Each of the two wings of an aeroplane has area `30m^(2)`. The speed of the air on the upper and lower surfaces of theon the wing of aeroplane are `90 ms^(-1)` and `70 ms^(-1)` respectively. If the plane is in level flight at constant speed, find the uplift and the mass of the aeroplane. Given density of air `=1.29 kg m^(-3)`.

Explanation

Here, Area of each wing, `A=30m^(2)`,
`v_(1)90 ms^(-1), v_(2)=70 ms^(-1), rho=1.29 kg m^(-3)`
Since the aeroplane is in level flighth, so
`P_(1)+(1)/(2)rho v_(1)^(2)=P_(2)+(1)/(2)rho v_(2)^(2)`
or `P_(2)=P_(1)=(1)/(2)rho(v_(1)^(2)-v_(2)^(2))=(1)/(2)xx1.29(90^(2)-70^(2))`
`2064 Nm^(-2)`
Upward from both the wings of aeroplane
`F_(1)=(P_(2)-P_(1))xx2A=2064xx2xx30=123840 N`
`=1.24xx10^(5) N`
Mass of the plane, `M=(F)/(g)=(1.24xx106(5))/(9.8)`
`=1.26xx10^(4) kg`