Psychrometrics
Wet-bulb temperature from temperature and RH (Stull)
- where
- arctangent terms, in radians
- relative humidity (%)
- dry-bulb temperature (°C)
- wet-bulb temperature (°C)
Explain this equation
Estimates the wet-bulb temperature from a dry-bulb and RH reading. Use it for evaporative cooling and cooling tower checks or to compare with a sling psychrometer.
t is the dry-bulb temperature and RH the relative humidity in percent. The terms a₁ to a₄ are arctangent shapes, in radians, that together trace the true wet-bulb surface. T_w is the result.
Stull fitted this empirical equation to exact psychrometric results at sea-level pressure, so it avoids the trial-and-error the exact method needs.
Sense check: 20 °C at 50 % gives about 13.7 °C, a 6.3 K depression. At 100 % RH the wet bulb equals the dry bulb.
Watch out: the arctangents must be in radians, and the fit is less accurate below about 5 % RH or in cold, dry air.
Estimates the wet-bulb temperature from a dry-bulb and RH reading. Use it for cooling-tower and evaporative cooler checks or to compare with a sling psychrometer.
Enter your values to see the result.
Good to know
The arctangents a1 to a4 are in radians (the × π/180 in the working converts from degrees). Stull’s fit is for standard sea-level pressure and has a typical error of under 0.3 °C. The wet-bulb depression (t − Tw) shows how much evaporative cooling is available.
Common mistake
Using a calculator set to degrees for the arctangents, which gives a nonsense answer.
Limits
Fitted for 5–99 % RH and −20 to 50 °C at 101.325 kPa; errors from −1 to +0.65 °C, worst at low humidity and low temperature. For exact work use the ASHRAE psychrometric equations.
Sources
- R. Stull, Wet-bulb temperature from relative humidity and air temperature, Journal of Applied Meteorology and Climatology 50(11), 2011, pp. 2267–2269 (20 °C, 50 % gives 13.7 °C)
- NCAR Command Language: wetbulb_stull (validity 5–99 % RH, −20 to 50 °C; example 20 °C, 50 % returns 13.69934 °C)
- ASHRAE Handbook — Fundamentals (2017), chapter 1 Psychrometrics: Hyland–Wexler saturation pressure (eq. 6), humidity ratio W = 0.621945 pw/(p − pw), enthalpy h = 1.006t + W(2501 + 1.86t), specific volume v = 0.287042(t + 273.15)(1 + 1.607858W)/p, adiabatic mixing
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.