During a windstorm, a 25 m/s wind blows across the flat roof of a small home. Find the difference in pressure between the air inside the home and the air just above the roof, assuming the doors and windows of the house are closed. (The density of air is 1.28 kg/m³)• ( 400 Pa)
Given:
Speed of the air inside the home = v₁ = 25 m s⁻¹
Speed of the air outside the home = v₂ = 0 m s⁻¹
Density of air = ⍴ = 1.28 kg m⁻³
To Find:
Pressure difference = P₁ - P₂ = ?
[where P₁ = pressure outside the home and P₂ = pressure inside the home]
Solution:
The pressure difference P₁ - P₂ can be calculated by the relation:
P₁ - P₂ = `\frac {1}{2}` ⍴ (v₂ - v₁)
by putting values
P₁ - P₂ = `\frac {1}{2}` 1.28 kg m⁻² ((25 m s⁻¹)² - (0 m s⁻¹)²)
P₁ - P₂ = `\frac {1}{2}` 1.28 kg m⁻² x625 m² s⁻²
P₁ - P₂ = 400 kg m s⁻²
or
P₁ - P₂ = 400 Pa --------------Ans.
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