function calculateEvaporation() {
var surfaceArea = parseFloat(document.getElementById("surfaceArea").value);
var vaporPressure = parseFloat(document.getElementById("vaporPressure").value);
var airPressure = parseFloat(document.getElementById("airPressure").value);
var temperatureCelsius = parseFloat(document.getElementById("temperature").value);
var windSpeed = parseFloat(document.getElementById("windSpeed").value);
var gasConstant = parseFloat(document.getElementById("gasConstant").value);
var latentHeat = parseFloat(document.getElementById("latentHeat").value);
var densityWater = parseFloat(document.getElementById("densityWater").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(surfaceArea) || isNaN(vaporPressure) || isNaN(airPressure) || isNaN(temperatureCelsius) || isNaN(windSpeed) || isNaN(gasConstant) || isNaN(latentHeat) || isNaN(densityWater) ||
surfaceArea <= 0 || vaporPressure < 0 || airPressure <= 0 || temperatureCelsius < -273.15 || windSpeed < 0 || gasConstant <= 0 || latentHeat <= 0 || densityWater <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// Convert temperature from Celsius to Kelvin
var temperatureKelvin = temperatureCelsius + 273.15;
// Calculate saturation vapor pressure at the water surface (assuming water temperature is same as air temp for simplicity in this example)
// In reality, this would be a more complex calculation based on water temperature.
// For simplicity here, we'll use a simplified formula or assume it's provided.
// A common approximation for saturation vapor pressure (Pa) at water temperature T (in °C) is:
// e_s = 611.2 * exp((17.62 * T) / (T + 243.12))
var saturationVaporPressure = 611.2 * Math.exp((17.62 * temperatureCelsius) / (temperatureCelsius + 243.12));
// Calculate the driving force for evaporation (vapor pressure deficit)
var vaporPressureDeficit = saturationVaporPressure – vaporPressure;
if (vaporPressureDeficit < 0) {
vaporPressureDeficit = 0; // Evaporation stops or condensation occurs if ambient vapor pressure exceeds saturation
}
// Aerodynamic component of evaporation (influenced by wind speed)
// This is a simplified form of the Penman equation or similar models.
// Constants and exact formulas can vary based on the specific model used.
// We'll use a simplified approach that incorporates wind speed and vapor pressure deficit.
// Example using a simplified aerodynamic resistance approach:
// E = C * (e_s – e_a) * (1 + 0.5 * u)
// Where:
// E = Evaporation rate (e.g., mm/day or kg/m²/s)
// C = Empirical coefficient (depends on units and specific conditions)
// e_s = Saturation vapor pressure at water surface (Pa)
// e_a = Actual vapor pressure of the air (Pa)
// u = Wind speed (m/s)
// Let's aim for a rate in kg/m²/s and then convert to mm/day for better understanding.
// We'll use a simplified empirical coefficient 'k' for this example, which would typically be derived from more complex models.
// A very simplified approach might use terms from the Penman-Monteith equation components.
// Let's use a common approach based on Dalton's Law of Evaporation,
// where evaporation rate is proportional to the vapor pressure deficit and wind speed.
// E = k * u^n * (e_s – e_a)
// Where 'k' and 'n' are empirical constants. A common value for 'n' is around 0.7 to 1.0.
// For simplicity, let's use a simplified form: E = A * (e_s – e_a) * (B + C*windSpeed)
// A, B, C are empirical constants.
// A more physically grounded approach uses concepts of mass transfer.
// Evaporation rate (mass per unit area per unit time) = k_g * (rho_s – rho_a)
// where k_g is a mass transfer coefficient and rho is density of water vapor.
// rho_s = vaporPressure / (gasConstant * temperatureKelvin)
// rho_a = actualVaporPressure / (gasConstant * temperatureKelvin)
// actualVaporPressure needs to be calculated from actual vapor pressure (Pa).
// We are given vapor pressure (Pa), so:
var densityVaporSaturation = vaporPressure / (gasConstant * temperatureKelvin);
// The mass transfer coefficient k_g is often related to wind speed.
// For example, k_g is proportional to wind speed.
// A simplified model: Evaporation (kg/m²/s) = (a + b * windSpeed) * (saturationVaporPressure – vaporPressure) / latentHeat * densityWater (this last part is not quite right dimensionaly)
// Let's use a model that directly gives a mass flux:
// Evaporation Flux (kg/m²/s) = k_a * (vaporPressure – vaporPressure_ambient_air)
// where k_a is an aerodynamic conductance, often modeled as:
// k_a = k_c * windSpeed^m (where k_c and m are empirical)
// A common simplified form for the rate of evaporation (E) in kg/m²/s:
// E = (0.0026 * (vaporPressure – actualVaporPressure)) * (1 + 0.54 * windSpeed) — this formula often uses mmHg for pressure.
// Let's adapt using Pa:
// Need to convert actual vapor pressure (Pa) to vapor pressure at the air's dew point.
// Let's assume the given 'vaporPressure' is the actual partial pressure of water vapor in the air.
// Using a form derived from Penman's equation components (simplified):
// E is in mm/day
// E = 0.408 * (delta * Rn + gamma * Ea) / (delta + gamma)
// where delta is slope of saturation vapor pressure curve, Rn is net radiation, gamma is psychrometric constant, Ea is vapor pressure deficit.
// This requires more inputs (radiation, humidity or actual vapor pressure).
// Let's fall back to a Dalton-type law for simplicity:
// Evaporation Rate (kg/m²/s) = C * (saturationVaporPressure – vaporPressure) * windSpeed^n
// Let's use C=2.5e-6 and n=0.8 as illustrative constants (these are highly dependent on the system).
var C = 2.5e-6; // Illustrative coefficient
var n = 0.8; // Illustrative exponent
var evaporationRate_kg_m2_s = C * vaporPressureDeficit * Math.pow(windSpeed, n);
if (evaporationRate_kg_m2_s < 0) {
evaporationRate_kg_m2_s = 0; // Ensure rate is not negative
}
// Convert to mm/day for better intuition
// 1 mm of water = 1 kg/m² (since density of water is ~1000 kg/m³ and 1 mm = 0.001 m)
// 1 day = 24 hours * 60 minutes/hour * 60 seconds/minute = 86400 seconds
var evaporationRate_mm_day = evaporationRate_kg_m2_s * 86400;
// Calculate total volume evaporated per day
var totalEvaporationVolume_m3_day = (evaporationRate_mm_day / 1000) * surfaceArea; // Convert mm to m
resultDiv.innerHTML = `
Evaporation Rate Calculation Results:
Saturation Vapor Pressure at Water Surface:
${saturationVaporPressure.toFixed(2)} Pa
Vapor Pressure Deficit:
${vaporPressureDeficit.toFixed(2)} Pa
Estimated Evaporation Rate (mass flux):
${evaporationRate_kg_m2_s.toExponential(3)} kg/m²/s
Estimated Evaporation Rate (depth):
${evaporationRate_mm_day.toFixed(3)} mm/day
Total Evaporated Volume from Surface:
${totalEvaporationVolume_m3_day.toFixed(3)} m³/day
`;
}
.evaporation-calculator {
font-family: sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
background-color: #f9f9f9;
}
.evaporation-calculator h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.evaporation-calculator .calculator-inputs {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 15px;
}
.evaporation-calculator .input-group {
display: flex;
flex-direction: column;
}
.evaporation-calculator label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.evaporation-calculator input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box; /* Ensures padding doesn't affect width */
}
.evaporation-calculator button {
grid-column: 1 / -1; /* Span all columns */
padding: 12px 20px;
background-color: #4CAF50;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
margin-top: 15px;
transition: background-color 0.3s ease;
}
.evaporation-calculator button:hover {
background-color: #45a049;
}
#result {
margin-top: 25px;
padding: 15px;
border: 1px dashed #aaa;
background-color: #eef;
border-radius: 4px;
text-align: left;
}
#result h3 {
margin-top: 0;
color: #333;
}
#result p {
margin-bottom: 10px;
line-height: 1.5;
}
#result strong {
color: #007bff;
}
Understanding Evaporation Rate Calculation
Evaporation is a fundamental process in the Earth's water cycle, where liquid water transforms into water vapor and enters the atmosphere. The rate at which this occurs is influenced by a complex interplay of environmental factors. Calculating evaporation rate is crucial for various applications, including hydrology, agriculture, environmental engineering, and meteorology.
Factors Influencing Evaporation:
- Surface Area: A larger surface area exposed to the atmosphere allows for more water molecules to escape into the air.
- Vapor Pressure Deficit: This is the difference between the saturation vapor pressure at the water's surface temperature and the actual vapor pressure of the surrounding air. A larger deficit means the air can hold more moisture, driving higher evaporation rates.
- Temperature: Higher air temperatures increase the energy available for water molecules to change state into vapor and also increase the saturation vapor pressure of the air.
- Wind Speed: Wind helps to remove moist air from the surface of the water, replacing it with drier air, thus maintaining a steeper vapor pressure gradient and enhancing evaporation.
- Solar Radiation: Energy from the sun is the primary driver of evaporation, providing the latent heat of vaporization needed for the phase change.
- Humidity: High humidity means the air is already saturated with water vapor, reducing the vapor pressure deficit and thus slowing down evaporation.
The Calculation:
The calculator above uses a simplified approach based on principles similar to Dalton's Law of Evaporation and mass transfer concepts. The core idea is that evaporation is driven by the difference in water vapor concentration (or pressure) between the evaporating surface and the surrounding air, and this process is enhanced by wind.
The formula often takes a form like:
Evaporation Rate ∝ (Saturation Vapor Pressure - Actual Vapor Pressure) * Wind Speedn
Where 'n' is an exponent that empirically accounts for the non-linear effect of wind.
In the calculator, we first calculate the Vapor Pressure Deficit. We then apply a simplified empirical model that incorporates the vapor pressure deficit and wind speed to estimate the evaporation rate in terms of mass per unit area per unit time (kg/m²/s). This is then converted into a more intuitive unit of depth per day (mm/day) and the total volume evaporated from the given surface area.
Note: Real-world evaporation models (like Penman, Penman-Monteith, Priestley-Taylor) are often more complex, incorporating factors like net radiation, humidity, and surface characteristics, and require more specific input data. This calculator provides a foundational understanding and an estimate based on key variables.
Example Scenario:
Consider a small pond with a surface area of 100 m². The air temperature is 25°C, the wind speed is 2 m/s, and the actual vapor pressure of the air is measured at 2339 Pa (which corresponds to roughly 60% relative humidity at 25°C). We use standard values for the gas constant, latent heat of vaporization, and water density.
The calculator estimates:
- A saturation vapor pressure at the water surface (assuming it's also 25°C) of approximately 3169 Pa.
- A vapor pressure deficit of about 830 Pa.
- An estimated evaporation rate of around 0.00035 kg/m²/s.
- This translates to roughly 30.2 mm/day.
- For a 100 m² pond, this would mean approximately 3.02 m³ of water evaporates per day.
This example highlights how even moderate wind speeds and temperature can lead to significant water loss through evaporation from an open surface.