Please enter valid numerical values for all fields.
Evaporation Rate (Metric)0.00 Liters/hour
Evaporation Rate (Imperial)0.00 Gallons/day
Vapor Pressure Differential0.00 kPa
Latent Heat of Vaporization0.00 kJ/kg
function calculateEvaporation() {
// Inputs
var waterTemp = parseFloat(document.getElementById('waterTemp').value);
var airTemp = parseFloat(document.getElementById('airTemp').value);
var humidity = parseFloat(document.getElementById('relHumidity').value);
var windSpeed = parseFloat(document.getElementById('windSpeed').value);
var area = parseFloat(document.getElementById('surfaceArea').value);
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('results');
// Validation
if (isNaN(waterTemp) || isNaN(airTemp) || isNaN(humidity) || isNaN(windSpeed) || isNaN(area)) {
errorDiv.style.display = 'block';
resultsDiv.style.display = 'none';
return;
}
errorDiv.style.display = 'none';
// 1. Calculate Saturation Vapor Pressure at Water Surface (Pw) in kPa
// Formula: Magnus equation
var Pw = 0.61121 * Math.exp((17.67 * waterTemp) / (waterTemp + 243.5));
// 2. Calculate Saturation Vapor Pressure of Air (Psat_a) in kPa
var Psat_a = 0.61121 * Math.exp((17.67 * airTemp) / (airTemp + 243.5));
// 3. Calculate Actual Vapor Pressure of Air (Pa) in kPa
var Pa = Psat_a * (humidity / 100);
// 4. Calculate Latent Heat of Vaporization (Y) in kJ/kg
// Approx Y = 2501 – 2.361 * T_water (Standard thermodynamic approximation)
var Y = 2501 – (2.361 * waterTemp);
// 5. Calculate Evaporation Rate (W) in kg/s
// Using Carrier's Equation / ASHRAE formulation modified for metric units
// W = [ (0.089 + 0.0782 * V) * (Pw – Pa) * A ] / Y
// This formula yields rate in kg/s
var pressureDiff = Pw – Pa;
// Handle condensation (if air is warmer/wetter than water, evap might be negative)
var evaporationRateKgPerSec = 0;
if (pressureDiff > 0) {
evaporationRateKgPerSec = ((0.089 + (0.0782 * windSpeed)) * pressureDiff * area) / Y;
} else {
// Condensation logic could go here, but for this calculator we default to 0 evap
evaporationRateKgPerSec = 0;
}
// Conversion
// 1 kg water = 1 Liter (approx)
var litersPerHour = evaporationRateKgPerSec * 3600;
// 1 Liter = 0.264172 US Gallons
var gallonsPerDay = litersPerHour * 24 * 0.264172;
// Display Results
document.getElementById('resMetric').innerText = litersPerHour.toFixed(2) + " Liters/hour";
document.getElementById('resImperial').innerText = gallonsPerDay.toFixed(2) + " Gallons/day";
document.getElementById('resPressure').innerText = pressureDiff.toFixed(3) + " kPa";
document.getElementById('resLatent').innerText = Y.toFixed(1) + " kJ/kg";
resultsDiv.style.display = 'block';
}
Understanding the Evaporation Rate Formula
Evaporation is the process by which liquid water turns into water vapor. Calculating the rate at which this occurs is critical for swimming pool maintenance, industrial engineering, hydrology, and HVAC system design. The rate depends on several environmental factors including temperature, humidity, and airflow.
The Calculation Logic
This calculator uses a standard hydrodynamic formula derived from the Carrier equation and ASHRAE guidelines. While exact evaporation is difficult to predict without complex simulations, the following empirical formula provides a robust estimation for open water surfaces:
W = [ (Θ + ω × V) × (P_w – P_a) × A ] / Y
Where:
W: Evaporation rate (mass/time)
V: Air velocity over the water surface (m/s)
P_w: Saturation vapor pressure at the water temperature (kPa)
P_a: Actual vapor pressure of the air (kPa)
A: Surface Area of the water (m²)
Y: Latent heat of vaporization (kJ/kg)
Θ & ω: Empirical coefficients characterizing convection (typically 0.089 and 0.0782 respectively for these units)
Key Factors Influencing Evaporation
1. Vapor Pressure Differential (Pw – Pa)
This is the driving force of evaporation. Water molecules are constantly escaping the surface. If the air is dry (low vapor pressure), more molecules can escape than return. If the air is saturated (100% humidity), the net evaporation is zero.
2. Air Velocity (Wind)
Stagnant air becomes saturated quickly right above the water surface, halting evaporation. Wind removes this saturated layer, replacing it with drier air, thereby maintaining a high rate of evaporation.
3. Water Temperature
Warmer water has higher kinetic energy, meaning molecules escape more easily. This increases the saturation vapor pressure at the surface ($P_w$), leading to a higher evaporation rate.
Example Calculation
Consider a swimming pool with the following conditions:
Water Temp: 25°C
Air Temp: 25°C
Relative Humidity: 50%
Wind Speed: 0.5 m/s
Surface Area: 50 m²
At these settings, the calculator would determine the vapor pressure deficit and apply the coefficients to estimate the water loss, helping pool owners determine how often they need to top up the water level or whether a pool cover is necessary to save energy and water.
Applications
Accurate evaporation calculations are used in:
Swimming Pools: Estimating water loss and heat loss (evaporative cooling).
Industrial Processes: Designing open tanks and cooling towers.
Agriculture: Managing irrigation requirements and reservoir storage.
Meteorology: Studying lake levels and weather patterns.