Question

A wind with speed $40\text{m/s}$ blows parallel to the roof of a house. The area of the roof is $250{\text{m}}^2$. 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 $({\rho }_{air}=1.2{\text{kg/m}}^3)$.

• A. $4.8\times {10}^5\text{N},\text{downwards}$
• B. $4.8\times {10}^5\text{N},\text{upwards}$
• C. $2.4\times {10}^5\text{N},\text{upwards}$
• D. $2.4\times {10}^5\text{N},\text{downwards}$

Answer 1

The correct option is C $2.4\times {10}^5\text{N},\text{upwards}$

By Bernoulli's theorem,
$p_1+\frac{1}{2}\rho v_1^2=p_2+\frac{1}{2}\rho v_2^2$
[assuming that root width is very small]
Pressure difference,
$p_1-p_2=\frac{1}{2}\rho (v_2^2-v_1^2)$
$p_1-p_2=\frac{1}{2}\times 1.2({40}^2-0^2)$
$=\frac{1}{2}\times 1.2\times 1600$
$=960{\text{N/m}}^2$
Force acting on the roof, $F=960\times 250=960\times \frac{1000}{4}$
$=24\times {10}^4\text{N}$
$=2.4\times {10}^5\text{N, upwards}$