Abstract
The effects produced by small-scale plane or axisymmetrical boundary irregularities on steady parallel flows of incompressible viscous fluid are investigated for the cases of (a) flow between two parallel planes and (b) flow in a cylindrical pipe of circular cross-section. The solutions for the stream function and pressure are determined when the Reynolds numbers of the perturbed flows are small enough to permit neglect of inertia terms. Expressions are derived for the change in pressure head when the unperturbed flow is Poiseuille flow between planes or in a circular pipe, and for the changes in wall drags when the unperturbed flow is Couette flow between parallel planes, and these expressions are shown to be applicable also for perturbed flows of any Reynolds number for which they exist as laminar flows.
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