Air of density `1.3 kg//m^(3)` flow horizontally with a speed `106 km//h`. A house has a plane roof of area `40 m^(2)`. Find the magnitude of aerodynamic lift on the roof.

Answer

[`2.25xx10^(4)` N]

Explanation

Here, `rho=3 kg//m^(3), v=106 km//h=29.44 m//s, A=40 m^(2)`. Air flows just above the roof and there is no air flow just outside and inside the roof, we have
`P_(1)+rho gh_(1)+(1)/(2)rho v_(1)^(2)=P_(2)+rho gh_(2)+(1)/(2)rho v_(2)^(2)`
Since, `h_(1)=h_(2)=h and v_(1)=v`
and `v_(2)=0, so P_(2)=P_(1)+(1)/(2)rho v^(2)`
or `P_(2)-P_(1)=(1)/(2)rho^(2)`
Aerodynammic force exerted on the roof,
`F=(P_(2)-P_(1))A`
or `F=(1)/(2)rho v^(2)xxA=(1)/(2)xx1.3xx(29.44)^(2)xx40=2.25xx10^(4) N`