COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS

COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS
Compressible fluids: are the fluids with variable density.
Incompressible fluid: are the fluids with constant density.
They could be liquids and gases.
An incompressible fluid is use where the change in density with pressure is so small as to be negligible. This is usually the case with liquids.
Gases are considered to be incompressible when the pressure variation is small compared with the absolute pressure.
In problems involving water hammer we must consider the compressibility of the liquid.
The flow of air in a ventilating system is a case where we may treat a gas as incompressible, for the pressure variation is so small that the change in density is of no importance.
But for a gas or steam flowing at high velocity through a long pipeline, the drop in pressure may be so great that a gas will be compressible.
For an airplane flying at speeds below 250 mph (100 m/s), we may consider the air to be of constant density.
But as an object moving through the air approaches the velocity of sound, which is of the order of 760 mph (1200 km/h) depending on temperature, the pressure and density of the air adjacent to the body become materially different from those of the air at some distance away, and we must then treat the air as a compressible fluid.
COMPRESSIBILITY OF LIQUIDS
The compressibility: change in volume due to change in pressure.
For a liquid, it is inversely proportional to its volume modulus of elasticity.
It is known as the bulk modulus. This modulus is defined as
E_v= -v (dp )/dv=-(v/dv)dp (2.1)
Where:
v= specific volume,
dv= change in volume due to change in pressure.
p= pressure,
dp= change in pressure.
As v/dv = a dimensionless ratio, the units of Ev = uits of P.
The bulk modulus is similar to the modulus of elasticity for solids.
For aliquid at constant temperature:

(?v )/v=-dp/E_v or (v_2 -v_1)/v=-(p_2 -p_1)/E_v
Where:
- Ev = the mean value of the modulus for the pressure range,
- and the subscripts 1 and 2 refer to the before and after conditions.

Example 1:
At a depth of 8 km in the ocean the pressure is 81.8 MPa. Assume that the specific weight of seawater at the surface is 10.05 kN/m3 and that the average volume modulus is 2.34 109 N/m2 for that pressure range. (a) What will be the change in specific volume between that at the surface and at that depth? (b) What will be the specific volume at that depth? (c) What will be the specific weight at that depth?
Sol: