Note on the Forces on an Elliptic Cylinder moving in a Viscous Liquid at Small Reynolds Numbers

Abstract

The steady flow of a viscous liquid past an elliptic cylinder at an arbitrary angle of attack is discussed on the basis of Reynolds number expansion using conformal transformation of the general solutions of Oseen’s equation, which are expressed in integral forms. Thus the expansion formulae for the lift and drag coefficients are obtained to the second approximation, which are in perfect agreement with the results obtained recently by Hasimoto and also by Imai. Although it seems difficult to obtain general expressions for various formulae, such as formulae for the lift and drag, the procedure gives not only a practical method of solving Oseen’s equation for the two-dimensional slow steady flow of an unbounded viscous liquid past an arbitray cylindrical body, but also an effective method to study the wall-effect upon a cylinder of arbitrary shape moving in a viscous liquid bounded either by a plane wall or by parallel plane walls, provided the mapping function is known for the cylinder.