If wind blows at 34m/s over a house, what is the net force on the roof if its area is 170m2 and is flat? (At 20 ∘ C dry air has a density of 1.2 kg/m3).
To find the net force on the roof, we need to calculate the pressure exerted by the wind on the roof.
The pressure exerted by a fluid (in this case, air) is given by the equation:
Pressure = Density × Velocity^2
First, let's find the pressure exerted by the wind on the roof.
Given:
Wind velocity (V) = 34 m/s
Density of air (ρ) = 1.2 kg/m^3
Using the equation for pressure, we have:
Pressure = ρ × V^2
Substituting the values:
Pressure = 1.2 kg/m^3 × (34 m/s)^2
Calculating:
Pressure = 1.2 kg/m^3 × 1156 m^2/s^2
= 1387.2 N/m^2
Now, let's calculate the net force acting on the roof.
The net force is the pressure multiplied by the area of the roof.
Given:
Roof area (A) = 170 m^2
Net Force = Pressure × Area
Substituting the values:
Net Force = 1387.2 N/m^2 × 170 m^2
Calculating:
Net Force = 235,224 N
Therefore, the net force on the roof is 235,224 Newtons.