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Question

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is equal to atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (ρair=1.2 kg/m3)

A
2.4×105 N, downwards
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B
4.8×105 N, downwards
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C
4.8×105 N, upwards
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D
2.4×105 N, upwards
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Solution

The correct option is D 2.4×105 N, upwards
Applying Bernoulli's equation just above and below the roof,
P1+12ρv21=P2+12ρv22 ...(i)
h=constant, since pressure P1 & P2 have been taken just above and below a point on the roof (elevation is constant)
P1=Patm=P0 is the pressure inside the house or just below the roof.


From equation (i), we get
ΔP=P1P2=12ρ(v22v21) ...(ii)
Net force on the roof is due to the pressure differential.
F=ΔP×A ...(iii)

From Eq.(ii) & (iii),
12ρ(v22v21)=FA
12×1.2×(40202)=F250
(P1>P2, hence net pressure differential is along upwards direction)
F=2.4×105 N, upwards

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