If you want equations to understand the flow, resistance, and overall fluid Dynamics of a ribbon burner, just look at the fluid Dynamics equations:
v=Q/A, where v is velocity (cm/sec), Q is flow (mL/sec), A is area (cm²).
Q=∆P/R, where ∆P is pressure difference (pressure beginning minus pressure at end), and R is resistance (see below next).
R=8nL/πr⁴, n is viscosity of fluid (negligible, or 1, for gas), L is length of tube (cm), r is radius of tube.
For ribbon burners, it is a parallel series of tubes, nozzels, etc. Point is, it's parallel. Now, the total resistance of a parallel system is:
1/R[total]= 1/R[1] + 1/R[2] + 1/R[3] ....
This means the total resistance of the entire parallel system will be LESS than any single individual "nozzel" resistance (calculate it if you dont believe me). Put another way, as the number of nozzels/outlet ports increases, the total resistance of the system (burner) will decrease. As the resistance decreases, the flow through the system will increase (ie: you will be using more gas overall--thats not a brain-buster). As the number of nozzels increases, you can push higher volumes of gas through. But, if you keep your PSI at the regulator the same, you'll obviously have less flow, and less velocity and pressure difference, coming out each nozzel.
So, again none of this should be surprising. I'm just explaining it so people will realize the equations are correct. Further, if you are designing something involving explosive gas, it doesn't hurt to "check" your plans with the equation. Hopefully the equations will be useful. Without having more info myself I can't provide much more. But, if you want my input feel free to ask. I'll tell you what I know. If I don't know the answer to something, I'll be the first person to say "I don't know". Best of luck.