Poiseuille flow in a rectangle channel

Dear Philip,

See, for example,

Frank M. White, "Viscous Fluid Flow," 2nd edition, McGraw-Hill, 1991. Pages 119-122.

White gives a formula for Poiseuille flow in a duct with a rectangular cross-section in the form of an infinite series. He also gives a reference to the source of this equation.

Olin Perry Norton

Thanks olin I'm unable to get hold of White at the moment. If it is convenient, can you provide that ref?

I actually found a series expansion solution attributed to Rosenhead (1963). Perhaps this is it.

philip

Ol>

No. The citation is Berker, R. (1963): "Handbuch der Physik," vol. VIII, pt. 2, pp. 10384, Sprinder, Berlin.

The text in White states this was a review of of exact solutions for noncircular shapes.

White's references are to:

Berker, A. R., (1963) "Integration des equations du mouvement d'un fluide visqueux incompressible," in S. Flugge (ed.), Encyclopedia of Physics, Vol. 8, pt. 2, pp.

Shah, R. K., and A. L. London, (1978) Laminar Flow Forced Convection in Ducts, Academic, New York.

I do not know if these are the original references, where the formula is derived, or to reviews or compilations.

I used the equation in White and tried to compute a profile numerically. Using scaled values (such that max velocity =1, depth =1), i first compute a dp/dx for flow through semi infinate parallel plates. And then use the dp/dx value for duct flow.

I'm surprise that this yields a max velocity of around 0.91. I thought the edge effect is going to be significant only near the wall (O(thickness of channel)). Is this possible?

Also, what should be a reasonable limit to the summation series? I sum it up to 10^5 but it still dosen't look good.

Thanks...

Ol>