Creeping flow through a pipe of varying radius

Creeping flow of a Newtonian fluid through tubes of varying radius is studied. Using an asymptotic series solution for low Reynolds number flow, velocity profiles and streamlines are obtained for constricted tubes, for various values of constriction wavelength and amplitude. A closed-form expression is derived to estimate the pressure drop through this type of tube. The results obtained with this new expression are compared to data from previous experimental and numerical studies for sinusoidally constricted tubes. Good agreement is found in the creeping flow regime for the pressure drop versus flow rate relationship. Our method offers an improvement over the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation), which does not account for the wavelength of the constrictions.

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