In a hurricane, the air (density 1.2 kg/m³) is blowing over the roof of a house at a speed of 110 km/h. (a) What is the pressure difference between inside and outside that tends to lift the roof? (b) What would be the lifting force on a roof of area 93 m²?

To solve this problem, we will use Bernoulli’s equation, which states:

P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂

Since we assume the height difference is negligible (h₁ ≈ h₂), the equation simplifies to:

P₁ + ½ ρ v₁² = P₂ + ½ ρ v₂²

Given Data:
Density of air, ρ = 1.2 kg/m³
Wind speed outside the house, v₂ = 110 km/h = (110 × 1000) / 3600 = 30.56 m/s
Wind speed inside the house, v₁ = 0 m/s (since air is relatively still inside)
Part (a): Pressure Difference
Applying Bernoulli’s equation:

P₁ - P₂ = ½ ρ v₂² - ½ ρ v₁²
= ½ (1.2) (30.56)² - ½ (1.2) (0)²
= 0.6 × 933.6
= 560.16 Pa

So, the pressure difference between the inside and outside of the house is 560.16 Pascals.

Part (b): Lifting Force on the Roof
The lifting force is given by:

F = Pressure Difference × Area
= (560.16) × (93)
= 52094.88 N

Thus, the lifting force acting on the roof is 52094.88 Newtons.