[johnreb11]

If I have a flat plate 3ft wide & 8ft long on a 45 degree angle what is the force (lbs per square ft) exerted on the plate by a wind force of 70mph? What is the equation for calculating the force?

Thanks for any help,
James

[harum]

There is a formula for this, but it takes some analysis to derive it. This is a second Newton's Law problem: the force on the plate exerted by the wind is due to and equal to the change in the momenum of the wind. Let the wind blow on the plate for time To, and let's find the force in this case. Note the in case of the constant wind the force will be the same. F=(P2-P1)/To, here P1 is the momentum of the air in the wind blowing horizontally before it hits the plate; P2 is the momentum of the air in the wind after it gets reflected by the plate vertically upward, and the bold type means it's a vector. Why it is reflected upwards? This is because of two things: (a) because we assume that the there is no friction between the air in the wind and the plate and (b) because the plate is tilted by 45 degrees. Use the momentum conservation law and energy conservation law together (the plate does not move) to prove this, because this is important. What is the momentum of the mass of the air in the wind hitting the plate for the time To? It is: P1=d*L*sin(45)*W*v*To*v1, here d is the density of the air, L - length of the plate, W - width of the plate, L*sin(45)*W is the effective cross section of the plate (which is tilted) for the incoming wind, v1 - wind vector before it hits the plate, v - magnitude of the wind speed. You can build a similar equation for P2.

So, the force F = d*L*sin(45)*W*v*(v2-v1). What you need to do to get the answer is to calculate (v2-v1). P1 and P2 are equal in magnitude and orthogonal wrt to each other. You can subtract vectors using many ways. E.g. dissolve the speed vectors into components perpendicular and parallel to the plate using a reference frame associated with the plate. Hope this helps, h.

[harum]

Please make a note that in my explanation I made a little mistake which I have edited already. Somehow, it occurred to me that a factor v was lost in the momentum calculation. Sorry about that.