Some comments on steady, laminar flow through twisted pipes
Abstract
Steady laminar flow through pipes of straight centre line and fixed crosssectional geometry is consideredfor pipes in which the orientation of the crosssection changes slowly with distance along the axis of the pipe. For small rates of twist, the (local) departure from (local) Poiseuille flow is small and it is shown that a part of the mathematical problem for this secondary flow is identical to that for the small, transverse displacement of a clamped elastic plate due to constant loading. A detailed examination of the loss of flow rate (due to the twist) is given. The special case of a pipe of elliptical crosssection is found to be analytically tractable (with the aid of a computer) and is considered in detail.
 Publication:

Journal of Engineering Mathematics
 Pub Date:
 January 1977
 DOI:
 10.1007/BF01535586
 Bibcode:
 1977JEnMa..11...29T
 Keywords:

 Biodynamics;
 Laminar Flow;
 Pipe Flow;
 Steady Flow;
 Twisting;
 Equations Of Motion;
 Flow Velocity;
 Secondary Flow;
 Tables (Data);
 Fluid Mechanics and Heat Transfer;
 Mathematical Modeling;
 Industrial Mathematic;
 Laminar Flow;
 Centre Line;
 Mathematical Problem