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

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SUMMARY

The discussion centers on applying Bernoulli's Equation to calculate the change in pressure on a flat roof during a hurricane with wind speeds of 140 km/h. The density of air is given as 1.28 kg/m³. The key manipulation involves recognizing that terms related to height (pgh) cancel out due to equal heights, simplifying the equation to p1 - p2 = 1/2 * ρ * v². The participant seeks clarity on the logic behind canceling terms and how to approach similar problems in the future.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Basic principles of fluid dynamics
  • Knowledge of pressure and velocity relationships in fluid flow
  • Familiarity with atmospheric pressure concepts
NEXT STEPS
  • Study the derivation and applications of Bernoulli's Equation in various fluid dynamics scenarios
  • Learn how to analyze pressure differences in fluid systems using real-world examples
  • Explore the effects of wind speed on structural integrity during extreme weather events
  • Investigate the principles of lift and how they apply to roofing and aerodynamics
USEFUL FOR

Students in physics or engineering, structural engineers, meteorologists, and anyone interested in the effects of wind pressure on buildings during hurricanes.

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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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