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Unsteady viscous flow in a curved pipe

  • W. H. Lyne (a1) (a2)

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 ω. 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 β = (2ν/ωa2)½, where ν is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number $R_s = \overline{W}^2a/R \omega\nu$, where $\overline{W}$ 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 β 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.

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References

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Unsteady viscous flow in a curved pipe

  • W. H. Lyne (a1) (a2)

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