Three temperatures describe a cooling tower and two differences grade it. Name them once: $T_h$ is the hot water returning from the condenser, $T_c$ is the cold water leaving the basin, and $T_{wb}$ is the ambient wet-bulb temperature of the air entering the tower — all in °C.

The range is $\Delta T = T_h - T_c$, water against water. It measures what the PLANT did: the chiller decided how much heat to put into the loop, and the range is the answer. A tower that is running well and a tower that is fouled can post the same range, so on its own the range grades nothing.

The approach is $A = T_c - T_{wb}$, water against air — and this is the number that grades the TOWER. An evaporative tower works by evaporating water into the air, so the coldest water it could ever theoretically produce is air at its wet-bulb temperature. The approach says how close it got. Five degrees is respectable; a fouled fill or a fan in trouble shows up here first, and it shows up before anything else on the plant complains.

The trap is worth stating flatly: the approach is taken to the WET bulb, never the dry bulb. A tower routinely makes water colder than the ambient air temperature, which surprises people the first time they meet it, and measuring to the dry bulb flatters the tower badly. An approach of zero is impossible; an approach quoted as negative means the wrong bulb was used.

The heat side reuses the water constant from the last lesson: $Q = \rho c\,R\,\Delta T$, with $R$ the recirculation rate over the fill in L/s, $\Delta T$ the range, and $\rho c = 4.18\ \mathrm{kJ}$ per litre per degree. Range, not approach — heat rejection is a water-side balance and the air never enters it.