A paradox concerning the extended Stokes series solution for the pressure drop in coiled pipes

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Abstract
While the extended Stokes series (ESS) solution for the laminar pressure drop in coiled pipes predicts that the friction ratio (the ratio of pressure drop in the coiled pipe to that in the straight pipe of the same flow rate) varies asymptotically as one‐fourth power of the Dean number, the existing experimental data largely support a square‐root variation; previous boundary layer analyses also predict a square‐root variation. The subject of this paper is an examination of this paradox. A detailed review shows that the existing set of experimental data can be grouped into various categories depending on the precise flow conditions. It is shown that none of the existing data satisfies the proper experimental conditions required by the ESS method. New experiments reveal that the pressure drop demanded by the ESS solution can actually be observed if they are expressly designed to satisfy the conditions demanded by the ESS solution. The implication is that the domains of initial conditions appropriate to the boundary layer and ESS solutions are quite different.

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