Bernoulli's Equation: Finding the net force of wind blowing over a house

In summary, The net force on the roof in this scenario can be found by using the Bernoulli equation, which states that P1 + 1/2pv^2 = constant. In this case, the air underneath the roof is stagnant, so its velocity is 0. The air above the roof is blowing at 35 m/s, so its velocity can be substituted into the equation. This leads to the conclusion that the net force on the roof is equal to the pressure difference between the stagnant air and the moving air above it.
  • #1
blueorchid
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Homework Statement


If wind blows at 35m/s over a house, what is the net force on the roof if its area is 240m^2 and is flat?

Homework Equations


P=F/A and P1 + 1/2pv^2 = constant

The Attempt at a Solution


I have no idea on how to find pressure, because if I sub it into P1 + 1/2pv^2 = constant, it wouldn't work because the pressures would turn out the same because the roof is flat.
 
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  • #2
That's funny. I don't see a term for 'flat roof' in the Bernoulli equation.

However, look at the situation this way. The air under the roof is stagnant and has no velocity. The air above the roof is blowing with a velocity of 35 m/s.
What you are saying is that P1 + 1/2p*0 = P1 + 1/2p*35^2
 

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between fluid pressure, velocity, and elevation along a streamline. It is commonly used to calculate the net force of wind blowing over a structure, such as a house.

2. How is Bernoulli's equation used to find the net force of wind?

Bernoulli's equation can be applied to determine the net force of wind by considering the change in pressure and velocity of the wind as it flows over the surface of the house. This allows us to calculate the difference in pressure on either side of the house, which can then be converted into a net force.

3. What are the assumptions made when using Bernoulli's equation for wind forces?

When using Bernoulli's equation to find the net force of wind, we assume that the wind is steady, incompressible, and inviscid. We also assume that the flow is irrotational, meaning there is no rotation or turbulence in the wind.

4. Can Bernoulli's equation be used for any shape of house?

No, Bernoulli's equation is most accurate for streamlined objects and may not be as accurate for more complex shapes. However, it can still provide a good estimate of the net force of wind on a house.

5. How does the angle of wind affect the net force calculated using Bernoulli's equation?

The angle of wind can have a significant impact on the net force calculated using Bernoulli's equation. For example, if the wind is hitting the house at a perpendicular angle, the net force will be greater compared to if the wind is hitting the house at an angle. This is because the pressure difference between the two sides of the house will be greater when the wind is perpendicular to the house.

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