Question

A wind speed 40 m/s blows parallel to the roof of a house. The area of the roof is $250m^2$ Assuming that the pressure inside the house is atmospheric pressure,the force exerted by the wind on the roof and the direction of the force will be:

Answer 1

Let p₁ and p₂are pressure inside and outside the roof and v₁ and v₂are velocities of the wind inside and outside the roof.

According to Bernoulli’s theorem

$p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$

$p_1-p_2=\frac{1}{2}\times 1.2\times ({40}^2-0)$

$p_1-p_2=960N/m^2$

Force is

$F=(p_1-p_2)A=960\times 250$

$F=24\times {10}^{4}N$.