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28 February, 21:17

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

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  1. 28 February, 23:51
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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.
  2. 1 March, 01:16
    0
    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.
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