Wet bulb temperature (WBT) is an essential measure that combines air temperature and humidity to indicate how the environment feels to the skin. Unlike the thermometer, which only measures air temperature, the wet bulb temperature reflects cooling effects due to evaporation. This is particularly important in high-humidity environments where evaporation is less effective at cooling the body, leading to higher heat stress.
Formula of Wet Bulb Calculator
To calculate the wet bulb temperature, we use the following formula:
Tw = T * arctan[0.151977 * (RH% + 8.313659)^(1/2)] + arctan(T + RH%) – arctan(RH% – 1.676331) + 0.00391838 * (RH%)^(3/2) * arctan(0.023101 * RH%) – 4.686035
where:
- Tw is the wet-bulb temperature
- T is the air temperature
- RH% is the relative humidity This formula accounts for the complex interplay between air temperature and relative humidity, offering a precise measure of the heat stress experienced by individuals in specific conditions.
Table for General Terms
| Air Temperature (°C) | Relative Humidity (%) | Wet Bulb Temperature (°C) |
|---|---|---|
| 25 | 50 | 17.3 |
| 25 | 70 | 19.6 |
| 30 | 50 | 21.1 |
| 30 | 70 | 24.0 |
| 35 | 50 | 24.9 |
| 35 | 70 | 28.3 |
| 40 | 50 | 28.7 |
| 40 | 70 | 32.6 |
Example of Wet Bulb Calculator
Suppose the air temperature (T) is 30 degrees Celsius and the relative humidity (RH%) is 70%. We want to calculate the wet bulb temperature (Tw) using the formula provided:
Formula:
Tw = T * arctan[0.151977 * (RH% + 8.313659)^(1/2)] + arctan(T + RH%) – arctan(RH% – 1.676331) + 0.00391838 * (RH%)^(3/2) * arctan(0.023101 * RH%) – 4.686035
Calculation Steps:
- Calculate the square root term:
- Compute 0.151977 * (70 + 8.313659)^(1/2)
- Result: 0.151977 * (78.313659)^(1/2) ≈ 0.151977 * 8.8462 ≈ 1.3444
- Compute each arctan term:
- arctan[1.3444] ≈ 0.9303
- arctan(30 + 70) ≈ arctan(100) ≈ 1.5608
- arctan(70 – 1.676331) ≈ arctan(68.323669) ≈ 1.5460
- Calculate the final components involving arctan and cubic terms:
- 0.00391838 * (70)^(3/2) * arctan(0.023101 * 70)
- 0.00391838 * 583.095 * arctan(1.61707) ≈ 0.00391838 * 583.095 * 1.0035 ≈ 2.2846
- Sum all components and subtract the constant:
- 30 * 0.9303 + 1.5608 – 1.5460 + 2.2846 – 4.686035
- 27.9090 + 1.5608 – 1.5460 + 2.2846 – 4.686035 ≈ 25.5224
Result:
The calculated wet bulb temperature for an air temperature of 30°C and 70% relative humidity is approximately 25.5°C.
Most Common FAQs
A: Wet bulb temperature measures potential cooling effect on the skin due to evaporation. It’s crucial for assessing heat stress, particularly in humid climates where traditional temperature readings fall short.
A: While a direct calculation involves complex equations, a simple estimation can be derived using a sling psychrometer and some basic calculations.
A: No, wet bulb temperature is typically lower than or equal to the air temperature because it considers the cooling effects of evaporation.