A hurricane wind blows across a 5.50 m × 17.4 m flat roof at a speed of 120 km/h

Question

A hurricane wind blows across a 5.50 m × 17.4 m flat roof at a speed of 120 km/hr

Part B

What is the pressure difference?

Express your answer with the appropriate units.

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Part C

How much force is exerted on the roof?

Express your answer with the appropriate units.

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Part D

If the roof cannot withstand this much force, will it “blow in” or “blow out”?

If the roof cannot withstand this much force, will it “blow in” or “blow out”?

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Explanation / Answer

bernoulli principle stated that in the atmosphere when pt#1 has high pressure and pt#2 has low pressure, the difference pressure created wind velocity blowing from high pressure point to low pressure point according to the following formula
p = (1/2)(d)(v^2)
p = pressure difference in N/m2 or Pa
d = air density 1.29 kg/m3
v = wind speed m/s

also bernoulli stated that still air has higher pressure than air in motion, which means that inside the house the pressure is higher than outside, the wind blows from inside to outside causing the roof to be lifted (not collapsed), as most people think

(a) and (b)
let p = pressure difference
p = (1/2)(1.29)(33.33)^2 = 716 N/m2 (or Pa)
pressure above the roof = 101325 - 716 = 100 609 Pa
pressure inside the house is still air at 101325 Pa

(c) lifting force on the roof = (p)(A) = (716)(70) = 50157 N

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