Taylor's Idealized Model
The configuration shown in the figure cannot actually be realized, as the two plates cannot extend infinitely in the flow direction. Sir Geoffrey Taylor was interested in shear-driven flows created by rotating co-axial cylinders. He reported a mathematical result in 1923 that accounts for curvature in the flow direction having the form
where C1 and C2 are constants that depend on the rotation rates of the cylinders. (Note that r has replaced y in this result to reflect cylindrical rather than rectangular coordinates.) It is clear from this equation that curvature effects no longer allow for constant shear in the flow domain, as shown above. This model is incomplete in that it does not account for near-wall effects in finite-width cylinders, although it is a reasonable approximation if the width is large compared to the space between the cylinders. Generalizations of Taylor's basic model have also been examined. For example, the solution for the time-dependent "start-up" process can be expressed in terms of Bessel functions.
Read more about this topic: Couette Flow
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