Question

A room has a window of area $A$. Out side of the room wind is blowing parallel to the window with a velocity $v$. If the density of air is $\rho$ , then the force acting on the window is:

• A. $\frac{1}{2}\frac{\rho v^2}{A}$
• B. $\frac{1}{2}\rho v^{2}A$
• C. $\rho v^{2}A$
• D. $2\rho v^{2}A$

Answer 1

The correct option is B $\frac{1}{2}\rho v^{2}A$

As the wind is blowing with velocity $v$ outside the window so, pressure will decrease from Bernoulli's equation as following :
Applying bernouillis theorem across the window ,
$p_1+\frac{1}{2}\rho v^2=p_2$
$\Rightarrow p_2-p_1=\frac{1}{2}\rho v^2$
So, force on the window =pressure difference x Area $=\Delta p\times A$$=\frac{1}{2}\rho A{v}^2$