If
pressure increases,
gasses and
fluids become
compressed. The relation between
volume (
V) and pressure (
p) for gasses and fluids under the
idealization of
elasticity1 is expressed, using the
compressibility modulus K, as follows:
And, using the fact that
mass is
conserved (
pV =
constant), this becomes:
It is apparent from the above
equation that
K has the same
dimension as a
stress; the dimension according to the
SI is the
Pascal (1 [Pa] = 1 [N/m
2] = 1 [kg m
-1 s
-2])
The value of
K increases with increasing pressure. However, for a large
range of pressures the value of
K for
water (without gas
bubbles!) is practically constant, namely equal to roughly 2.2 x 10
9 [Pa].
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1 In reality this is not the case, but the idealization holds up in most cases
July 8, 2001