Engineering task and calculation objective
The PSYC module calculates the state of moist air from a psychrometer measurement. In an aspirated psychrometer (Assmann type), two thermometers are force-ventilated: a dry one and one with a moistened wick. Evaporative cooling makes the wet-bulb thermometer settle at a lower temperature; from the psychrometric difference between the dry-bulb and wet-bulb temperatures, together with the total pressure, the water vapour content of the air can be determined.
As a result, the calculation delivers the water vapour partial pressure, the relative humidity, the moisture content (humidity ratio) and further state variables of the moist air. Stored for this purpose are the molar masses of air and water, the specific gas constants of both components and the specific heat of evaporation of water, from which the enthalpy and density of the air-vapour mixture can also be determined consistently.
This evaluation is needed wherever air humidity is measured and has to be converted into process quantities: in drying processes, in HVAC engineering, at cooling towers and in the acceptance testing of air coolers. Anyone who wants to calculate air humidity from wet-bulb and dry-bulb temperatures obtains here the complete air state as the input for downstream heat and mass transfer calculations.
Calculation workflow
- Enter the measured values: The dry-bulb and wet-bulb temperatures measured at the aspirated psychrometer and the total pressure of the air are entered; the total pressure matters because both the psychrometer equation and the humidity ratio are pressure-dependent.
- Determine the saturation vapour pressure: For the wet-bulb temperature, the saturation vapour pressure of water is calculated from the stored vapour pressure curve; it is the starting value of the psychrometric evaluation.
- Water vapour partial pressure from the psychrometer equation: Via the psychrometer equation, an amount proportional to the psychrometric difference and to the total pressure is subtracted from the saturation vapour pressure at wet-bulb temperature; the result is the water vapour partial pressure of the unsaturated air.
- Calculate the humidity quantities: From the partial pressure follow the relative humidity (referred to the saturation vapour pressure at dry-bulb temperature), the moisture content via the ratio of the molar masses or gas constants of water and air, and the dew point.
- Report the state variables of the moist air: Finally, using the specific gas constants and the heat of evaporation of water, the density and specific enthalpy of the moist air are provided for the measured state.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Molar mass of air MA | Luft | kg/kmol |
| Molar mass of water | MW | kg/kmol |
| Specific heat of evaporation (at 0°C) | Δhv | J/kg |
| Specific gas constant of air RA | Luft | J/(kg·K) |
| Specific gas constant of water | RW | J/(kg·K) |
| 1 | ϑ1 | °C |
| 2 | ϑ2 | °C |
| 1 | p1 | Pa |
| 2 | p2 | Pa |
| 1 | φ1 | % |
| 2 | φ2 | % |
| cpA | 1 | J/(kg·K) |
| cpA | 2 | J/(kg·K) |
| cpV | 1 | J/(kg·K) |
| cpV | 2 | J/(kg·K) |
| 1 | cpW | J/(kg·K) |
| 2 | cpW | J/(kg·K) |
| 1 | ps1 | Pa |
| 2 | ps2 | Pa |
| 1 | pi1 | Pa |
| 2 | pi2 | Pa |
| 1 | x1 | kg/kg |
| 2 | x2 | kg/kg |
| 1 | xs1 | kg/kg |
Worked example
At an aspirated psychrometer, a dry-bulb temperature of 25.0 °C and a wet-bulb temperature of 18.0 °C are read; the barometric pressure is 1013.25 hPa. Find the water vapour partial pressure, the relative humidity and the moisture content of the air.
Given values
| Dry-bulb temperature t | 25.0 °C |
| Wet-bulb temperature tf | 18.0 °C |
| Total pressure p | 1013.25 hPa |
| Psychrometer coefficient A | 6.62 · 10⁻⁴ 1/K (aspirated psychrometer) |
Solution
Saturation vapour pressure at wet-bulb temperature
Using the Magnus formula pws(t) = 6.112 hPa · exp[17.62 · t / (243.12 + t)], at tf = 18.0 °C:
pws(18.0 °C) = 6.112 · exp(17.62 · 18.0 / 261.12) = 20.59 hPa
Water vapour partial pressure from Sprung's psychrometer equation
pD = pws(tf) − A · p · (t − tf)
pD = 20.59 hPa − 6.62 · 10−4 1/K · 1013.25 hPa · 7.0 K = 20.59 hPa − 4.70 hPa = 15.90 hPa
Relative humidity
The reference quantity is the saturation vapour pressure at dry-bulb temperature: pws(25.0 °C) = 6.112 · exp(17.62 · 25.0 / 268.12) = 31.60 hPa.
φ = pD / pws(t) = 15.90 / 31.60 = 0.503 → φ ≈ 50.3%
Moisture content (humidity ratio)
With the molar mass ratio of water vapour to air (0.622):
x = 0.622 · pD / (p − pD) = 0.622 · 15.90 / (1013.25 − 15.90) = 0.00991 kg/kg → x ≈ 9.9 g of water per kg of dry air
The corresponding dew point is around 13.9 °C.
Result
| Water vapour partial pressure p_D | 15.90 hPa |
| Relative humidity φ | ≈ 50.3% |
| Moisture content x | ≈ 9.9 g/kg dry air |
| Dew point | ≈ 13.9 °C |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why must the psychrometer be force-ventilated?
The psychrometer constant is valid only at a sufficient air velocity over the wet-bulb thermometer (about 2 to 4 m/s for the Assmann psychrometer). With insufficient ventilation, evaporation is distorted by diffusion and radiation, the wet-bulb temperature reads too high and the calculated humidity too high as well. Non-ventilated psychrometers require different, larger constants and are considerably less accurate.
Is the wet-bulb temperature the same as the adiabatic saturation temperature?
For the air-water-vapour system, the two temperatures are practically equal because the Lewis number of moist air is close to 1. Strictly speaking, the psychrometric wet-bulb temperature is a measured quantity of the ventilated thermometer, whereas the adiabatic saturation temperature is a thermodynamic limit of adiabatic humidification; for other gas-vapour systems, the two can differ significantly.
Which sources of error dominate in psychrometer measurements?
A dirty or dried-out wick, insufficient ventilation, radiation effects at high ambient temperatures and reading errors of the small psychrometric difference at high humidity. Since the difference is formed from two temperatures, even a few tenths of a kelvin of measurement error have a noticeable effect on the relative humidity – especially at humidities above 80%.
Why does the total pressure enter the evaluation?
First, the correction term of the psychrometer equation is proportional to the total pressure; second, the moisture content x depends on the ratio of the vapour partial pressure to the remaining pressure of the dry air. A measurement at 800 m altitude therefore yields a different air state than at sea level for the same thermometer readings.