How Does Bernoulli's Equation Apply to Hurricane Wind Pressures on a Roof?

[Nellen2222]

Homework Statement

A hurricane wind blows across a flat roof (5m x 17.1m) at a speed of 140km/h

What is the change in pressure on the roof? (1.28kg/m^3 density of air)

Homework Equations

Bernoulli's Equation: p₁+1/2pv₁^{^2}+ pgh₁ = p₂+1/2pv₂² + pgh₂

The Attempt at a Solution

I don't understand how to manipulate bernoulli's equation in order to solve these problems. I understand all of the theory, such that the pressure will be lower on the top part of the roof which makes the wind blow faster because the streamlines will be closer together, and the pressure underneath the roof would be at atmosphereic pressure thus creating lift by "blowing the roof off".

However, How do I know how to cancel terms? I can ee that pgh(1) and pgh(2) in the equation will cancel because the height of the roof is reletivly the same and gravity/density will cancel because we are not comparing it in two different densities anyway. So I get left with..

P₁+ 1/2pv₁² = p₂ + 1/2pv₂² .

I know the final formula is p₁-p₂ = 1/2pv₂² . How do i know that one of the rho and velocities will cancel? what is the logic behind that. Adn for future problems what should I be thinking when looking and slving for my variables with bernoulli's eq.

Thanks.

 

[voko]

There is no wind under the roof. What is the speed of the air under the roof?

 

[Nellen2222]

Don't know. 0 I guess?

 

[szynkasz]

No wind means the velocity is zero

 

[Nellen2222]

https://www.physicsforums.com/showthread.php?p=4093887#post4093887

Can you please help me on this one instead? Thank you.