First slide

Fluid dynamics

Question

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

Moderate

A

$4.8 \times 10^{5} N, downwards$
B

$4.8 \times 10^{5} N, upwards$
C

$2.4 \times 10^{5} N, upwards$
D

$2.4 \times 10^{5} N, downwards$

Solution

Applying Bernoulli's theorem just above and just below the roof,
$P+ \frac{1}{2} {ρv}^{2} = P_{0} + 0$
$(P_{o} - P) = \frac{1}{2} {ρv}^{2} = ∆ P$
Hence lift of the roof
F = $∆ P . A = \frac{1}{2} {ρAv}^{2}$
= $\frac{1}{2} \times 1.2 \times {(40)}^{2} \times 250 = 2.4 \times 10^{5} N$

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