Calculation formulas - HMP155

HMP155 User Guide
Document code
M210912EN
Revision
G.1
Language
English
Product
HMP155
Document type
User guide

HMP155 measures relative humidity and temperature. The following equations are used for calculating dew point and frost point, mixing ratio, wet bulb temperature, absolute humidity, and enthalpy in normal pressure.

Dew point / frost point (1)

T d / f = 237.3 ( 7.5 log ⁡ 10 ⁢ ( P w 6.1078 ) − 1 ) + 273.15
Parameter Description
Pw Water vapor pressure. Dew point/frost point is measured in Kelvin.

Mixing ratio (2)

x = 621.99 × P w p − P w ⁢              

Absolute humidity (3)

A = C ⋅ P w T ⁢    
Parameter Description
C 216.679

Enthalpy (4)

h = T ⋅ ( 1.01 + 0.00189 ⋅ x ) + 2.5 ⋅ x ⁢  

The water vapor saturation pressure at temperature Tpws is calculated over water and over ice by using 4 equations (5-8). These formulas are taken from Hyland, R.,Wexler, A.: Formulations of the Thermodynamic Properties of the Saturated Phases of H2O from 173.15 K to 473.15 K, Ashrae transactions 1983, Part 2A. pp. 500-513.

PWS over water (5)

Θ = T − ∑ i = 0 3 C i T p w s i ⁢    

PWS over ice (6)

Θ = T p w s
Parameter Description
Tpws Temperature in K
C0 0.4931358
C1 -0.46094296 * 10-2
C2 0.13746454 * 10-4
C3 -0.12743214 * 10-7

Over water (7)

100 ⁢     x ⁢   ln ⁡ P w s W A T E R = b − 1 Θ + ∑ b = 0 3 b i Θ i + b 4 ln ⁡ Θ
Parameter Description
b-1 -0.58002206 * 104
b0 0.13914993 * 101
b1 -0.48640239 * 10-1
b2 0.41764768 * 10-4
b3 -0.14452093 * 10-7
b4 6.5459673

Over ice (8)

100 ⁢   x ⁢   ln ⁡ P w s I C E = a − 1 Θ + ∑ b = 0 4 a i Θ i + a 6 ln ⁡ Θ
Parameter Description
bi Coefficients over water
a-1 -0.56745359 * 104
a0 0.63925247 * 101
a1 -0.96778430 * 10-2
a2 0.62215701 * 10-6
a3 0.20747825 * 10-8
a4 -0.94840240* 10-12
a6 0.41635019 * 101

The water vapor pressure (9)

P w = R H x P w s 100

Parts per million by volume (10)

p p m v = 10 6 x P w ( p − P w )
Parameter Description
Td Dew point temperature (°C)
Pw Water vapor pressure (hPa)
Pws Water vapor saturation pressure (hPa)
RH Relative humidity (%)
x Mixing ratio (g/kg)
p Atmospheric pressure (hPa)
A Absolute humidity (g/m3)
T Temperature (K)
h Enthalpy (kJ/kg)
Θ Virtual temperature