CFD Online Discussion Forums - fractional step method in cylindrical coordinates, help please?

I am trying to solve developing internal flow in a circular duct using a staggered grid and cylindrical navier stokes equations.

At the moment I am using a fractional step method with primitive variables but my code is currently wrong and I think it has to do with the pressure correction step and I think I might be using the wrong equations. Please let me know if you see anything wrong. My process is listed below.

fractional step for advection terms
$U^* = U^n-\Delta t(\frac{\partial UV}{\partial r}+\frac{\partial U^2}{\partial z})$
$V^* = V^n-\Delta t(\frac{\partial V^2}{\partial r}+\frac{\partial UV}{\partial z})$

fractional step for diffusion terms
$U^{**} = U^*+\frac{\Delta t}{Re}(\frac{1}{r}\frac{\partial U^{**}}{\partial r}+\frac{\partial^2 U^{**}}{\partial r^2} + \frac{\partial^2 U^{**}}{\partial z^2})$
$V^{**} = V^*+\frac{\Delta t}{Re}(\frac{1}{r}\frac{\partial V^{**}}{\partial r}+\frac{\partial^2 V^{**}}{\partial r^2} + \frac{\partial^2 V^{**}}{\partial z^2}-\frac{V^{**}}{r^2})$

pressure correction
$U^{n+1} = U^{**} - \Delta t(\frac{\partial P}{\partial z})$
$V^{n+1} = V^{**} - \Delta t(\frac{\partial P}{\partial r})$

where Pressure is calculated by
$\frac{1}{r}\frac{\partial P}{\partial r}+\frac{\partial^2 P}{\partial r^2}+\frac{\partial^2 P}{\partial z^2} = \Delta t(\frac{U^{**}}{r}+\frac{\partial U^{**}}{\partial r}+\frac{\partial V^{**}}{\partial z})$