# Consider the flow in cylindrical coordinates with no dependence on (theta). How is the streamfunction defined? What

## Question:

Consider the flow in cylindrical coordinates with no dependence on \(\theta\). How is the streamfunction defined? What is the non-vanishing component of vorticity. Show that the \(E^{2}\) operator takes the form

\[\begin{equation*}E^{2}=\frac{\partial^{2}}{\partial r^{2}}-\frac{1}{r} \frac{\partial}{\partial r}+\frac{\partial^{2}}{\partial z^{2}} \tag{15.82}\end{equation*}\]

and \(E^{4} \psi=0\) for Stokes flow.

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**Related Book For**

## Advanced Transport Phenomena Analysis Modeling And Computations

**ISBN:** 9780521762618

1st Edition

**Authors:** P. A. Ramachandran