Abstract
In this paper we shall use a geometrical method to show that the Poiseuille flow of any simple fluid in Noll's meaning is only possible in a pipe of circular cross-section, between two coaxial pipes of circular cross-section or between two parallel planes. A similar result was obtained by Fosdick and Serrin (1) under other assumptions than classical analytical techniques. In each of these three cases this geometrical method makes it possible to solve the Poiseuille problem. Moreover, we shall show that Poiseuille flows exist in tubes of any cross-section for some special simple fluids. To illustrate this result we shall exhibit, for these special fluids, Poiseuille flows for which the curves of constant speed of the flow have constant curvature and which are not radially symmetric; a flow between two eccentric circular cylinders is considered. © 1989 Oxford University Press.
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