Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T02:49:43.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady viscous flow in a curved pipe

Published online by Cambridge University Press:  29 March 2006

W. H. Lyne
W. H. Lyne*
Affiliation:
Department of Mathematics, Imperial College, London S.W. 7
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency . The radius of the pipe a is assumed small in relation to the radius of curvature of its axis R. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter = (2/a2), where is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number , where is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 1 , 15 January 1971 , pp. 13 - 31
Copyright
Copyright © Cambridge University Press 1971

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.)

Footnotes

Present address: E.C.L.P. and Co. Ltd., St Austell, Cornwall.

References

Barua, S. N. 1963 Quart. J. Mech. Appl. Math. 16, 6177.Google Scholar
Batchelor, G. K. 1956 J. Fluid Mech. 1, 17790.Google Scholar
Burggraf, O. R. 1966 J. Fluid Mech. 24, 11351.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids (2nd edn). Macmillan.Google Scholar
Dean, W. R. 1927 Phil. Mag. (7) 4, 20823.Google Scholar
Dean, W. R. 1928 Phil. Mag. (7) 5, 67395.Google Scholar
Harper, J. F. 1963 J. Fluid Mech. 17, 14153.Google Scholar
Harper, J. F. & Moore, D. W. 1968 J. Fluid Mech. 32, 36791.Google Scholar
Kuwahara, K. & Imai, I. 1969 Phys. Fluids Supplement II 12, 94101.Google Scholar
Lyne, W. H. 1970 Thesis submitted for Ph.D. University of London.Google Scholar
McConalogue, D. J. & Srivastava, R. S. 1968 Proc. Roy. Soc A 307, 3753.Google Scholar
Moore, D. W. 1963 J. Fluid Mech. 16, 16176.Google Scholar
Riley, N. 1967 J. Inst. Maths. Applics. 3, 41934.Google Scholar
Stewartson, K. 1957 Proc. Symp. Boundary Layer Res., Int. Union theoret. appl. Mech. Freiburg i. Br. pp. 5971. (Springer, 1968).10.1007/978-3-642-45885-9_6CrossRefGoogle Scholar