Steady flow in locally exponential tubes

Abstract

Daniels & Eagles (1979) developed a theory for steady, axisymmetric, viscous flow in tubes of a slowly varying radius. This flow, for tubes of exponentially varying radius, was governed to a first approximation by a nonlinear ordinary differential equation when the Reynolds number was high and the scale of the axial variation in radius was proportional to the Reynolds number. In the present work this theory is modified and extended so that the Daniels & Eagles solutions may be applied to a wide variety of ‘locally exponential’ tubes. Numerical calculations are made of several terms in the series for the Stokes stream function, and a number of examples are presented, which indicate that the theory has a wide applicability.