Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 50

in one of three states (i.e., liquid, solid, and vapor), and its
properties are a function of temperature and pressure.

Table 2.3 Density of Water at Various Temperatures

Temperature ( ◦ C) Density (kg/m 3 )

2.3.2.1 Density of Water
The density of water, ρ w , is defined as

+ 100 958.4

+ 80 971.8

M w
V w

+ 60 983.2

ρ w = (2.11)

+ 40 992.2

+ 30 995.65

+ 25 997.05

Water is essentially a homogeneous substance the world
over, except for variations produced by salts and isotopes of
hydrogen and oxygen (Dorsey, 1940). Distilled water under
the pressure of its saturated vapor is called pure, saturated
water. The density of pure, saturated water can be measured
experimentally. Figure 2.31 shows the density of pure water
under various applied pressures and temperatures.
The variation in the density of water due to tempera-
ture differences is more significant than its variation due
to applied pressure for geotechnical engineering problems.
McCutcheon et al. (1993) proposed an empirical equation
for the density of water with respect to changes in tempera-
ture. The closed-form equation proposed for the density of
pure water as a function of temperature is as follows:

+ 20 998.21

+ 15 999.10

+ 10 999.70

+ 4 999.97

0 999.84

− 10 998.12

− 20 993.55

− 30 983.85

Source : From Lide, 1990.

2.3.2.2 Salt-Water Mixture
The density of salty water increases from that of pure water.
Either the mass or the volume of water needs to change in
order for the density of a mixture of pure water and salt to
change. The density of pure water is about 1000 kg/m 3 and
common salt (NaCl) has a considerably higher density of
2160 kg/m 3 .
Let us suppose that a 1000-mL flask is filled to the 1000-
mL mark with distilled water at 23 o C. Now let us add 30 g
NaCl. The weight of the flask plus its contents will obvi-
ously increase by 30 g, but it is interesting to observe what
will happen to the volume of water plus the salts. It might
come as a surprise to discover that there is a reduction in
overall volume of about 0.66%. The density of the salt-water

1000 1

3 . 9863 ) 2

(T + 288 . 9414 )(T −

ρ w = − (2.12)

508929 . 2 (T + 68 . 12963 )

where:

density of water, kg/m 3 , and ρ w =

temperature, ◦ C.

T =

The density of water under isothermal conditions is com-
monly taken as 1000 kg/m 3 for most geotechnical engineer-
ing problems. Table 2.3 shows more precise densities of
water over a range of temperatures.

30

5060 kPa

20,300 kPa

10,100 kPa

25

101.3 kPa

7600 kPa

20

15

Equilibrium
with
saturated
water vapor

10

2530
kPa

5

0

998 1000 1002 1004 1006 1008

ρ w (kg/m 3 ) Density of water,

Figure 2.31 Density of pure water for various applied pressures and temperatures (from

Dorsey, 1940).