Page 396 - Introduction to Continuum Mechanics

380 CouetteFlow

Note that in the case of bi = 0, v\' = (v 0/b{)X2, which is the case of plane Couette flow
of a single fluid.

6.15 Couette Flow

The laminar steady two-dimensional flow of an incompressible Newtonian fluid between
two coaxial infinitely long cylinders caused by the rotation of either one or both cylinders with
constant angular velocities is known as Couette flow.
For this flow, we look for the velocity field in the following form in cylindrical coordinates

This velocity field obviously satisfies the equation of continuity [Eq. (6.8.2)] for any v(r).

In the absence of body forces and taking into account the rotational symmetry of the flow
(i.e., nothing depends on 0), we have, from the second Navier Stokes-equation of motion, Eq.
(6.8.1b), for the two-dimensional flow,

Fig. 6.10