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