Modern Engineering Thermodynamics

652 CHAPTER 16: Compressible Fluid Flow
like an incompressible fluid in this system. Conversely, air flowing at high speed through a gas turbine engine is
exposed to large pressure and density changes inside the engine; therefore, it does not behave like an incompressible
fluid. In general, if the kinetic energy of a compressible fluid is much less than the ratio of the pressure
change to its density change in the flow, then the fluid’s compressibility is negligible and it may be treated as
an incompressible fluid for engineering analysis purposes.
Consequently, a compressible flow is any flow in which the fluid density is not constant in time and space.
Though all real substances are compressible to some extent, in normal engineering practice, only gases and
vapors are significantly compressible. Liquids and solids are normally considered to be incompressible, except at
extremely high pressures, on the order of 10 5 psia (0.7 GPa) or more. Because many modern engineering systems
deal with thermodynamic processes involving gases or vapors, it is important to understand the unique
flow characteristics of these substances.
In the previous chapters, we discuss the conservation of mass and energy and make extensive use of the onedimensional
mass, energy, and entropy balance equations for open and closed systems. In this chapter, we introduce
the conservation of linear momentum law and the corresponding closed and open system one-dimensional
momentum balance equations and we apply these equations to systems containing compressible substances. The
conservation of linear momentum law, along with the conservation of mass and the two laws of thermodynamics,
complete the set of fundamental physical laws and corresponding balance equations necessary for
proper engineering design and analysis of all substances.
In this chapter, we characterize the basic properties of a compressible flow and apply them to subsonic and
supersonic flows. One of the main areas of application of compressible flows is in converging-diverging nozzles
and diffusers. Fluid compressibility produces the additional phenomena of choked flow and shock waves in these
flow systems. In Chapters 6 and 9 we studied the energy and entropy characteristics of nozzles and diffusers.
In this chapter, we discover that the conservation of linear momentum adds new facets to nozzle and diffuser
efficiency analysis for compressible fluids.
16.2 STAGNATION PROPERTIES
The stagnation state of a moving fluid is the state it would achieve if it underwent an adiabatic, aergonic deceleration
to zero velocity. The energy rate balance (ERB) for an adiabatic, aergonic, steady state, steady flow, singleinlet,
single-outlet open system with negligible change in flow stream potential energy reduces to
h in + V 2 in /ð2g cÞ = h out + V 2 out /ð2g cÞ
If we let the subscript o refer to the stagnation (or zero velocity) state, then V ο = 0, and the preceding equation
can be used to define the stagnation specific enthalpy h o as
h o = h + V 2 /ð2g c Þ (16.1)
WHY IS COMPRESSIBLE FLUID FLOW PART OF THERMODYNAMICS?
At the beginning of the 19th century, when the Industrial Revolution was in full swing and the technology of the highpressure
steam engine was in the process of being developed, it became clear that, under certain circumstances, some very
peculiar things were happening inside the engine. At that time, engineers were trying to determine how to increase the
power output of a given engine while at the same time improving its operating efficiency. The relation between power output
and operating conditions of an adiabatic engine can be easily understood by applying the energy rate balance (neglecting
any changes in flow stream kinetic and potential energies):
_W = _mðh in − h out Þ
This equation clearly indicates that an effective way to increase the power output _W is simply to increase the mass flow rate
_m through the engine. This can be done by either increasing the inlet pressure or decreasing the exhaust pressure. As the inlet
pressure was increased, engineers found that the power output did in fact increase. But, when the exhaust pressure was
decreased, the power also increased, but only up to a certain point. Beyond a certain operating point, something “mysterious”
occurred. No matter how much the exhaust pressure was decreased below a certain level, the mass flow rate and consequently
the engine’s power did not increase further. They called this phenomenon choked flow, and it was not fully understood until
the study of compressible fluid flow was completely developed in the early 20th century. Therefore, compressible fluid flow is of
vital importance in the study of applied thermodynamics, because it helps engineers understand the effect that fluid compressibility
has on the thermodynamic performance of systems containing high-speed compressible working fluids.