Streamline flow through a curved annulus

Theoretical calculations are carried out for the steady laminar incompressible flow of an ordinary viscous fluid in a curved annulus. At first the flow parameters are evaluated for the general case and then a particular example is solved numerically. The graphical representations of the flowline in the plane of symmetry and the projection of the stream-lines on a normal section are given. Only the case of large radius of curvature of the annulus is considered; more precisely this means that the ratio of the radius of the outer curved pipe to that of the circle in which the common axis of the two curved pipes is coiled is sufficiently small