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Consider a plane wall located at <math>\theta=0</math> in the cylindrical coordinates <math>(r,\theta)</math>, moving with a constant velocity <math>U</math> towards the left. Consider another plane wall(scraper), at an inclined position, making an angle <math>\alpha</math> from the positive <math>x</math> direction and let the point of intersection be at <math>r=0</math>. This description is equivalent to moving the scraper towards right with velocity <math>U</math>. The problem is singular at <math>r=0</math> because at the origin, the velocities are discontinuous, thus the velocity gradient is infinite there.
Taylor noticed that the inertial terms are negligible as long as the region of interest is within <math>r\ll\nu/U</math>( or, equivalently [[Reynolds number]] <math>Re = Ur/\nu \ll 1</math>), thus within the region the flow is essentially a [[Stokes flow]]. For example, [[George Batchelor]]
:<math>\nabla^4 \psi =0, \quad u_r = \frac 1 r \frac{\partial\psi}{\partial\theta}, \quad u_\theta = -\frac{\partial\psi}{\partial r}</math>
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