On the flow of viscous fluids through smooth circular pipes

Abstract

1.The problem of the flow of a viscous fluid through a tube of circular section is of considerable interest both to physicists and to engineers. Since Stokes showed the connection between the viscosity of the fluid and the empirical formula given by Poiseuille for the rate of slow or stream-line flow of the fluid through a capillary tube, the tube method has been one of the most useful and accurate for the determination of viscosity. On the other hand, the extensive use of pipes for the transmission of gas, compressed air, water and oil, at speeds much above those which obtain in a Poiseuille experiment, rendered it necessary to investigate the laws of "turbulent" flow of viscous fluids through tubes, and there are at the present time several formulae in use by engineers giving the mean rate of flow of such a fluid through a pipe and the difference of pressure between its ends.