_(2)-v_(1)=(DeltaP)/(rholtvgt)=(6468)/(1.2xx266.6)` `=20.21ms^(-1)` `therefore(v_(2)-v_(1))/(ltvgt)=(20.21)/(267)"" (because` From equation (1)) `=0.0756` `=0.8` Hence , speed above the wing needs to be only `8%` higher than that below.