Extension of stokes expansion for laminar flow through a loosely curved pipe

We consider fully developed steady laminar flow through a toroidal pipe of small curvature ratios The solution is expanded up to 40 terms by computer in powers of Dean number. The major conclusion of this investigation is that the friction ratio in a loosely coiled pipe grows asymptotically as the 1/4 power of the similarity parameter and not as the 1/2 power as previously deduced from boundary-layer analysis. This work confirmed the results obtained by [1]. The,goal of this analysis is to provide as complete a description as possible of the flow. The analysis yields a solution for all values of Reynolds number from zero to infinity in a continuous fashion.