Consider a disk of radius \(R\) rotating in an incompressible fluid at a speed \(\omega\). The equations that describe the boundary layer on the disk are:

\[\begin{aligned}& \frac{1}{r}\left(\frac{\partial\left(r v_{r}\right)}{\partial r}\right)+\frac{\partial v_{z}}{\partial z}=0 \\& ho\left(v_{r} \frac{\partial v_{r}}{\partial r}-\frac{v_{\theta}^{2}}{r}+v_{z} \frac{\partial v_{r}}{\partial z}\right)=\mu \frac{\partial^{2} v_{r}}{\partial z^{2}}\end{aligned}\]

Use the characteristic dimensions to normalize the differential equation and obtain the dimensionless groups that characterize the flow.

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P7.6 @) R