Question

Air in a 120 km/h wind strikes head on the face of abuilding 45m wide by 75m high and is brought to rest. if air has a mass of 1.3 kg per cubic meter determine the average force of the wind on the building

Answer 1

Note that 120 km/hr = 33.33 m/s 
F = dp/dt 
= (1.3 kg/m^3)(33.33 m/s)(3000 m^2)(33.33 m) So the answer is 4874025 N but the other 4874025 N is one of the three measurements of the fluid volume that contains the mass of air that will be stopped in one second.

Answer 2

From conservation of momentum, the ram force can be calculated similarly to rocket thrust:
 F = d(mv)/dt = vdm/dt.
 In other words, the force needed to decelerate the wind equals the force that would be needed to produce it. 
 v = 120/3.6 = 33.33 m/s 
 dm/dt = v*area*density
 dm/dt = (33.33)*((45)*(75))*(1.3) 
 dm/dt =  146235.375 kg/s 
 F = v^2*area*density
 F = (33.33)^2*((45)*(75))*(1.3) =  4874025 N 
 This differs by a factor of 2 from Bernoulli's equation, which relates velocity and pressure difference in reference not to a head-on collision of the fluid with a surface but to a fluid moving tangentially to the surface. Also, a typical mass-based drag equation, like Bernoulli's equation, has a coefficient of 1/2; however, it refers to a body moving through a fluid, where the fluid encountered by the body is not stopped relative to the body (i.e., brought up to its speed) like is the case in this problem.