A two-dimensional flow exists between fixed boundaries at \(\theta=\pi / 4\) and \(\theta=-\pi / 4\). The flow is due to a source of strength, \(m\), at \(r=a, \theta=0\), and a sink of equal strength at \(r=b, \theta=0\). The stream function for such a flow is given by:

\[\psi=-m \operatorname{Tan}^{-1}\left[\frac{r^{4}\left(a^{4}-b^{4}\right) \sin 4 \theta}{r^{8}-r^{4}\left(a^{4}-b^{4}\right) \cos 4 \theta+a^{4} b^{4}}\right]\]

a. Determine the velocity components.

b. Calculate the vorticity for this flow. Does it obey the vorticity transport theorem?

\[\frac{D \vec{\omega}}{D t}=\overrightarrow{\boldsymbol{\omega}} \cdot \vec{abla} \overrightarrow{\mathbf{u}}\]