Question

A hurricane wind blows across a 7.50 m × 18.7 mflat roof at a speed of 170 km/hr .

A) Is the air pressure above the roof higher or lower than the pressure inside the house?

B) What is the pressure difference?

C) How much force is exerted on the roof?

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

Answer 1

(A) Is the air pressure above the roof higher or lower than the pressure inside the house?

The air pressure above the roof will be lower than the pressure inside the house due to the higher velocity of air.

(B) What is the pressure difference?

According to Bernoulli's theorem, we have

P_inside = P_outside + (1/2) _air v²

P = (1/2) _air v²

where, _air = density of the air = 1.28 kg/m³

v = speed of hurricane wind = 170 km/hr = 47.2 m/s

then, we get

P = [(0.5) (1.28 kg/m³) (47.2 m/s)²]

P = 1425.8 Pa

converting Pa into kPa :

P = 1.42 kPa

(C) How much force is exerted on the roof?

we know that, F_roof = (P) A

F_roof = (1425.8 Pa) (7.50 m) (18.7 m)

F_roof = 199968.4 N

F_roof = 1.99 x 10⁵ N

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

The roof will blow up.

{ Because the pressure inside the house is greater than the pressure on the top of the roof }