How Does Bernoulli's Equation Apply to Wind Over a House Roof?

[khai06]

I'm so confused here's the question...

The wind blows with a speed of 30.0m/s over the roof of your house.

A. Assuming the air inside the house is relatively stagnant, what is the pressure difference at the roof between the inside air and the outside air?

B. What net force does this pressure difference produce on a roof having an area of 175m^2?

I know that the first velocity is 30.0m/s and since the air inside is motionless therefore the second velocity is 0 m/s. Also the density of air is 1.29kg/m^3 and gravity is 9.81 m/s.

My teacher said its a straight plug using this formula:

P + 1/2 pv^2 + pgh which will equal the constant.

But I don't get how to plug it in? Can anyone show me how is it done?

 

[HallsofIvy]

Please show us what you have done. What is "Benouilli's Equation"?

 

[wais]

Bernoulli's equation is a fundamental equation in fluid mechanics that relates the pressure, velocity, and height at different points in a fluid flow. It states that the total energy of a fluid remains constant at any point in the flow. This equation can be applied to various situations, including the one given in the question.

To solve part A, we can use the Bernoulli's equation as follows:

P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2

Where P1 and P2 are the pressures at points 1 and 2 (inside and outside the house), ρ is the density of air, v1 and v2 are the velocities at points 1 and 2, and h1 and h2 are the heights at points 1 and 2.

In this case, we know that v1 = 0 m/s, v2 = 30.0 m/s, and h1 = h2 (since the roof is at the same height). We also know the density of air (ρ = 1.29 kg/m^3) and the acceleration due to gravity (g = 9.81 m/s^2).

So, the equation becomes:

P1 + 0 + 0 = P2 + 1/2(1.29)(30.0)^2 + 1.29(9.81)(h)

Simplifying and rearranging, we get:

P1 - P2 = 1/2(1.29)(30.0)^2 + 1.29(9.81)(h)

P1 - P2 = 587.07 + 12.67h

This is the pressure difference between the inside and outside of the house. To find the net force, we can use the standard formula:

F = PA

Where F is the force, P is the pressure difference, and A is the area of the roof.

Substituting the value of P1 - P2 that we found above, and the given area of the roof (A = 175 m^2), we get:

F = (587.07 + 12.67h)(175)

= 102,719.25 + 2,215.75h

So, the net force produced on the roof is 102,719.25 + 2