Calculate Evaporation Rate from Vapor Pressure

Evaporation Rate Calculator

Understanding Evaporation Rate from Vapor Pressure

Evaporation is a crucial process in hydrology, meteorology, and various industrial applications. It's the process by which water changes from a liquid to a gas or vapor. The rate at which this occurs is influenced by several factors, including the vapor pressure of the water, the surrounding atmospheric pressure, temperature, wind speed, the surface area exposed, and the duration of the period considered.

Key Factors Influencing Evaporation Rate:

  • Vapor Pressure of Water: This is the pressure exerted by water vapor in equilibrium with its liquid phase. Higher vapor pressure indicates more water molecules are transitioning into the gaseous state, thus increasing the potential for evaporation.
  • Atmospheric Pressure: The total pressure of the air surrounding the water surface. A higher atmospheric pressure can impede the escape of water vapor into the atmosphere, thus reducing the evaporation rate.
  • Temperature: Higher temperatures provide water molecules with more kinetic energy, making it easier for them to break free from the liquid surface and enter the atmosphere as vapor. This directly increases the evaporation rate.
  • Wind Speed: Wind plays a significant role by removing the humid air layer that forms just above the water surface. As moist air is replaced by drier air, the concentration gradient for water vapor diffusion increases, leading to a higher evaporation rate.
  • Surface Area: A larger surface area exposed to the atmosphere allows for more water molecules to interact with the air, thereby increasing the total amount of water that can evaporate.
  • Time Period: The longer the time over which evaporation is measured, the greater the total volume of water that will have evaporated, assuming other factors remain constant.

Calculating Evaporation Rate:

A common empirical formula used to estimate evaporation rate, often referred to as the Penman-Monteith equation or simplified versions, considers these factors. While complex, a simplified approach for estimation can involve calculating the difference between the water vapor pressure and the actual vapor pressure in the air, then factoring in other atmospheric conditions.

A widely accepted model, though simplified here for illustrative purposes, considers the saturation vapor pressure at the water surface temperature and the actual vapor pressure of the air. The driving force for evaporation is the vapor pressure deficit (VPD), which is the difference between the saturation vapor pressure at the surface temperature and the actual vapor pressure of the air. This deficit is then modulated by atmospheric pressure, wind speed, and the duration of exposure.

For this calculator, we use a simplified approximation that acknowledges the interplay of these elements. The calculation is an estimation and can vary based on the specific model and empirical constants used.

Formula Basis (Conceptual):

The core idea is that evaporation is driven by the vapor pressure deficit (VPD). A simplified representation can be:

Evaporation Rate ≈ k * (e_s - e_a) * f(wind_speed) * Area * Time

Where:

  • k is a conversion factor.
  • e_s is the saturation vapor pressure at the water surface temperature.
  • e_a is the actual vapor pressure of the air.
  • f(wind_speed) is a function of wind speed that enhances mass transfer.
  • Area is the surface area.
  • Time is the time period.

In this calculator, we're approximating e_s based on the given temperature and assuming the input 'Vapor Pressure of Water' represents the saturation vapor pressure at the water surface. The 'Vapor Pressure of Water' input is often directly related to temperature. The 'Vapor Pressure of Water' input effectively serves as an approximation of saturation vapor pressure at the surface. The term (Vapor Pressure - Actual Vapor Pressure in Air) is a primary driver. The other factors (wind speed, area, time) scale this rate. The atmospheric pressure acts as a resistance to vapor escape.

Example Calculation:

Let's assume:

  • Vapor Pressure of Water (saturation vapor pressure at water surface): 2.34 kPa (This is approximately the saturation vapor pressure of water at 20°C)
  • Atmospheric Pressure: 101.3 kPa
  • Temperature: 25 °C (This influences the actual vapor pressure in the air if not explicitly given, but for this calculator, we'll assume the "Vapor Pressure of Water" input is the primary driver of saturation)
  • Wind Speed: 2.0 m/s
  • Surface Area: 10 m²
  • Time Period: 1 hour

Using a simplified model for demonstration, the effective vapor pressure driving evaporation is influenced by the difference between the vapor pressure of water and atmospheric conditions. A higher vapor pressure deficit (difference between saturation vapor pressure and actual air vapor pressure) leads to greater evaporation. Wind speed enhances this by removing saturated air. Atmospheric pressure slightly impedes it. The formula is a complex interplay.

If we use a simplified empirical approach:

Vapor Pressure Deficit ≈ (Vapor Pressure of Water) – (Actual Vapor Pressure in Air). We'll assume the input "Vapor Pressure of Water" is a proxy for the saturation vapor pressure at the surface.

A rough estimation might look at the ratio of vapor pressure to atmospheric pressure, multiplied by a factor related to wind and area over time.

Let's use a conceptual, simplified formula for this calculator: Evaporation (Liters) = (Vapor Pressure of Water / Atmospheric Pressure) * Wind Speed Factor * Surface Area * Time Period * Constant

Where the 'Wind Speed Factor' is a multiplier that increases with wind speed (e.g., 0.1 * wind_speed), and 'Constant' is an empirical coefficient (e.g., 0.5).

Using the example values:

Wind Speed Factor ≈ 0.1 * 2.0 m/s = 0.2

Evaporation ≈ (2.34 kPa / 101.3 kPa) * 0.2 * 10 m² * 1 hour * 0.5

Evaporation ≈ 0.0231 * 0.2 * 10 * 1 * 0.5 ≈ 0.0231 Liters

This demonstrates how the inputs combine. A more sophisticated model would involve calculating saturation vapor pressure from temperature and estimating actual vapor pressure from dew point or relative humidity.

function calculateEvaporation() { var vaporPressure = parseFloat(document.getElementById("vaporPressure").value); var airPressure = parseFloat(document.getElementById("airPressure").value); var temperature = parseFloat(document.getElementById("temperature").value); // Temperature is not directly used in the simplified calculation below but is good context var windSpeed = parseFloat(document.getElementById("windSpeed").value); var surfaceArea = parseFloat(document.getElementById("surfaceArea").value); var timePeriod = parseFloat(document.getElementById("timePeriod").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(vaporPressure) || isNaN(airPressure) || isNaN(windSpeed) || isNaN(surfaceArea) || isNaN(timePeriod) || vaporPressure <= 0 || airPressure <= 0 || windSpeed < 0 || surfaceArea <= 0 || timePeriod <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for all fields."; return; } // Simplified empirical formula for demonstration. // This is NOT a scientifically rigorous model like Penman-Monteith, // but illustrates how inputs might combine. // The constants here (0.1, 0.5) are arbitrary for example purposes. // A factor to increase evaporation with wind speed. This is highly simplified. // Real models use more complex functions. var windSpeedFactor = 0.1 * windSpeed; // Basic calculation: Vapor Pressure Deficit proxy * wind effect * area * time // The ratio (vaporPressure / airPressure) acts as a normalized driving force. // Higher vapor pressure of water (relative to atmospheric pressure) means more potential evaporation. var evaporationRate = (vaporPressure / airPressure) * windSpeedFactor * surfaceArea * timePeriod * 0.5; // 0.5 is an arbitrary empirical constant // In many contexts, evaporation is measured in units like mm/day or kg/m²/day. // Converting the calculated volume (Liters) to a rate per area per time can be more meaningful. // Let's assume the result is in Liters for the given surfaceArea and timePeriod. // To express as a depth (e.g., mm), we'd divide volume by area and convert units. // 1 Liter = 0.001 m^3. 1 m^3 = 1,000,000 mm^3. 1 m^2 = 1,000,000 mm^2. // 1 Liter / m^2 = 0.001 m^3 / m^2 = 0.001 m = 1 mm. // So, Liters / m² is directly equivalent to mm. var evaporationDepthMm = evaporationRate; // Since 1 Liter / 1 m^2 = 1 mm resultDiv.innerHTML = "Estimated Evaporation: " + evaporationRate.toFixed(4) + " Liters"; resultDiv.innerHTML += "Equivalent to: " + evaporationDepthMm.toFixed(4) + " mm over " + timePeriod + " hour(s) for " + surfaceArea + " m²."; } .calculator-container { font-family: Arial, sans-serif; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; background-color: #f9f9f9; } .calculator-title { text-align: center; color: #333; margin-bottom: 20px; } .calculator-inputs { display: grid; grid-template-columns: repeat(auto-fit, minmax(200px, 1fr)); gap: 15px; margin-bottom: 20px; } .input-group { display: flex; flex-direction: column; } .input-group label { margin-bottom: 5px; font-weight: bold; color: #555; } .input-group input[type="number"] { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1rem; } .calculator-button { display: block; width: 100%; padding: 12px 20px; background-color: #4CAF50; color: white; border: none; border-radius: 4px; font-size: 1.1rem; cursor: pointer; transition: background-color 0.3s ease; margin-bottom: 20px; } .calculator-button:hover { background-color: #45a049; } .calculator-result { background-color: #e7f3fe; border: 1px solid #2196F3; padding: 15px; border-radius: 4px; text-align: center; font-size: 1.1rem; color: #333; } .calculator-article { margin-top: 30px; padding-top: 20px; border-top: 1px solid #eee; color: #444; line-height: 1.6; } .calculator-article h2, .calculator-article h3, .calculator-article h4 { color: #333; margin-bottom: 15px; } .calculator-article ul { margin-left: 20px; margin-bottom: 15px; } .calculator-article li { margin-bottom: 8px; } .calculator-article code { background-color: #f0f0f0; padding: 2px 6px; border-radius: 3px; font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace; }

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