How Does Wind Speed Affect Roof Pressure and Force Calculation?

[stormnebula]

Can anyone help me with this question. I'm not really sure where to start.

A wind with speed 45m/s blows across a roof 20m long and 12m wide. The pressure inside the room is 1x10^5 Pa. Neglecting the small difference in thickness of the roof, what is the net force on this roof due to the pressure difference inside and outside? The density of air is equal to 1.3kg/m^3.

Please help.

 

[Andrew Mason]

A wind with speed 45m/s blows across a roof 20m long and 12m wide. The pressure inside the room is 1x10^5 Pa. Neglecting the small difference in thickness of the roof, what is the net force on this roof due to the pressure difference inside and outside? The density of air is equal to 1.3kg/m^3.

To begin, have a look at the Bernoulli equation.

AM

 

[wais]

Sure, I can help you with this question. To start, we need to understand the concept of pressure and how it relates to wind speed. Pressure is defined as the force exerted per unit area. In this case, the pressure inside the room is 1x10^5 Pa, which means that there is a force of 1x10^5 Newtons acting on every square meter of the room's surface.

Now, let's consider the wind blowing across the roof. The wind has a speed of 45m/s, which means that it is exerting a force on the roof as well. This force is known as the wind load and is given by the formula F = ½ ρv^2A, where ρ is the density of air, v is the wind speed, and A is the area of the roof.

In this case, we know the wind speed (45m/s) and the density of air (1.3kg/m^3), but we need to calculate the area of the roof. Since the roof is 20m long and 12m wide, the area is 20m x 12m = 240m^2.

Plugging in these values into the formula, we get F = ½ (1.3kg/m^3)(45m/s)^2(240m^2) = 140400N.

Now, to find the net force on the roof, we need to subtract the force due to the pressure difference inside and outside the room from the wind load. This is because the pressure inside the room is pushing down on the roof, while the wind load is pushing up.

The force due to the pressure difference is given by the formula F = PA, where P is the pressure (1x10^5 Pa) and A is the area of the roof (240m^2). Plugging in the values, we get F = (1x10^5 Pa)(240m^2) = 24000000N.

Therefore, the net force on the roof is 140400N - 24000000N = -23859600N. The negative sign indicates that the force is acting downwards, which means that the roof is under a lot of pressure and may be at risk of collapsing.

I hope this helps you understand the concept of wind speed and pressure and how they relate to the net force on a roof. Let me know if you have