Blowdown Rate from Cycles

Every mineral entering with the makeup leaves either in the blowdown or as scale on a tube. Write the salt balance — makeup in equals blowdown out, at COC times the concentration — and with makeup being evaporation plus blowdown the algebra collapses to B = E/(COC − 1). A tower evaporating 20 gpm and asked to hold 5 cycles must bleed 20/4 = 5 gpm; ask it to hold 10 cycles and the bleed drops to 2.2 gpm.

The shape of that curve is the whole economic argument for a chemical program. Going from 2 to 4 cycles cuts blowdown by two thirds; going from 8 to 10 barely moves it. Beyond about six cycles you are paying scale-inhibitor money for very little additional water saving, which is why most well-run comfort-cooling towers settle in the 4–7 range. And note what COC = 1 means physically: makeup with no concentration at all, which would require infinite bleed — the solver refuses it rather than dividing by zero.