A cooling tower that leaves water just 5°F above the wet-bulb temperature is operating at near-optimal efficiency, but achieving this consistently requires understanding the precise mathematical relationship between three temperature measurements.
The Formula
The core calculation for cooling tower approach is deceptively simple: Approach = T_cold,leave − T_wb,enter. Each variable represents a specific physical measurement with engineering significance. T_cold,leave is the temperature of water exiting the tower after cooling, measured at the cold-water basin outlet. This value represents the actual cooling performance achieved. T_wb,enter is the entering ambient wet-bulb temperature, measured at the air intake. This represents the thermodynamic limit of evaporative cooling under current atmospheric conditions.
Why subtract wet-bulb from leaving water temperature? The wet-bulb temperature defines the lowest possible temperature achievable through evaporative cooling under ideal conditions. The difference between what's actually achieved (T_cold,leave) and what's theoretically possible (T_wb,enter) quantifies the tower's thermal performance gap. A secondary calculation, Range = T_hot,enter − T_cold,leave, provides context about the total temperature drop across the tower but doesn't indicate efficiency relative to environmental limits.
Worked Example 1
Consider a commercial office building cooling tower operating on a humid summer day. The entering hot water temperature (T_hot,enter) measures 95°F as it returns from the building's chillers. After passing through the tower, the leaving cold water temperature (T_cold,leave) reads 85°F. The ambient wet-bulb temperature (T_wb,enter) at the tower intake is 78°F. First, calculate approach: Approach = 85°F − 78°F = 7°F. This indicates the tower is cooling water to within 7°F of the wet-bulb limit. Next, calculate range for context: Range = 95°F − 85°F = 10°F. The water experiences a 10°F temperature drop through the tower.
Worked Example 2
Now examine an industrial cooling tower during a dry winter morning. The entering hot water from process equipment measures 120°F (T_hot,enter). After cooling, the leaving water temperature is 80°F (T_cold,leave). The ambient wet-bulb temperature is unusually low at 40°F (T_wb,enter) due to dry air. Approach calculation: Approach = 80°F − 40°F = 40°F. Despite a massive 40°F range (Range = 120°F − 80°F = 40°F), the approach of 40°F indicates poor thermal performance relative to environmental potential. The tower isn't leveraging the dry air's cooling capacity effectively.
What Engineers Often Miss
First, many engineers focus exclusively on range, interpreting larger temperature drops as better performance. However, a tower can have a large range with poor approach if it's not exploiting wet-bulb conditions efficiently. Second, sensor placement errors frequently corrupt wet-bulb measurements. Wet-bulb sensors must be positioned in the entering air stream, away from tower discharge plumes or reflective surfaces that create microclimates. Third, engineers sometimes use dry-bulb instead of wet-bulb temperature in calculations, particularly during design phases. Since evaporative cooling depends on moisture evaporation into air, dry-bulb temperatures overestimate achievable cooling, leading to undersized towers.
Try the Calculator
For quick calculations without manual arithmetic, use the Cooling Tower Approach Calculator. It automatically computes both approach and range from your temperature inputs, helping you focus on performance analysis rather than calculation mechanics.
Originally published at calcengineer.com/blog
