Question

During a hurricane, the atmospheric pressure inside a house may blow off the roof because of the reduced pressure outside. If air (density 1.293 kg/m³) is blowing over the roof of a house at a speed of 144 km/hr.

a) What is the pressure difference between the inside and the outside of the house?

b) What would be the lifting force on a roof of area 79 m²?

Thank you for your help

Answer 1

To solve this problem, use Bernoulli's Principle.

(a) Write the Bernoulli's theorem for the pressure difference:

(1/2)d*v^2 + P = P0

P0 - P = (1/2)d*v^2

Where,

d = density of air = 1.293 kg/m^3

v = velocity of air = 144 km/hr = (144 x 1000) / (60 x 60) = 40 m/s

P = pressure of the flowing air

P0 = pressure inside the house

P0 - P = (1/2)(1.293)40^2 = 1034.4 Pa

Therefore,

The pressure difference between the inside and outside of the house = 1034.4 Pa (Answer)

(b) Force is just the pressure difference times the area of the roof.

Force = (Po - P)*Area = 1034.4 * 79 = 81717.6 N (Answer)