Range and Approach: the two spans that set a cooling tower's duty

A worked Range and Approach ladder with the effectiveness curve, and the formulas behind both spans.

The three temperatures of one example — entering wet bulb, cold water and hot water — as a ladder, with Range and Approach drawn as the spans between them; below it, the cooling effectiveness R ÷ (R + A) against Range, with the example marked on its curve.

Reference conditions: entering wet bulb 27.00 °C, cold water 31.00 °C, hot water 37.00 °C — Range 6.00 °C, Approach 4.00 °C, effectiveness 60.00 %.

Formula: Range = Th − Tc, Approach = Tc − Twb, Cooling effectiveness = Range ÷ (Range + Approach) × 100 %.

Cooling Range and Approach: a temperature ladder of 27.00 °C wet bulb, 31.00 °C cold water and 37.00 °C hot water, giving a Range of 6.00 °C and an Approach of 4.00 °C, with the effectiveness curve R ÷ (R + A) and the example marked on it at 60.00 % (illustrative)Illustrative Range and Approach chart. The ladder carries the post's three stated temperatures: entering wet bulb 27.00 °C, cold water 31.00 °C and hot water 37.00 °C. The hatched spans are the post's own two relations: Range = hot water − cold water = 37.00 − 31.00 = 6.00 °C, and Approach = cold water − entering wet bulb = 31.00 − 27.00 = 4.00 °C; their sum is the hot-water-to-wet-bulb difference, 10.00 °C. The lower panel plots the post's cooling effectiveness, R ÷ (R + A), against the Range with A held at the example's own Approach of 4.00 °C. The example is marked on that curve at Range 6.00 °C, Approach 4.00 °C, effectiveness 60.00 %, computed as 6.00 ÷ (6.00 + 4.00) × 100. Values are computed from the post's own relations, not measured. (chart-approach-range)Range and approach — Illustrative — not a measurementRange, approach and effectiveness26283032343638Temperature (°C)Hot water 37.00 °CCold water 31.00 °CWet bulb 27.00 °CRange 37.00 − 31.00 = 6.00 °CApproach 31.00 − 27.00 = 4.00 °C0246810020406080Cooling Range (°C)Cooling effectiveness (%)R ÷ (R + A)60.00 %Range 6.00 °CReference: wet bulb 27.00 °C · cold water 31.00 °C · hot water 37.00 °CR = Range, A = Approach; the curve holds A at the example's 4.00 °CRange = hot − cold (°C)6.00Approach = cold − wb (°C)4.00Effectiveness = R ÷ (R + A) (%)60.00Hot − wb = R + A (°C)10.00Computed from the formula — not field data.
Illustrative, computed from the definitions above — not a measurement. The ladder carries the example’s three temperatures and the two spans between them; the curve is the same effectiveness relation with Approach held at the example’s own 4.00 °C.

Sources

This chart evaluates the guide's own definitions; the guide cites no external source for them.

Guide: Cooling Range and Approach explained with a worked example