Water Vapor Saturation Pressure Formulae and Calculator

Related Resources: calculators

Water Vapor Saturation Pressure Formulae and Calculator

Water Vapor Saturation Pressure

Increasing temperature of liquid (or any substance) enhances its evaporation that results in the increase of vapor pressure over the liquid. By lowering temperature of the vapor we can make it condense back to the liquid. These two phase transitions, evaporation and condensation, are accompanied by consuming/evolving enthalpy of transition and by a change in entropy of the material.

The water vapor saturation pressure is required to determine a number of moist air properties, principally the saturation humidity ratio. Saturated water vapor pressure is a function of temperature only and independent on the presence of other gases. The temperature dependence is exponential. For water vapor the semi empirical dependence reads as :

Equation 1
p_{w, s} = e^{A + B/T + C lnT +Dt}

Where:

p_{w, s} = water vapor saturation pressure (Pa)
T = Temperature in Kelvin, K = °F + 255.927778
A = 77.34,
B = -7235,
C = - 8.2,
D = 0.005711,
e = 2.718281828,
t = saturation temperature

Reference:
Lecture Notes
Sampo Smolander
University of Helsinki

Alternative (recommended) formula given by IPAWS R7-97(2012) and R14-08 (2011). The saturation pressure over liquid water for the temperature range of 32 to 392°F is given by:

Equation 2
ln p_{w, s} = C₈/T + C₉ + C₁₀T + C₁₁T² + C₁₂T³ + C₁₃ ln T

Where:

p_{w, s} = saturation pressure, psia
T = absolute temperature, °R = °F + 459.67
C₈ = –1.0440397 E+04
C₉= –1.1294650 E+01
C₁₀ = –2.7022355 E–02
C₁₁ = 1.2890360 E–05
C₁₂ = –2.478068 1 E–09
C₁₃ = 6.5459673 E+00

The coefficients of Equations (2) were derived from the Hyland-Wexler equations, which are given in SI units.

Above the surface of liquid water there always exists some amount of gaseous water and consequently there exists a vapor pressure. When a container containing water is open then the number of the escaping molecules is larger than the number of molecules coming back from the gaseous phase (Fig. 1). In this case vapor pressure is small and far from saturation. When the container is closed then the water vapor pressure above the surface increases (concentration of molecules increases) and therefore the number of molecules coming back increases too (Fig. 2). After some time, the number of molecules escaping the liquid and that coming back becomes equal. Such situation is called by dynamic equilibrium between the escaping and returning molecules (Fig. 3). In this case, it is said that the water vapor pressure over the liquid water is saturated.

urface of liquid water
Figues 1, 2 and 3

Table 1 - Derived from Equation 2

Temperature		Saturation Pressure
˚ F	˚ R	psia	Pa
32	491.7	0.0886	611.21
44	503.7	0.1420	979.27
56	515.7	0.2220	1530.79
68	527.7	0.3392	2338.80
80	539.7	0.5074	3498.08
92	551.7	0.7439	5129.31
104	563.7	1.0709	7383.46
116	575.7	1.5151	10446.37
128	587.7	2.1093	14543.35
140	599.7	2.8926	19943.75
152	611.7	3.9110	26965.43
164	623.7	5.2183	35978.96
176	635.7	6.8765	47411.59
188	647.7	8.9562	61750.80
200	659.7	11.5374	79547.49
212	671.7	14.7095	101418.67
224	683.7	18.5720	128049.71
236	695.7	23.2345	160196.16
248	707.7	28.8168	198685.05
260	719.7	35.4495	244415.77
272	731.7	43.2735	298360.56
284	743.7	52.4405	361564.68
296	755.7	63.1126	435146.16
308	767.7	75.4625	520295.41
320	779.7	89.6731	618274.54
332	791.7	105.9380	730416.57
344	803.7	124.4604	858124.52
356	815.7	145.4541	1002870.48
368	827.7	169.1422	1166194.58
380	839.7	195.7580	1349704.14
392	851.7	225.5442	1555072.74

References:

Adapted from NASA (1976).