Physics - Fluid Question with Solution | TestHub

Using Bernoulli's equation just inside and outside the roof:

$P_{in}+\frac{1}{2}\rho v_{in}^2=P_{out}+\frac{1}{2}\rho v_{out}^2$

Since the air inside the house is at rest, $v_{in}=0$ and $P_{in}=P_0$ (atmospheric pressure).

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

The pressure difference across the roof is $\Delta P=P_0-P_{out}=\frac{1}{2}\rho v^2$.

The upward force exerted on the roof is $F=\Delta P\times A=\frac{1}{2}\rho v^{2}A$.

Substituting the given values:

$F=\frac{1}{2}\times 1.2\times (50{)}^2\times 300$

$F=0.6\times 2500\times 300$

$F=450000\text{ N}=4.5\times 10^5\text{ N}$

Answer: $4.5\times 10^5\mathrm{N}$