Question

Air is flowing horizontally with a speed $v=10m/s$. A house has a plane roof of area $A=50m^2$. If the density of air is $1.2kg/m^3$ then determine the magnitude of aerodynamic lift on the roof.

• A. $1000N$
• B. $1500N$
• C. $2000N$
• D. $3000N$

Answer 1

Answer: (D)

$3000N$

Considering there is no air below the roof.

Applying Bernoulli's theorem at the points inside and outside the roof, we get:

$\frac{1}{2}\rho v_1^2+\rho g{h}_1+p_1=\frac{1}{2}\rho v_2^2+\rho g{h}_2+p_2$ ................(i)

Here:- $h_1=h_2=h,v_1=0$ and $v_2=v$

From eq. (i) -

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

$\Rightarrow p_1-p_2=\Delta p=\frac{1}{2}\rho v^2$

Aerodynamic force exerted on the area of the roof $A$ is:-

$F=\left(\Delta p\right)A=\frac{1}{2}\rho v^{2}A$
For $\rho =1.2\text{kg}/m^3,A=50m^2,v=10m/s$

$\Rightarrow F=3000N$
Correct Option - (D)