A horizontal tin roof has area 100 m². During a strong storm, air immediately above the roof moves at 40 m/s while the air inside the house is approximately at rest. In a simplified Bernoulli model, take the air density as 1.2 kg/m³. What upward force acts on the roof because of the pressure difference?
Options

Question

A horizontal tin roof has area 100 m². During a strong storm, air immediately above the roof moves at 40 m/s while the air inside the house is approximately at rest. In a simplified Bernoulli model, take the air density as 1.2 kg/m³. What upward force acts on the roof because of the pressure difference?

Options

G1 Physics · Accepted Answer

Apply Bernoulli's equation to air inside and above the roof at approximately the same height. Inside the house, take v(in) ≈ 0. Above the roof, v(out) = 40 m/s. Therefore, P(in)−P(out) = ½ρ[v(out)²−v(in)²]. Hence, ΔP = ½×1.2×40² = 960 Pa. The upward force is F = ΔP A = 960×100 = 96000 N = 96 kN. Correct option: C.