Question

A 40 mph wind is blowing past your house and speeds up as it flows up and over the roof. If the elevation effects are negligible, determine (a) the pressure at the point on the roof where the speed is 60 mph if the pressure in the free stream blowing toward your house is 14.7 psi. Would this effect tend to push the roof down against the house, or would it tend to lift the roof

Answer 1

The pressure at the point on the roof where the speed is 60mph is 14.66 psi

Explanation:

The question follows Bernoulli's equation

P1 + 1/2 ρ V1² = P2 + 1/2 ρ V2²

V1 = 40 X 5280 / 3600 = 58.7 ft/s

V2 = 60 X 5280 / 3600 = 88 ft/s

P2 = P1 + 1/2 ( 0.00238 ) [(58.7)² - (88)²]

P2 - P1 = -5.12lb/ft²

The negative pressure created tends to lift the roof.

We know,

P1 = 14.7 psi = 2116.8 lb/ft²

P2 = 2116.8 - 5.12 lb/ft²

P2 = 2111.68 lb/ft²

P2 = 14.66 psi

Therefore, the pressure at the point on the roof where the speed is 60mph is 14.66 psi