Consider a building in the form of a hemisphere that has an open ventilation window at the top of the roof. The entrance door, which is situated at point O on the ground level, is initially sealed and...

Consider a building in the form of a hemisphere that has an open ventilation window at the top of the roof. The entrance door, which is situated at point O on the ground level, is initially sealed and does not allow air to penetrate through it. The building is exposed to wind, which is directed such that the entrance door finds itself at the front stagnation point; see Figure 3.20

Show that the force that has to be applied to the door to open it outwards is F = 9 8 ρV 2 ∞A, where ρ is the air density, V∞ the wind speed, and A the area of the door surface. Suggestion: You may assume that the ventilation window is small compared with the radius of the dome, and so is the door.