Relative humidity

material.humid.rh_pct Unit: % Step 04 · Material

The water content of humid air, given as the relative humidity at the gas temperature and the operating static pressure. It is converted to a water-vapour mole fraction, which sets the molar mass, the heat capacity and the speed of sound of the gas.

Last updated 2026-11-04

Theory

Humid air is treated as an ideal-gas mixture of dry air and water vapour. The relative humidity $\phi$ is the ratio of the partial pressure of the vapour to its saturation pressure at the gas temperature. The saturation pressure follows the formula of Annex B of ISO 9613-1 (1993); the mole fraction of water vapour is the partial pressure divided by the absolute static pressure of the gas, which is the operating pressure of the Material step (the outlets' absolute pressure when the flow is solved).

The mixture's molar mass and its heat-capacity polynomial are the mole-fraction-weighted values of dry air and water vapour, from the same species data as dry air and exhaust gas. The viscosity remains the Sutherland law of dry air, as for exhaust gas.

The formula of the standard is written for atmospheric conditions. Compared with the saturation pressure of IAPWS (2012) it gives $-0.11\,\%$ at 20 °C, $+0.34\,\%$ at 85 °C, $+0.62\,\%$ at 100 °C and $+1.71\,\%$ at 150 °C. A warning appears above 100 °C; above 200 °C only the mole fraction can be entered. Liquid water is not modelled: a humidity whose vapour pressure would reach the static pressure is refused.

Equations

\frac{p_{sat}}{p_r} = 10^{C}, \qquad C = -6.8346\left(\frac{T_{01}}{T}\right)^{1.261} + 4.6151

(1)

where	meaning	unit
$p_{sat}$	Saturation vapour pressure of water at $T$	Pa
$p_r$	Reference pressure, 101 325	Pa
$T_{01}$	Triple-point isotherm temperature, 273.16	K
$T$	Gas temperature	K

x_{H_2O} = \frac{\phi}{100}\,\frac{p_{sat}}{p}

(2)

where	meaning	unit
$x_{H_2O}$	Mole fraction of water vapour	-
$\phi$	Relative humidity	%
$p$	Absolute static pressure of the gas (operating pressure)	Pa

M = (1 - x_{H_2O})\,M_{air} + x_{H_2O}\,M_{H_2O}

(3)

where	meaning	unit
$M$	Molar mass of the humid gas	kg/kmol
$M_{air}$	Molar mass of dry air	kg/kmol
$M_{H_2O}$	Molar mass of water	kg/kmol

Default and rule

Default: 0 %
Rule: 0 % (dry air).
Source: Saturation pressure: ISO 9613-1 (1993), Annex B. Deviation figures: computed against the saturation-pressure equation of IAPWS (2012), whose own verification values the program reproduces to all printed digits.

Valid range 0 - 100 %; refused when the vapour pressure would exceed the static pressure

Condensation

$\phi\,p_{sat} \ge p$ is refused: the water would condense, and liquid water is not modelled.

Hot gas

Above 100 °C the saturation formula is used outside the range it was written for; the deviation from IAPWS-IF97 grows from 0.6 % at 100 °C to 1.7 % at 150 °C.

Mole fraction

Above 200 °C, or when the water content is known as a mole fraction, enter Water-vapour mole fraction instead.

Theory

Equations

Default and rule

Valid range 0 - 100 %; refused when the vapour pressure would exceed the static pressure

Related 5

References 2