1. Relative humidity definitions:
Relative
humidity is at all temperatures and pressures defined as the ratio of the water
vapour pressure to the saturation water vapour pressure ( over water) at the
gas temperature:
RH=Pw/Pws
*100% (1)
The total
pressure does not enter the definition. Above 100°C the same definition is
valid. But as the saturation vapour pressure Pws is greater than 1013 hPa
(normal ambient pressure) the RH can't reach 100 % in an unpressurised system.
Below 0 °C the definition is also valid.
Here 100 %RH is also impossible because condensation will occur at a lower
humidity than 100 % (when the vapour is saturated against ice).
2. Water vapour saturation pressure:
|
The following
formula gives the water vapour saturation pressure to sufficient accuracy between 0 °C and 373°C
(W. Wagner andA. PruB:" The IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use", Journal of Physical and Chemical Reference Data, June
2002 ,Volume 31, Issue 2, pp. 387535):
|
T= temperature
in K
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Pn= vapor
pressure at triple point temperature, 6.11657 hPa
|
Tn= triple point
temperature 237.16 K
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Pwi = saturation
vapor pressure (hPa)
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αi
|
=
|
coefficients,
|
αo
|
=
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-13.928169
|
αl
|
=
|
34.707823
|
If lower
accuracy or a limited temperature range can be tolerated, a simpler formula
can be used for the water vapour saturation pressure over water (and over
ice):
 |
Temperature
range(°C)
|
A
|
m
|
Tn
|
max error
|
over water:
|
||||
-20 ... 50
|
6.1162
|
7.5892
|
240.71
|
0.09%
|
50 ... 100
|
5.9987
|
7.3313
|
229.1
|
0.01%
|
100 ... 150
|
5.8493
|
7.2756
|
225
|
0.01%
|
150 ... 200
|
6.2301
|
7.3033
|
230
|
0.01%
|
200 ... 350
|
10.20614
|
7.364473
|
262.76
|
0.59%
|
0 ... 200
|
6.0964
|
7.33354
|
230.5
|
0.38%
|
3. Calculation
of dew point from RH:
|
Calculate Pws using formula (3) or (6) Calculate Pw=Pws*RH/100
(in hPa!)
|
Calculate dew
point using formula (7):
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The constants in formula (7) are the same as in formula (6).
3.1 Calculation
of dew point at different pressure
|
1. Calculate Pws using formula (3) or (6)
|
2. Calculate
measured vapor pressure (at measurement pressure)
|
3.2 Calculation of RH from dew point and ambient
temperature
Values for the constants M and Tn for the appropriate temperature range can be found in
Table 1.
|
4. Using psychrometers:
The drybulb-temperature Tdry and the wetbulb-temperature Twet can be converted into Pw
using formula (13):
Pw=Pws(Twet) - Ptot*K*(Tdry - Twet) ,where (13)
Pws = Water vapour saturation pressure from formula (6)
Ptot = Total ambient pressure
K = Psychrometer constant 0.000662 °C-1
When Pw is known RH can be calculated using (1) or Td can be calculated using (7)
5. Mixing ratio:
The mixing ratio (mass of water vapour/mass of dry gas) is calculated using (14):X=B*Pw/(Ptot-Pw) [g/kg] ,where (14)
B=621.9907 g/kg
The value of B depends on the gas. 621.9907 g/kg is valid for air.
In general the constant can be calculated using:
B=M(h2o)/M(gas)*1000 [g/kg] ,where (15)
M(h2o) = molecular weight of water
M(gas) = molecular weigth of gas
For instance for hydrogen we get
B=18.015/2.016*1000=8936 g/kg
6. Enthalpy
Enthalpy can be calculated from mixing ratio using (16):
h=T*(1.01 + 0.00189X) + 2.5X (kJ/kg) ,where (16)
T = temperature (°C)
X = mixing ratio (g/kg)
To convert to Btu/lb divide by 2.324
7. Absolute humidity
Absolute humidity is defined as the mass of water vapour in a certain volume. If ideal gas
behaviour is assumed the absolute humidity can be calculated using (17):
A=C*Pw/T (g/m3) ,where (17)
C = constant 2.16679 gK/J
Pw = vapour pressure in Pa
T = temperature in K
8. Parts per million (ppm)
Parts per million values are usually given vs. the amount of dry air:
I: Volume/volume PPMv(dry):
Where :
Pw = water vapour pressure
Ptot = total pressure
II: Mass/mass PPMm(dry)
Where:
Pw = water vapour pressure
Ptot = total pressure
Mw = molecular mass of water
Md = molecular mass of dry air
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