Question

A flat roof is very susceptible to wind damage during a thunderstorm and/or tornado. If a flat roof has an area of 500 m2 and winds of speed 39.0 m/s blow across it, determine the magnitude of the force exerted on the roof. The density of air is 1.29 kg/m3.

Answer 1

Answer: The magnitude of the force exerted on the roof is 490522.5 N.

Explanation:

The given data is as follows.

Below the roof, $v_{1}$ = 0 m/s

At top of the roof, $v_{2}$ = 39 m/s

We assume that $P_{1}$ is the pressure at lower surface of the roof and $P_{2}$ be the pressure at upper surface of the roof.

Now, according to Bernoulli's theorem,

$P_{1} + 0.5 \times \rho \times v^{2}_{1} = P_{2} \times 0.5 \rho \times v^{2}_{2}$

$P_{1} - P_{2} = 0.5 \times \rho \times (v^{2}_{2} - v^{2}_{1})$

             = $0.5 \times 1.29 \times [(39)^{2} - (0)^{2}]$

             = $0.645 \times 1521$

             = 981.045 Pa

Formula for net upward force of air exerted on the roof is as follows.

          F = $(P_{1} - P_{2})A$

             = $981.045 \times 500$

             = 490522.5 N

Therefore, we can conclude that the magnitude of the force exerted on the roof is 490522.5 N.