Question

Air in a 124 km/h wind strikes head-on the face of a building 42 m wide by 73 m high and is brought to rest. If air has a mass of 1.3 kg per cubic centimeter, determine the average force of wind on the building.

Answer 1

The average force of wind on the building is 4.728 x 10¹² N

Step-by-step explanation:

Given;

speed of the air wind, v = 124 km/h

dimension of the building, 42 m wide by 73 m high

density of the air, ρ = 1.3 kg/cm³ =

speed of the air in m/s = 124/3.6 = 34.44 m/s

Area of the building, A = 42 m x 73 m = 3066 m²

density of the air in (k.g/m³);

`\rho = (1.3 \ kg)/(cm^3) *((100\ cm)/(1 \ m) )^3\\\\\rho = (1.3 \ kg)/(cm^3) *(10^6\ cm^3)/(1 \ m^3) = (1.3*10^6 \ kg)/(m^3)`

The average force of wind on the building;

F = mass flow rate x velocity

F = (ρvA) x V

F = ρAv²

F = 1.3 x 10⁶ x 3066 x (34.44)²

F = 4.728 x 10¹² N

Therefore, the average force of wind on the building is 4.728 x 10¹² N