If

pressure increases,

gasses and

fluids become

compressed. The relation between

volume (

*V*) and pressure (

*p*) for gasses and fluids under the

idealization of

elasticity^{1} 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].

Support write-up for Fluid mechanics

**Sources:**

Node your homework...or better yet, node your entire curriculum

^{1} In reality this is not the case, but the idealization holds up in most cases

*July 8, 2001*