Water flow rate through a filter

[Melawrghk]

Homework Statement

Hello everyone, I'm working on a summer project with filters (they're rather simple). Anyways, my professor suggested that I calculate flux through the final surface of the filter, which I guess is speed of water?
Long story short, I'm having a real problem with this... I have the Rose equation for hydraulics and Bernoulli's equation. I don't know how to approach this exactly?
I just finished my first year of engineering, so I only know the basics of pipe flow, but I'm willing up to read on things as long as it's not covering an entire course or something.

Any help or suggestions would be appreciated. I just need a push in the right direction... Thanks in advance!

 

[Melawrghk]

Alright, I think I got somewhere, but I'm not sure if I'm allowed to do that at all. I took the Rose equation for head loss and substituted it into bernoulli's, which gave me:

\frac{1.067*Cd*D}{\Phi*g*\epsilon^{2}*d}*V²=D - \frac{V^{2}}{2g} - \frac{P}{\gamma}

Where Cd is the drag coefficient, D is depth of filter bed, \Phi is shape factor, \epsilon is porosity of hte material, d is average diameter of pieces in the filter, V is average speed through layer, P is pressure on the exit side of the filter bed (well difference in pressure really) and \gamma is specific gravity.

I rearranged it and it looks better, but I'm not sure I'm allowed to do it this way. Can someone please please tell me if this makes any sense.