How to Calculate Evaporation Rate from Vapor Pressure

The vapor pressure at the water's surface temperature.

The vapor pressure in the surrounding air.

Measured at approximately 2 meters height.

Calculation Results:

Evaporation Rate: 0 mm/day

Daily Water Loss: 0 Liters/day

Mass Transfer Rate: 0 kg/m²·day

How to Calculate Evaporation Rate from Vapor Pressure

Calculating the evaporation rate is critical for civil engineering, meteorology, and agricultural management. The primary driver of evaporation is the difference between the vapor pressure at the water surface and the vapor pressure of the overlying air, often referred to as the Vapor Pressure Deficit (VPD).

The Physics of Evaporation: Dalton's Law

John Dalton first proposed that evaporation is proportional to the difference in vapor pressures. A common empirical mass-transfer formula used for open water bodies is:

E = (N + P * u) * (e_s – e_a)

• E: Evaporation rate (mm/day).
• e_s: Saturation vapor pressure at the temperature of the water surface.
• e_a: Actual vapor pressure of the air.
• u: Wind speed in meters per second (m/s).
• N & P: Empirical constants (standard values are often 0.5 for small bodies).

Step-by-Step Example

Suppose you have a swimming pool with a surface area of 30 m² under the following conditions:

1. Water Surface Temp: 25°C (leads to e_s ≈ 3.17 kPa).
2. Air Humidity: Actual vapor pressure (e_a) is 1.20 kPa.
3. Wind Speed: 3.0 m/s.

Step 1: Calculate the difference.
3.17 kPa – 1.20 kPa = 1.97 kPa.

Step 2: Apply the wind factor.
(0.5 + 0.5 * 3.0) = 2.0.

Step 3: Multiply the components.
2.0 * 1.97 = 3.94 mm/day.

Step 4: Total Volume Loss.
3.94 mm is 0.00394 meters. 0.00394 m * 30 m² = 0.1182 m³, which is approximately 118 Liters per day.

Why Vapor Pressure Matters

Unlike simple temperature readings, vapor pressure accounts for both temperature and relative humidity. Evaporation stops when the air is fully saturated (100% humidity at the water surface temperature), regardless of how hot the water is. Wind accelerates the process by removing the saturated "boundary layer" of air immediately above the water, replacing it with drier air that has a lower vapor pressure.

function calculateEvaporationRate() { var es = parseFloat(document.getElementById('vapor_saturation').value); var ea = parseFloat(document.getElementById('vapor_actual').value); var u = parseFloat(document.getElementById('wind_speed').value); var area = parseFloat(document.getElementById('surface_area').value); if (isNaN(es) || isNaN(ea) || isNaN(u)) { alert("Please enter valid numeric values for vapor pressures and wind speed."); return; } if (es < ea) { alert("Saturation vapor pressure at the surface is usually higher than air vapor pressure for evaporation to occur. If air vapor pressure is higher, condensation occurs instead."); } // Empirical formula: E (mm/day) = (0.5 + 0.5 * u) * (es – ea) // Using common constants for small to medium water bodies var diff = es – ea; var windFactor = 0.5 + (0.5 * u); var rate = windFactor * diff; if (rate < 0) rate = 0; // Total water loss in Liters // 1 mm depth = 1 Liter per m2 var totalLiters = 0; if (!isNaN(area)) { totalLiters = rate * area; } // Mass rate in kg/m2/day (1mm = 1kg water per m2) var massRate = rate; document.getElementById('rate_mm_day').innerText = rate.toFixed(2); document.getElementById('total_liters_day').innerText = totalLiters.toFixed(2); document.getElementById('mass_rate').innerText = massRate.toFixed(2); document.getElementById('evap_results_box').style.display = 'block'; }