If wind blows at a speed of 30 m/s over the roof of your house, what is the pressure diference on your roof between the air inside and the air outside? What net force does this produce on a roof having an area of 175 m^2?
1.3 kg/m^3 is the density of air.
(1/2)*(air density)*V^2*(roof area), but depends upon what the pressure inside the house is, and that depends upon which windows or doors are open.
Wind pressure (suction) over a roof is the same phenomenon as the force that lifts an airplane by air flowing past the wings.
When there is an obstruction to the wind, the air flow speeds up to compensate for the reduced sectional area, and in doing so, creates a negative pressure on the leeward side of the building.
Most of the time, the magnitude of the negative pressure is compared with the stagnation pressure ((1/2)ρv²) and thus creates a factor which is dependent on the shape of the building, shape of the roof, and the location. See ref. below.
Different building codes in different states/countries adopt values for these factors. For the purpose of this question, your teacher has probably given you a shape factor for the house in question.
The net force is the product of the negative pressure and the area of the roof.
See:
(Broken Link Removed)
Good
To calculate the pressure difference on the roof of your house, we can use Bernoulli's principle, which states that the total pressure at any point in a fluid is the sum of the static pressure and the dynamic pressure.
The static pressure is the pressure exerted by the air molecules on a surface, and the dynamic pressure is the pressure exerted by the moving air.
First, let's calculate the dynamic pressure using the formula:
Dynamic pressure = (1/2) * density of air * velocity^2
Given:
Density of air = 1.3 kg/m^3
Velocity = 30 m/s
Plugging in the values:
Dynamic pressure = (1/2) * 1.3 kg/m^3 * (30 m/s)^2
Next, we need to calculate the static pressure. The static pressure inside the house is the atmospheric pressure, which is typically around 101,325 pascals. The static pressure outside the house is the atmospheric pressure plus the dynamic pressure.
Static pressure inside = 101,325 pascals
Static pressure outside = 101,325 pascals + dynamic pressure
Now, we can find the pressure difference:
Pressure difference = Static pressure outside - Static pressure inside
Finally, to calculate the net force on the roof, we can use the formula:
Net force = Pressure difference * Area
Given:
Area of the roof = 175 m^2
Plugging in the values:
Net force = Pressure difference * 175 m^2
By substituting the calculated values, you can find the pressure difference on the roof between the air inside and the air outside, as well as the net force produced on the roof.