Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T13:41:25.763Z Has data issue: false hasContentIssue false
  • English
  • Français

Entry of conducting and non-conducting fluids in pipes

Published online by Cambridge University Press:  24 October 2008

J. A. Shercliff
J. A. Shercliff
Affiliation:
Engineering DepartmentCambridge University
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of estimating the entry length over which the laminar motion of an electrically conducting, viscous fluid in a pipe under a transverse field adjusts to a steady state from some initial state is linearized by a Rayleigh approximation adapted for cases where there is a pressure gradient. Solutions are found which express the difference between the initial and ultimate velocity profiles as a series of orthogonal, exponentially decaying terms. Approximate entry lengths for the most persistent terms are calculated for flow between two infinite parallel planes and in rectangular tubes when magnetic effects are present. Entry lengths in circular and rectangular pipes and between infinite planes are calculated in the case where magnetic effects are negligible to permit a comparison of the results with those derived by other methods. Pressure losses at entry are considered in the simpler cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 573 - 583
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Batchelor, G. K.Proc. roy. Soc. A, 201 (1950), 405.Google Scholar
(2)Goldstein, S.Modern Developments in Fluid Dynamics, vol. 1. (Oxford, 1938.)Google Scholar
(3)Hartmann, J.Math.-fys. Medd. 15 (1937), no. 6.Google Scholar
(4)Shercliff, J. A.Proc. Camb. phil. Soc. 49 (1953), 136.CrossRefGoogle Scholar