If wind blows at 44 m/s over a house, what is the net force on the roof if its area is 180 m^2 and is flat?
Net force in which direction? There are two forces here, the force upward due to The Bernoulli effect(there is zero velocity below the roof), and wind shear force trying to blow the roof away. Most of the shear is due to the area normal to the wind.
It is not a problem most teachers would try to reduce to a simple calculation.
It is approximately
(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.
Air density is about 1.2 kg/m^3.
I get about 209,000N or 46,000 lb.
If this is a flat roof, approximate the force with Bernoulli alone.
To calculate the net force on the roof, we need to use the formula for force:
Force = Pressure x Area
In this case, we can assume that the pressure exerted by the wind is equal to the atmospheric pressure, since the wind is blowing over the roof. The atmospheric pressure is typically around 101,325 pascal (Pa).
First, let's convert the wind speed from meters per second to pascal. Since the wind speed represents the velocity of the air, we can use the formula:
Pressure = 0.5 x Density x Velocity^2
The density of air is approximately 1.225 kg/m^3.
Plugging in the values, we get:
Pressure = 0.5 x 1.225 kg/m^3 x (44 m/s)^2
Now we have the pressure in pascal.
To find the force, we use the formula:
Force = Pressure x Area
Force = (0.5 x 1.225 kg/m^3 x (44 m/s)^2) x 180 m^2
Evaluating this expression will give you the net force on the roof.