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

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Homework Help Overview

The discussion revolves around applying Bernoulli's Equation to analyze the change in pressure on a roof subjected to hurricane winds. The original poster presents a scenario involving a flat roof and seeks to understand the manipulation of the equation in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how to manipulate Bernoulli's Equation, questioning the cancellation of terms and the logic behind it. There is also a discussion about the velocity of air under the roof, with participants exploring the implications of having no wind in that area.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning assumptions about the conditions under the roof. Some guidance has been offered regarding the velocity of air beneath the roof, but there is no explicit consensus on the interpretation of the problem or the application of Bernoulli's Equation.

Contextual Notes

Participants are navigating the complexities of applying Bernoulli's Equation in a real-world scenario, particularly concerning the assumptions about air velocity and pressure differences. The original poster expresses uncertainty about the manipulation of the equation and the implications of the conditions described.

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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.
 
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There is no wind under the roof. What is the speed of the air under the roof?
 
Don't know. 0 I guess?
 
No wind means the velocity is zero
 

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