Mark Drela wrote:

In article . com,
"Edward Green" writes:

Almost, but not quite! How to fix?


Your F3 should be simply
F3 = P dA
There is no momentum flow contribution to F3,
since the wall has no flow though it.

I thought that might be the case: F3 gave me the most doubt, and in
particular whether to include the rho v^2 term. But I can't justify
your assertion quite so sanquinely.

If a flow of velocity v turns a right angle, then is not the total
force projected on either face of the elbow P + rho v^2? The reason
for this is that the momentum coming down one leg of the elbow simply
disappears -- from the point of view of the fluid -- as the flow turns
90 degrees. This momentum must end up somewhere, as so represents a
force acting on the pipe. And yet there is no flow through the wall of
the pipe elbow.

So what is different about the tapering pipe section? Does it have
something to do with the fact that flow is ultimately not redirected,
but continues in the same direction in a tighter bundle?

You also will also have to invoke mass conservation,
d(Av) = 0
or
dA = -A dv/v
to eliminate the resulting dA which will now appear.

I had expected that input and was worried it didn't occur. I also was
worried about the sign of the three forces; I don't have a solid
feeling I've got them right. But mainly I'm worred about the above
argument: what you say may be so, but it may be for a different reason,
I think.