What is the force exerted on a paddle in a river in the following situation?

[jaguar7]

If a paddle of area, A, is submerged in a river of water-velocity, v, and (assumed constant) water pressure, P, the paddle at an angle, m, what is the force exerted on the paddle by the moving water of the river?

the paddle is being held still from a bridge...

 

[haruspex]

Try here: http://en.wikipedia.org/wiki/Drag_coefficient, but it doesn't discuss cavitation, which can occur at high velocities.

 

[jaguar7]

Okay, the article (and its related articles) don't seem to give me everything I was looking for, and they seem a bit different from what I'd get.

I'm wondering if I'd be correct in my reasoning:

We could find out the mass per second that collides with the paddle, by the water's velocity, and its density, to give ρAvsinΘt = mass

where ρ is density, and Θ is the angle between the water and the paddle.

And with that, we could find its rate of change of momentum (imparted from the water to the paddle) per second which would be ρAv^2sinΘ

which would be force (Δp/Δt = F), where p = momentum

We add in the drag coefficient. But we are missing the one half, from the article.

Did I make a mistake somewhere? I had some help.