Question

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 $m^2$, 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 :

$(P_{air}=1.2kg/m^3)$.

• A. 2.4 × 10⁵ N downwards
• B. 4.8 × 10⁵ N, downwards
• C. 4.8 × 10⁵ N, upwards
• D. 2.4 × 10⁵ N, upwards

Answer 1

The correct option is D

2.4 × 10⁵ N, upwards

From Bernoulli's equation

$P=P_0+\frac{1}{2}\rho v^2$

Force will act due to pressure difference

$\therefore P=P_0=\frac{1}{2}\rho v^2$

$=\frac{1}{2}\times 1.2\times (40{)}^2$
$=0.0096\times {10}^5$

$\therefore$ Force acting upwards

$F=0.0096\times {10}^5\times 250=2.4\times {10}^5$ N upwards