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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

User Umbersar
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1 Answer

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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.
User Rohin
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