Where a tower's water goes
A cooling tower cools by throwing water away. That is not a flaw, it is the mechanism — and it means the water chemistry inside the loop is a bookkeeping problem with exactly three exits.
Evaporation is the first and the biggest: , where is the evaporation rate in L/s, is the recirculation rate over the fill in L/s, and is the range in °C. The rule of thumb behind it is one tenth of one percent of the recirculation per Fahrenheit degree of range; a Celsius degree is 1.8 times as big, which is where 0.0018 comes from. Using 0.001 against a Celsius range is the standing trap of this lesson, and it under-reports the loss by nearly half.
Evaporation leaves EVERY dissolved mineral behind. So the basin concentrates, and the measure of that is cycles of concentration: , where is the makeup coming in and is the blowdown bled to drain, both in L/s. Four cycles means the tower water is four times as concentrated as the water fed to it. Cycles can never be below 1.
To HOLD a target cycles you must bleed: . The minus one is the part everyone drops, and it is the whole argument — only water that leaves as LIQUID carries minerals out with it, so the balance is written against the difference, not the total. Note what it says about the economics: going from 2 cycles to 4 halves the bleed, but going from 6 to 8 barely moves it. The savings are all at the bottom of the range.
And the makeup line has to replace all of it: , with the drift — droplets carried out bodily in the air stream, typically a few hundredths of a percent of recirculation on modern eliminators. Small, but real, and unlike evaporation it carries minerals AND treatment chemical out with it.