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

In summary, the question asks for the change in pressure on a flat roof (5m x 17.1m) when a hurricane wind blows across it at a speed of 140km/h. The given density of air is 1.28kg/m^3 and the relevant equation is Bernoulli's Equation: p1+1/2pv1^2+ pgh1 = p2+1/2pv22 + pgh2. The student is having trouble manipulating the equation and understanding which terms cancel out. They understand the theory that the pressure will be lower on the top part of the roof due to the closer streamlines, and the pressure underneath the roof will be at atmospheric pressure. They also correctly identify
  • #1
Nellen2222
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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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  • #2
There is no wind under the roof. What is the speed of the air under the roof?
 
  • #3
Don't know. 0 I guess?
 
  • #4
No wind means the velocity is zero
 

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

What is Bernoulli's Equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid along a streamline. It states that as the speed of a fluid increases, the pressure decreases, and vice versa.

How is Bernoulli's Equation used in real life?

Bernoulli's equation has many practical applications, such as in aerodynamics, where it is used to calculate the lift and drag forces on an airplane. It is also used in the design of pipelines and ventilation systems, and in weather forecasting to explain the movement of air masses.

What are the assumptions made in Bernoulli's Equation?

Bernoulli's equation assumes that the fluid is incompressible, inviscid (has no viscosity), and that the flow is steady and laminar (smooth). It also assumes that the fluid is flowing along a streamline, and that there is no energy loss due to friction.

Can Bernoulli's Equation be applied to all types of fluids?

No, Bernoulli's equation can only be applied to ideal fluids, which are fluids that have no viscosity and are incompressible. Real fluids, such as air and water, have some level of viscosity and therefore do not follow the exact behavior predicted by Bernoulli's equation.

What are the units of measurement for the variables in Bernoulli's Equation?

The pressure and elevation terms in Bernoulli's equation are typically measured in units of pressure, such as Pascals or pounds per square inch (psi). The velocity term is measured in units of velocity, such as meters per second or feet per second. The units of all three terms must be consistent for the equation to be valid.

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