Gordon - Your formula assumes that the full momentum of the stream of water is absorbed by the plate, and the velocity of the water once it hits the plate is zero. It is derived from:
For a stream of water of area A
and velocity v
you get your formula.
For this to be true the plate must be larger in area than the area of the stream of water. However, The aerodynamic drag formula I gave is for a body immersed
in the air, so the area of the stream of air is larger than the area of the body, and the wind is deflected around
the body. Also note that for the formula I gave A
is the area of the body, whereas for your formula A
is the area of the stream.