Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 54

dioxide (CO 2 ) content in air may vary depending on envi-
ronmental conditions such as the rate of consumption of
fossil fuels.
The constituent of air that can vary most is water vapor.
The volumetric percentage of water vapor in air can range
from as little as 0.000002% to as high as 4-5% (Harrison,
1965). The molecular mass of air is affected by the change in
each constituent. Consequently, the molecular mass affects
the density of air.

Table 2.7 Density of Air at Different Absolute
Pressures, Temperatures, and Relative Humidity

Density of Air, ρ a (kg/m 3 )

Absolute Air Pressure,
¯ 10 ◦ C20 ◦ C 30 ◦ C u a (kPa)

80 0.982 0.946 0.910

85 1.043 1.005 0.968

2.3.3.2 Properties of Water Vapor in Air
The concentration of water vapor in the air is commonly
expressed in terms of relative humidity:

90 1.105 1.065 1.025

95 1.167 1.124 1.083

100 1.228 1.184 1.140

101 1.240 1.196 1.152

u v ( 100 )
u vo

RH = h r = (2.20)

105 1.290 1.243 1.198

where:
RH

Density Adjustments for Humidity (kg/m 3 )

= relative humidity, h r = %,

u v = partial pressure of water vapor in the air, kPa, and

Relative Humidity,
RH (%)

u vo =

saturation pressure of water vapor at the same tem-
perature, kPa.

10 ◦ C 20 ◦ C

+ +

20 0.003 0.006

Table 2.7 shows values of air density for different absolute
air pressures and temperatures. The numbers in the top por-
tion of Table 2.7 are computed for air with a relative humidity
of 50% and 0.04% carbon dioxide by volume. For air having
a relative humidity other than 50%, a correction should be
applied as shown in the bottom portion of Table 2.7. The
correction for relative humidity is small, but it should be
noted that the density of air decreases as the relative humidity
increases. This indicates that moist air is lighter than dry air.
There are other variables used for defining the amount of
water vapor in an air mixture. The variables take the form
of a mass ratio or a mass-volume ratio. Some variables bear
a relationship to the partial pressure of water vapor.
Humidity ratio, mixing ratio, or moisture content, MR i ,is
defined as the ratio of the mass of water vapor, M w ,tothe
mass of dry air, M d , at a given pressure:

30 + 0.002 + 0.004

40 + 0.001 + 0.002

50 0 0

60 − 0.001 − 0.002

70 − 0.002 − 0.004

80 − 0.003 − 0.006

Source : From Kaye and Laby, 1973.

Specific humidity, SH, is defined as the ratio of the mass of
water vapor, M w , to the mass of moist air (i.e., M a + M w ):

M w
M a +

SH = (2.23)

M w

Specific humidity, SH, is related to the moisture content
of air and can be written as

M w
M d

MR i = (2.21)

MR i

The moisture content of air is a common measure used on
psychrometric charts. The moisture content of air can also
be expressed in terms of the partial pressure of water and
atmospheric air pressure:

=

SH (2.24)

1 + MR i

Substituting Eq. 2.21 into Eq. 2.24 gives

δ

u v

δ

MR i = (2.22)

¯

u v /u v +

SH = (2.25)

u a − ¯ u v

u a − δ

where:

Absolute humidity, AH, is defined as the mass of water
vapor, M w , in a particular volume of air, V a :

δ = 0.62197 or the ratio of specific gas constants (i.e.,

water vapor to dry air),

M w
V a

u v =

partial pressure of water vapor, and

AH = (2.26)

¯ u a =

absolute atmospheric pressure of moist air.