Strong winds blow past the roof-top of a house. Assume a flat roof with an area

Question

Strong winds blow past the roof-top of a house. Assume a flat roof with an area of 250 m^2 that is bolted to the frame of the house. The bolts can withstand a total force of 75,000 N in either direction but will fail and break is a stronger force is applied to the roof. The roof is located 15 m above the ground and has a total weight of 1200 kg. Assume a density of air of 1.2 g/liter and a density of a roof of 0.5 kg/l. (a) Is the roof pushed down, or pushed up by the strong winds? (b) Calculate the air pressure above the roof if the wind speed is 30 m/s. Assume a normal air pressure of 1000 hPa with no wind at all. (c) Calculate at what minimum wind speed the roof will break off and separate from the house.

Explanation / Answer

(a) the roof will be pushed up as pressure will be more inside the room so net force will be downward

(b) using bernouli theorem

P1-P2=0.5*density*v*v=540 pa

We got P2 =pressure outside room=100000pa-540000 pa=99460 pa pr 996.6 hpa

(C) let the velocity is v

Force=75000 N

(P1-P2)*area =75000+(1200*9.8)=86760 N

So P1-P2=0.5*density*v*v=347.04 pa

We got v=24.04 m/s

So roof will blow at v=30 m/s

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