Water Evaporation Rate vs Temperature Calculator
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Calculation Results
Hourly Evaporation Rate
0.00 kg/hr
Mass Loss
0.00 L
Liters per Day
0.00 mm
Depth Loss per Day
0.00 kWh
Heat Loss per Day
0.00 kPa
Vapor Pressure Delta
*Results are estimates based on the standard engineering mass transfer formulas (ASHRAE) relating to vapor pressure differentials and wind velocity coefficients.
Understanding Water Evaporation and Temperature
The rate at which water evaporates is fundamentally tied to the relationship between the water temperature and the surrounding environment. This calculator uses thermodynamic principles to estimate the rate of mass transfer from a liquid water surface to the atmosphere, a critical calculation for managing swimming pools, industrial reservoirs, and HVAC systems.
How Temperature Drives Evaporation
Temperature is the primary driver of evaporation. As the temperature of the water increases, the kinetic energy of the water molecules increases. This allows more molecules to escape the surface tension of the liquid and enter the air as vapor. Specifically:
- Vapor Pressure: Higher water temperature increases the saturation vapor pressure at the water's surface.
- The Gradient: Evaporation occurs when the vapor pressure at the water surface is higher than the vapor pressure of the moisture in the air. The wider this gap (the delta), the faster the evaporation.
- Dew Point: If the air temperature drops but humidity remains constant, the air's capacity to hold water changes, affecting the evaporation potential.
The Physics Formula
This calculator utilizes a variation of the Dalton equation, often adapted for engineering applications (like the ASHRAE formulas for open water surfaces). The core logic determines the difference in humidity ratios:
E = Θ × A × (Xs – X)
- E: Evaporation rate (kg/hr)
- Θ: Activity coefficient based on wind speed (e.g., 25 + 19v)
- A: Surface Area (m²)
- Xs: Humidity ratio of saturated air at the water temperature
- X: Humidity ratio of the ambient air
Why Wind Speed and Humidity Matter
While temperature provides the energy, wind and humidity regulate the efficiency of the process:
- Relative Humidity: High humidity means the air is already saturated with water vapor, reducing the rate at which it can accept new evaporation. Low humidity accelerates evaporation.
- Wind Speed: Wind removes the boundary layer of saturated air sitting immediately above the water surface. By constantly replacing this with drier air, wind significantly increases the evaporation rate.
Applications of This Calculation
Understanding evaporation rates vs. temperature is essential for:
- Swimming Pool Management: Calculating water replacement costs and heat loss (evaporation is the primary source of heat loss in pools).
- Industrial Cooling: Estimating efficiency in cooling towers and reservoirs.
- Environmental Science: Studying reservoir levels during droughts where temperature spikes can lead to massive water volume loss.
function calculateEvaporation() {
// 1. Get Inputs
var waterTemp = parseFloat(document.getElementById('waterTemp').value);
var airTemp = parseFloat(document.getElementById('airTemp').value);
var rh = parseFloat(document.getElementById('relativeHumidity').value);
var wind = parseFloat(document.getElementById('windSpeed').value);
var area = parseFloat(document.getElementById('surfaceArea').value);
var errorMsg = document.getElementById('errorMsg');
// 2. Validation
if (isNaN(waterTemp) || isNaN(airTemp) || isNaN(rh) || isNaN(wind) || isNaN(area)) {
errorMsg.style.display = 'block';
return;
}
if (rh 100) {
errorMsg.innerHTML = "Relative Humidity must be between 0 and 100.";
errorMsg.style.display = 'block';
return;
}
errorMsg.style.display = 'none';
// 3. Constants
// Atmospheric pressure (standard sea level) in hPa
var P_atm = 1013.25;
// 4. Calculate Saturation Vapor Pressure at WATER Temperature (Magnus formula)
// Result in hPa
var P_sat_water = 6.112 * Math.exp((17.67 * waterTemp) / (waterTemp + 243.5));
// 5. Calculate Saturation Vapor Pressure at AIR Temperature
// Result in hPa
var P_sat_air = 6.112 * Math.exp((17.67 * airTemp) / (airTemp + 243.5));
// 6. Calculate Actual Vapor Pressure of Air
var P_vapor_air = P_sat_air * (rh / 100);
// 7. Calculate Humidity Ratios (kg water / kg dry air)
// Formula: W = 0.622 * P_vap / (P_atm – P_vap)
var W_sat_water = 0.62198 * P_sat_water / (P_atm – P_sat_water);
var W_actual_air = 0.62198 * P_vapor_air / (P_atm – P_vapor_air);
// 8. Evaporation Formula (ASHRAE / Carrier / Stelling adaptation for metric)
// E (kg/hr) = (25 + 19 * v) * A * (W_sat – W_air)
// Note: The coefficients (25 and 19) are empirical for standard open tanks/pools
var evaporationCoefficient = 25 + (19 * wind);
// If water is colder than dew point, condensation might occur (negative evaporation),
// but typically we clamp to 0 for simple evaporation calculators or show condensation.
// Let's allow negative to show condensation (mass gain) or clamp if requested.
// We will compute raw diff.
var humidityRatioDiff = W_sat_water – W_actual_air;
// Evaporation Rate in kg/hr
var E_rate_hr = evaporationCoefficient * area * humidityRatioDiff;
// Handle condensation (if E_rate_hr is negative, it's condensation)
var isCondensation = false;
if (E_rate_hr Height in m = 0.001 * L / A -> mm = L/A
var depthLossMmDay = litersPerDay / area;
// Latent Heat of Vaporization approx 2260 kJ/kg = 0.628 kWh/kg
var energyLossKwh = litersPerDay * 0.628;
// Pressure Delta for display (kPa)
var pressureDeltaKpa = (P_sat_water – P_vapor_air) / 10; // hPa to kPa
// 10. Update UI
var label = isCondensation ? "Condensation Rate" : "Hourly Evaporation Rate";
document.querySelector('.result-box .result-label').innerText = label;
document.getElementById('resultKgHr').innerHTML = E_rate_hr.toFixed(3) + "
kg/hr";
document.getElementById('resultLitersDay').innerText = litersPerDay.toFixed(2) + " L";
document.getElementById('resultDepthDay').innerText = depthLossMmDay.toFixed(2) + " mm";
// Energy is only lost during evaporation, gained during condensation.
var energyLabel = isCondensation ? "Heat Gain per Day" : "Heat Loss per Day";
document.querySelectorAll('.sec-res-lbl')[2].innerText = energyLabel;
document.getElementById('resultEnergy').innerText = energyLossKwh.toFixed(1) + " kWh";
document.getElementById('vaporPressureDiff').innerText = pressureDeltaKpa.toFixed(2) + " kPa";
}