Understanding Wet Bulb Temperature and Its Calculation
The wet bulb temperature is a crucial indicator in meteorology, environmental science, and agriculture. It represents the lowest temperature to which air can be cooled by the evaporation of water into the air at a constant pressure. Unlike the dry bulb temperature (which is what a standard thermometer measures), the wet bulb temperature takes into account the cooling effect of evaporation, which is directly related to the air's humidity.
Why is Wet Bulb Temperature Important?
Human Comfort and Heat Stress: High wet bulb temperatures indicate a reduced ability for the body to cool itself through sweating, leading to increased risk of heat exhaustion and heatstroke. A wet bulb temperature of 31°C (88°F) or higher is considered dangerous, and 35°C (95°F) is considered the theoretical limit for human survival, even for healthy individuals in the shade.
Agriculture: It helps in predicting crop stress and managing irrigation.
HVAC and Industrial Processes: Essential for designing cooling towers and other systems that rely on evaporative cooling.
Meteorology: Aids in forecasting fog, dew, and other weather phenomena.
The Math Behind the Calculation
Calculating the wet bulb temperature precisely involves complex psychrometric formulas that often require iterative solutions or lookup tables. A common approximation, especially for temperatures above freezing and not excessively humid, can be derived from the dry bulb temperature and relative humidity.
A widely used, albeit simplified, approach involves using formulas that relate the saturation vapor pressure at the dry bulb temperature to the actual vapor pressure, and then iteratively solving for the wet bulb temperature where the latent heat of vaporization balances the sensible heat transfer.
For practical purposes, especially in web calculators, empirical formulas or approximations are often employed. One such approximation, based on the work of Stull (2011), provides a reasonably accurate estimation without complex iterative methods. The formula used in this calculator is a simplified approximation derived from psychrometric charts and empirical fitting, aiming for reasonable accuracy within common ranges:
The wet bulb temperature ($T_{wb}$) can be approximated using the dry bulb temperature ($T_{db}$) and relative humidity ($RH$). A commonly used empirical formula is:
Note: This is a simplified empirical approximation. More precise calculations may involve iterative solutions to the psychrometric energy balance equation. The accuracy of this formula is generally good for typical atmospheric conditions.
Example Calculation
Let's consider a scenario:
Dry Bulb Temperature: 30°C
Relative Humidity: 60%
Plugging these values into the approximate formula (or using a reliable calculator), we would expect a wet bulb temperature around 24.2°C. This indicates that while the air temperature is 30°C, the cooling effect of evaporation reduces the effective temperature to 24.2°C. If the relative humidity were higher, say 80%, the wet bulb temperature would be closer to the dry bulb temperature (around 27.5°C), meaning less evaporative cooling is possible, and the heat stress would be greater.
function calculateWetBulb() {
var temperature = parseFloat(document.getElementById("temperature").value);
var humidity = parseFloat(document.getElementById("humidity").value);
var resultElement = document.getElementById("wetBulbResult");
// Clear previous result
resultElement.innerHTML = "–";
// Validate inputs
if (isNaN(temperature) || isNaN(humidity)) {
resultElement.innerHTML = "Invalid Input";
return;
}
if (humidity 100) {
resultElement.innerHTML = "Humidity must be between 0 and 100%";
return;
}
if (temperature 60) { // Reasonable range for atmospheric temp
resultElement.innerHTML = "Temperature out of typical range";
return;
}
// Constants for the empirical formula (Stull, 2011 – simplified and adjusted)
// This is a common approximation. Precise psychrometric calculations are more complex.
var T = temperature;
var R = humidity;
// Simplified approximation formula (often cited and used in many online calculators)
// Note: Different approximations exist. This one is a balance of simplicity and accuracy.
var a = (17.27 * T) / (237.7 + T) + Math.log(R / 100);
var Twb = (237.7 * a) / (17.27 – a);
// Ensure wet bulb temp is not higher than dry bulb temp
if (Twb > T) {
Twb = T;
}
// Ensure wet bulb temp is not below absolute zero equivalent if calculation goes awry for extreme low temps
if (Twb < -273.15) {
Twb = -273.15;
}
resultElement.innerHTML = Twb.toFixed(1) + " °C";
}