Environmental Engineering Reference
In-Depth Information
vapor bubbles are collapsed, the fluid (water) is said to no
longer have any cavitation nuclei. It is estimated that water
can withstand tensions of 500,000 - 1,000,000 kPa in the
absence of cavitation nuclei (Harvey et al., 1947). Plesset
(1969) suggested that the tensile strength of water without
cavitation nuclei could be in excess of 1,000,000 kPa.
The primary process for collapsing the cavitation nuclei in
water has been pressurization.
The cavitation nuclei in water can be collapsed through
a pressurization process; however, it must be realized that
the water is not in a stable state. The water has crossed the
boundary from a stable liquid state into the vapor state without
changing phase. In other words, the water is in a metastable
state (Apfel, 1970). It is simply a matter of time and surround-
ing conditions until nucleation will produce vapor cavities
within the boundaries of the liquid (Trevena, 1987). Even
though it has not been possible to produce a suction sensor
containing water in a stable state (over a long time period),
there has still been significant success in producing direct,
high-suction sensors for laboratory usage through use of the
pressurization procedure. Further information is provided on
direct, high-suction sensors in Chapter 4.
Table 2.6 Composition of Dry Air
Molecular Mass
(Basis of Natural
Percentage
Density
Scale, O
=
16)
(kg/m 3 )
by Volume
(kg/kmol)
Nitrogen (N 2 )
78.08
1.25055
28.016
Oxygen (O 2 )
20.95
1.42904
32.000
Other gases
0.97
Air
100.0
1.2929
28.966
a Under standard conditions (i.e., 101.3 kPa and 0 C) with
no water vapor.
u atm =
¯
atmospheric pressure (i.e., 101.3 kPa or 1 atm),
volume of air, m 3 ,
V a
=
M a
=
mass of air, kg,
ω a
=
molecular mass of air, kg/kmol,
R
=
universal
(molar)
gas
constant
[i.e.,
8.31432
J/(mol K)],
T K
=
absolute temperature (i.e., T K =
T
+
273 . 16), K,
2.3.3 Air Phase
The air phase has physical properties that vary significantly
with temperature and pressure.
and
temperature, C.
T
=
The right-hand side of Eq. 2.16 [i.e., (M a a ) RT K ]isa
constant for a gas in a closed system with constant mass
and temperature. Under closed-system conditions, Eq. 2.16
can be written as Boyle's law:
2.3.3.1 Density of Air
The density of air, ρ a , can be expressed as
M a
V a
ρ a =
(2.14)
u a 1 V a 1
¯
u a 2 V a 2
(2.17)
The specific volume of air, ν ao , is given as
where:
¯
V a
M a
u a 1 =
absolute air pressure at condition 1,
v ao =
(2.15)
volume of air (m 3 ) at condition 1,
V a 1
=
u a 2 =
¯
absolute air pressure at condition 2, and
Air behaves as a mixture of several gases (Table 2.6) and
also varying amounts of water vapor.
The mixture of gases is called dry air when no water vapor
is present and moist air when water vapor is present. It is
important to note that water vapor behaves as a gas and not
as small liquid drops of water. Dry and moist air can be
considered to behave as an ideal gas under pressures and
temperatures commonly encountered in geotechnical engi-
neering. The ideal gas law can be written as
volume of air (m 3 ) at condition 2.
V a 2
=
Rearranging the ideal gas equation (i.e., Eq. 2.17) gives
M a
V a =
ω a
RT K ¯
u a
(2.18)
Substituting Eq. 2.14 into Eq. 2.18 gives an equation for
the density of air:
ω a
RT K ¯
M a
ω a
ρ a =
u a
(2.19)
u a V a =
¯
RT K
(2.16)
The molecular mass of air, ω a , depends on the composi-
tion of the mixture of dry air and water vapor. Dry air has
a molecular mass of 28.966 kg/kmol (Table 2.6), and the
molecular mass of the water vapor (H 2 O) is 18.016 kg/kmol.
The composition of air, namely, nitrogen (N 2 ) and oxygen
(O 2 ), is essentially constant in the atmosphere. The carbon
where:
u a
¯
=
absolute air pressure where the overbar indicates
absolute pressure (i.e.,
u atm )kN/m 2
u a =
¯
u a
or
kPa,
gauge air pressure, kN/m 2
u a
=
or kPa,
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