|September 12, 2008, 05:31||
Re: Vorticity and pressure drop
For laminar incompressible channel flows (and if i'm not wrong this should be right for circular pipe flows also with r instead of y) we have simply:
dp/dx = -mu dw/dy = costant anywhere
with w the component of vorticity parallel to the channel wall. But, this is actually interpreted as:
the known pressure drop (net pressure force) is exactly balanced by the net shear stress (Panton).
We can also say that the vorticity flux dw/dy is costant and to be sustained needs the necessary pressure gradient.
This is actually the same mechanism that works for any incompressible flow at stationary walls. But in this case the particles at the walls cannot gain linear momentum so the pressure gradient at the wall is balanced by the flux of vorticity.
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