On the distribution of velocity in a viscous fluid over the cross-section of a pipe, and on the action at the critical velocity

Abstract

1. Introduction .—An expression for the velocity at which stream-line motion breaks down in cylindrical pipes has been obtained by Osborne Reynolds, and together with many others he has measured the fall of pressure occurring in different lengths. Lord Kelvin, Lord Rayleigh, and Reynolds have investigated the stability of different kinds of flow for viscous and non-viscous fluids, but how nearly the theoretical conditions of velocity distribution actually occur has not hitherto formed the subject of research. Experiments have often been made on the variation of mean linear velocities in the eddying state, but when the motion is irrotational, these are too low to admit of accurate measurement by any method so far employed. The objects of the present paper are to determine these velocities, to investigate the change which takes place at the critical velocity, and to find the relation between the velocity and the pressure to which it gives rise in a “ Pitot ” gauge of the form used.