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# Uniform Flow

Consider a uniform steady stream of velocity . Consider the flux (in the minus -direction) across a plane circle of radius that lies in the - plane, and whose center coincides with the -axis. From the definition of the Stokes stream function (see Section 7.3), we have , or (7.25)

When expressed in terms of spherical coordinates, the previous expression yields (7.26)

Of course, uniform flow is irrotational [this is clear from a comparison of Equations (7.10) and (7.25)], so we can also represent the flow pattern in terms of a velocity potential: that is (see Section 5.4), (7.27)

or (7.28)

It follows, from the previous analysis, that the velocity field of a uniform stream, running parallel to the -axis, can either be written , with specified by Equations (7.25)-(7.26), or , with specified by Equations (7.27)-(7.28).   Next: Point Sources Up: Axisymmetric Incompressible Inviscid Flow Previous: Axisymmetric Irrotational Flow in
Richard Fitzpatrick 2016-03-31