Page 71 - 48Fundamentals of Compressible Fluid Mechanics

3.5. SPEED OF SOUND IN ALMOST INCOMPRESSIBLE LIQUID 33

The correction of speed of sound of air in normal condition (atmospheric condition
plus even increase of pressure) is minimal on the speed of sound. However, the
change of temperature can have dramatical change in the speed of sound. For ex-
ample, at relative moderate pressure but low temperature common in atmosphere,
which means that speed of sound is
factor (0.5) to calculated by ideal gas model.
the compressibility factor,

and

3.5 Speed of Sound in Almost Incompressible Liquid
only

Even liquid normally is assumed to be incompressible in reality has a small and
important compressible aspect. The ratio of the change in the fractional volume
to pressure or compression is referred to as the bulk modulus of the material. For
. At a depth of about
. The fractional volume change

is only about 1.8% even under this pressure nevertheless it is a change.

example, the average bulk modulus for water is

The compressibility of the substance is the reciprocal of the bulk modu-
4,000 meters, the pressure is about

#
lus. The amount of compression of almost all liquids is seen to be very small as
#
given in Table (3.5). The mathematical definition of bulk modulus as following
(3.35)

In physical terms can be written as
(3.36)

For example for water
1

1
1

1

This agrees well with the measured speed of sound in water, 1482 m/s
#
at 20
C. Many researchers have looked at this velocity, and for purposes of com-
parison it is given in Table (3.5)
The effect of impurity and temperature is relatively large, as can be ob-
served from the equation (3.37). For example, with an increase of 34 degrees
from 0
C there is an increase in the velocity from about 1430 m/sec to about 1546
5
[m/sec]. According to Wilson , the speed of sound in sea water depends on tem-
perature, salinity, and hydrostatic pressure.
Wilson’s empirical formula appears as follows:
(3.37)
5 J. Acoust. Soc. Amer., 1960, vol.32, N 10, p. 1357. Wilson’s formula is accepted by the National

Oceanographic Data Center (NODC) USA for computer processing of hydrological information.