Chapter 7, Problem 6P

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

$\begin{array}{l}\frac{1}{r}\left(\frac{\partial \left(r{v}_r\right)}{\partial r}\right)+\frac{\partial v_z}{\partial z}=0\hfill \\ \rho \left(v_r\frac{\partial v_r}{\partial r}-\frac{v_{\theta }^2}{r}+v_z\frac{\partial v_r}{\partial z}\right)=\mu \frac{{\partial }^2{v}_r}{\partial z^2}\hfill \end{array}$

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

P7.6