Pressure Loads on Cone - Conservation of Momentum

[minger]

Wow, I should really know this but I can't think of it. Let's assume (totally assume, haha) that I have a flanged cone with a flow through it. The flange is of course going to have a reaction force on it based on the flow. I know that summing forces, I have forces at the inlet and outlet
(pA)_1 = (pA)_2 + R

Now, will the static pressure inside the cone also generate a force normal to the walls? I know that any radial component of that force will cancel. However, I'm concerned about the axial component. Is this static pressure force taken into account in the summation of forces?

I just don't want to count the force twice is all (but definitely don't want to leave it out).

edit: shoot, I also need to sum momentum and consider the change in (\dot{m} v)

edit Part Deux - I guess it doesn't matter since the flow is at ambient pressure. I suppose it there was a dP across the cone, then there would be a component.

 

[FredGarvin]

There is a good example in Munson, Young and Okiishi for this very problem. It all comes down to how you select the control volume. I'll scan it in and post it.

Edit: Enjoy

 

[minger]

Thanks Fred, I appreciate the annotations.