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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 atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (ρair = 1.2 kg/m³)

2.4×10⁵N, upward

4.8×10⁵N, downward

4.8×10⁵N, upward

2.4×10⁵N, downward

Solution:

Applying Bernoulli's theorem to two points just inside the house and outside the house,
P + 1/2ρv² = constant
Inside the pressure is Patm
The pressure outside is P
v is zero inside.
∴ P − Patm = 1/2ρv² = 1/2 × 1.2 × 40² = 960
Force is : F = (P − Patm) × Area = 960 × 250 = 2.4 × 10⁵ N
in upward direction as pressure goes from higher to lower pressure area.