Bernoulli equation Question 4: In a hurricane where wind speeds approach 250 km/

Question

Bernoulli equation

Question 4: In a hurricane where wind speeds approach 250 km/hr, what would be a plausible cause for the entire roof (trusses and all) getting torn off of a house? If the horizontal area of the roof is 140 m2, use Bernoulli to calculate the upward force that it would experience if the wind is moving at 250 km/hr over it (assume the air inside the house is still). The density of air is 1.2 kg/m3. Compare this to the weight of the roof if each square meter of roof has a mass of 73 kg.

Explanation / Answer

a)

Let us first find pressure on the roof,

By Bernoulli’s eqn,

P1+1/2v1^2+gh1 = P1+1/2v1^2+gh1

Since the roof is horizontal,

h1=h2

P1+1/2v1^2 = P2+1/2v2^2

P=P2-P1= ½**(v2^2-v1^2)

F= P*A = ½**(v2^2-v1^2)*A = ½*1.2*140*[(250000/3600)^2 – (140000/3600)^2]

F = 278055.6 N

b)

W = mg = 140*73*9.8 = 100156 N

F/W = 278055.6/100156 = 2.776

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