Evaporation Water Surface

Overview

Engineering reference data for Evaporation Water Surface in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Symbol	Description	Unit
$U$	Internal energy	J
$Q$	Heat	J
$W$	Work	J
$P$	Pressure	Pa
$V$	Volume	m³
$T$	Temperature	K

Evaporation Coefficient and Heat Supply

The evaporation coefficient $\Theta$ and required heat supply $q$ are derived from the core equations:

Evaporation Coefficient: $\Theta = 25 + 19v \quad (\text{kg/m}^2\text{h})$

Required Heat Supply: $q = h_{we} \cdot g_s$

Definitions

• $\Theta$: Empirical evaporation coefficient (kg/m²h), representing the combined effect of air temperature and velocity.
• $g_s$: Mass evaporation rate (kg/s).
• $g_h$: Mass evaporation rate (kg/h).
• $A$: Water surface area (m²).
• $x_s$: Humidity ratio of saturated air at water temperature (kg H₂O/kg dry air).
• $x$: Humidity ratio of ambient air (kg H₂O/kg dry air).
• $q$: Heat transfer rate required to maintain temperature (kW).
• $h_{we}$: Specific evaporation enthalpy (latent heat) of water (kJ/kg).

Swimming Pool Example

A 50 m × 20 m pool with water at 20°C. Air velocity is 0.5 m/s.

Parameter	Value	Calculation
Area, $A$	1000 m²	$50 \times 20$
$x_s$ (at 20°C)	0.014659 kg/kg	(Given)
$x$ (25°C, 50% RH)	0.0098 kg/kg	(From psychrometric chart)
Evaporation coefficient, $\Theta$	34.5 kg/m²h	$25 + 19 \times 0.5$
Evaporation rate, $g_s$	0.047 kg/s	$\frac{34.5 \times 1000 \times (0.014659 - 0.0098)}{3600}$
Heat loss, $q$	115.3 kW	$2454 \times 0.047$

Methods to Reduce Evaporation Loss

• Reduce air velocity above the surface – Limited effect.
• Reduce water temperature – Not comfortable for swimmers.
• Reduce air temperature – Not a comfort solution.
• Increase indoor air humidity – Risk of condensation and structural damage.
• Use pool covers/blankets – Very effective and commonly used during off-operation hours.

Note: Bather activity significantly increases evaporation. Heat pumps are commonly used to recover latent heat from the air and reduce energy consumption.

References

• Original Source