bernoulli examples

Question

A building has a flat roof of area 42.0 m2. Wind blows over the top of the roof at 14.8 m/s. The air inside the building is stationary. What is the TOTAL force acting on the roof?

Answer 1

Bernoulli's equation is P_roof+ 1/2 x ρ x V²_roof + hρg = P_house + 1/2ρV²_house + hρg.

P_roof is air pressure on the roof

P_house is the air pressure in the house (standard atmospheric pressure)

ρ is the density of the air (1.225 Kg/m³)

h is the height of the roof which is approximately the same in the house or on the roof.

V_roof is the velocity of the wind over the roof.

V_house is the velocity of the air in the house ( = 0)

g is the acceleration of gravity

Putting the values above into Bernoulli's equation gives

P_roof + 1/2 x ρ x V²_roof = P_house

P_house - P_roof = 1/2 x ρ x V²_roof ( P_house - P_roof = the pressure difference between roof and house)

P_house - P_roof = 1/2 x 1.225 Kg/m³ x 14.8 ²m/s = 134.2 Kg x m²/m³s² = N/m²

Total force = 134.2 N/m² x 42.0 m² = 5636 N. To 3 sig figs, this is 5640 N

This result can vary depending on the value used for air density.

Please check all math.