The Flow of Conducting Fluids in Circular Pipes under Uniform Transverse Magnetic Fields

Abstract

In the field of learning called "magnetohydrodynamics" the study on the flow of electrically conducting fluids in circular pipes not only is apparently one of the most essential but also has, from engineering point of view, various interesting applications. There exists, however, very little knowledge about it and the almost only analytical result ever obtained is Shercliff's approximate solution. In this paper the author improved and developed the Shercliff's work and obtained an exact solution as follows for the case of steady flow in a non-conducting pipe. [numerical formula] where P : Poiseuille number k : one-half the Hartmann number [numerical formula] Furthermore, experiments were conducted in which steady-state pressure drop and flow rate were measured using mercury as a conducting fluid, and the rightness of the theoretical analyses was proved thereby. note : Poiseuille number P=αa²/ηv₀ α : pressure gradient, a : channel radius η : fluid viscosity, v₀ : average fluid velocity