Estimate the rate of liquid water evaporation based on environmental conditions.
Evaporation Rate (Mass):– kg/hr
Volumetric Loss:– Liters/day
Heat Loss (Latent):– kW
Specific Rate:– kg/m²/hr
How to Calculate Rate of Evaporation of Liquid
Calculating the rate of evaporation is crucial for various industries, from HVAC engineering and swimming pool maintenance to environmental science and chemical processing. Evaporation occurs when liquid molecules gain enough kinetic energy to escape the surface and become vapor.
While the exact rate depends on complex fluid dynamics, this calculator uses standard empirical formulas (derived from ASHRAE and Carrier engineering data) to estimate evaporation based on vapor pressure differentials.
The Physics Behind the Calculation
The core driver of evaporation is the difference between the vapor pressure at the liquid's surface and the vapor pressure of the surrounding air. If the air is dry (low vapor pressure), evaporation is faster. If the air is saturated (100% humidity), evaporation stops.
The general formula used for water surfaces is:
gs = Θ × A × (xs – x)
Where:
• gs = Evaporation rate
• Θ = Evaporation coefficient (dependent on wind speed)
• A = Surface area
• xs = Humidity ratio of saturated air at the water temperature
• x = Humidity ratio of the ambient air
Key Factors Influencing Evaporation
Water Temperature: Warmer water has higher saturation vapor pressure, leading to faster evaporation. This is why heated pools lose water rapidly in winter.
Air Temperature & Humidity: These determine how much moisture the air can hold. Low humidity accelerates the process significantly.
Air Velocity (Wind): Wind removes the boundary layer of saturated air sitting just above the liquid surface, replacing it with drier air and drastically increasing the evaporation rate.
Surface Area: Evaporation is a surface phenomenon. Doubling the surface area directly doubles the total evaporation amount.
Why This Calculation Matters
Swimming Pools: A typical uncovered residential pool can lose thousands of liters of water per month. Calculating this rate helps in sizing heaters (as evaporation is the primary source of heat loss) and estimating water refill costs.
Industrial Tanks: In chemical processing, knowing the evaporation rate of solvents or water is vital for maintaining concentration levels and ensuring safety.
Environmental Studies: Estimating evaporation from lakes and reservoirs is essential for water resource management, especially in arid climates.
function calculateEvaporation() {
// 1. Get Inputs
var tWater = parseFloat(document.getElementById("waterTemp").value);
var tAir = parseFloat(document.getElementById("airTemp").value);
var rh = parseFloat(document.getElementById("relHumidity").value);
var velocity = parseFloat(document.getElementById("airVelocity").value);
var area = parseFloat(document.getElementById("surfaceArea").value);
// 2. Validation
if (isNaN(tWater) || isNaN(tAir) || isNaN(rh) || isNaN(velocity) || isNaN(area)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (rh 100) {
alert("Relative Humidity must be between 0 and 100.");
return;
}
// 3. Constants and Physics Calculations
// Using standard engineering formulas for atmospheric pressure (approx 101.325 kPa)
var patm = 101.325; // kPa
// Helper: Calculate Saturation Vapor Pressure (Psat) in kPa using Tetens Formula
// P = 0.61078 * exp((17.27 * T) / (T + 237.3))
function getSatVaporPressure(temp) {
return 0.61078 * Math.exp((17.27 * temp) / (temp + 237.3));
}
// 3a. Vapor Pressure at Water Surface (assume saturated air at water temp)
var P_sat_water = getSatVaporPressure(tWater);
// 3b. Vapor Pressure of Air (Psat at air temp * Relative Humidity)
var P_sat_air = getSatVaporPressure(tAir);
var P_vapor_air = P_sat_air * (rh / 100);
// 3c. Calculate Humidity Ratios (x) – kg water / kg dry air
// x = 0.622 * P_vapor / (P_atm – P_vapor)
// Humidity ratio at water surface (saturated)
var x_s = 0.622 * P_sat_water / (patm – P_sat_water);
// Humidity ratio of ambient air
var x_a = 0.622 * P_vapor_air / (patm – P_vapor_air);
// 4. Calculate Evaporation Coefficient (Theta)
// Using a standard engineering approximation for pools/water surfaces:
// Theta = 25 + 19 * v (kg/m²·h)
// This is a common metric adaptation of the Carrier equation.
var theta = 25 + (19 * velocity);
// 5. Calculate Evaporation Rate (Mass Flux)
// Rate = Theta * Area * (x_s – x_a)
// Result is in kg/hr
var evaporationRateKgHr = theta * area * (x_s – x_a);
// Handle condensation (negative evaporation)
if (evaporationRateKgHr 0 ? (evaporationRateKgHr / area) : 0;
// Energy Loss (Latent Heat of Vaporization)
// Latent heat approx 2440 kJ/kg at 25°C (varies slightly with temp)
// Power (kW) = (kg/s) * kJ/kg
// kg/s = kg/hr / 3600
var latentHeat = 2440; // kJ/kg avg
var powerKW = (evaporationRateKgHr / 3600) * latentHeat;
// 7. Display Results
document.getElementById("results").style.display = "block";
document.getElementById("resKgHr").innerHTML = evaporationRateKgHr.toFixed(3) + " kg/hr";
document.getElementById("resLitersDay").innerHTML = litersPerDay.toFixed(1) + " Liters/day";
document.getElementById("resEnergy").innerHTML = powerKW.toFixed(2) + " kW";
document.getElementById("resFlux").innerHTML = flux.toFixed(3) + " kg/m²/hr";
}