Abstract
AbstractThe method of least‐squares fitting of harmonic functions to known boundary conditions has been employed to obtain closed‐form solutions for laminar flow of an incompressible fluid through the constant area annulus between a regular polygonal duct and a centered circular core. The product of Fanning friction factor and Reynolds number has been determined for the entire range between the extreme case of no core and the other extreme case where the core touches the outerwalls. For the latter case, it is shown that when the number of sides of the polygon approaches infinity, f.Re approaches a minimum value of 6.22. The analysis of this case is further extended to corner angles less than 60°, the minimum imposed by an equilateral triangular duct.
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