Question

A hurricane wind blows across a 5.60 m × 18.4 mflat roof at a speed of 120 km/hr .

1- What is the pressure difference?

2-How much force is exerted on the roof?

Answer 1

1)
let P1 is the presure inside the home and P2 is the pressure above the roof.

inside home, speed of air, v1 = 0

above the roof speed of air, v2 = 120 km/hr

= 120*5/18

= 33.3 m/s

we know, density of air, erho = 1.225 kg/m^3

use Bernoulli's theorem,

P1 + (1/2)*rho*v1^2 = P2 + (1/2)*rho*v2^2

P1 - P2 = (1/2)*rho*(v2^2 - v1^2)

= (1/2)*1.225*(33.3^2 - 0^2)

= 679 Pa <<<<<<<<<<<<-------------------Answer

2) Force exerted by air on the roof, F = (P1-P2)*A

= 679*5.6*18.4

= 7.00*10^4 N <<<<<<<<<<<<-------------------Answer