Fluids that are compressible have much more complex equations to deal with, due to density
changes, and have property relationships that vary more rapidly than incompressible fluids. In
addition, fixing the state of a liquid can be done easily by knowing its temperature and pressure.
Once the substance becomes a gas, the process becomes more difficult.
Constant Pressure Process
To determine the work done in a constant pressure process, the following equation is used:
W1-2 = P(DV)
Constant Volume Process
The solution of Equation 1-45 for a constant volume process is also not difficult. The work
done in a constant volume process is the product of the volume and the change in pressure.
W1-2 = V(DP)
In addition to gases, Equation 1-45 also applies to liquids. The power requirement for pumps
that move incompressible liquids (such as water) can be determined from Equation 1-44.
Replacing the volume (V) with the product of the specific volume and the mass yields Equation
W1-2 = mv(DP)
Taking the time rate of change of both sides of Equation 1-46 determines the power
requirements of the pump.
Effects of Pressure Changes on Fluid Properties
The predominant effect of an increase in pressure in a compressible fluid, such as a gas, is an
increase in the density of the fluid. An increase in the pressure of an incompressible fluid will
not have a significant effect on the density. For example, increasing the pressure of 100 °F
water from 15 psia to 15,000 psia will only increase the density by approximately 6%.
Therefore, in engineering calculations, it is assumed that incompressible fluids' density remain