Problem: A hurricane wind blows across a 7.50 m x 11.2 m flat roof at a speed of 190 km/hr.a) Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.b) What is the pressure difference?

FREE Expert Solution

The equation of continuity:

$\overline{){\mathbf{\rho }}{{\mathbf{A}}}_{{\mathbf{1}}}{{\mathbf{V}}}_{{\mathbf{1}}}{\mathbf{=}}{\mathbf{\rho }}{{\mathbf{A}}}_{{\mathbf{2}}}{{\mathbf{V}}}_{{\mathbf{2}}}}$

Bernoulli's equation:

$\overline{){{\mathbf{p}}}_{{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{{\mathbf{v}}}_{{\mathbf{1}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{\rho }}{\mathbf{g}}{{\mathbf{y}}}_{{\mathbf{1}}}{\mathbf{=}}{{\mathbf{p}}}_{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{\mathbf{v}}_{\mathbf{2}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{\rho }}{\mathbf{g}}{{\mathbf{y}}}_{{\mathbf{2}}}}$

a)

From the equation of continuity, the speed of the hurricane wind increases at the outside of the roof.

Inside the roof, the pressure is greater and the velocity is smaller.

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Problem Details

A hurricane wind blows across a 7.50 m x 11.2 m flat roof at a speed of 190 km/hr.

a) Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.
b) What is the pressure difference?