Hydrodynamics in the renal tubule

Abstract

Explicit solutions of the Navier-Stokes equations are presented for axially symmetric slow flow in an infinite cylinder whose walls reabsorb fluid at a rate which varies exponentially with the longitudinal coordinate. Results similar to those of a previous paper which assumed a constant rate of reabsorption are obtained. When the radius of the tube is small the solutions resemble Poiseuille flow; the longitudinal velocity profile is parabolic, and the drop in mean pressure is proportional to the mean axial flow, the length of tube between reference points, and inversely proportional to the fourth power of the radius. By expressing the tubular reabsorption as a Fourier integral, solutions are obtained for the general case where the rate of reabsorption is an arbitrary function of the longitudinal coordinate.