Modern Engineering Thermodynamics

CHAPTER 16
Compressible Fluid Flow
CONTENTS
16.1 Introducerea (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
16.2 Stagnation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
16.3 Isentropic Stagnation Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
16.4 The Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655
16.5 Converging-Diverging Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660
16.6 Choked Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
16.7 Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669
16.8 Linear Momentum Rate Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
16.9 Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
16.10 Nozzle and Diffuser Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
16.1 INTRODUCEREA (INTRODUCTION)
This chapter focuses the application of the laws of thermodynamics on the behavior of a very specific type of
fluid, a compressible fluid. An incompressible fluid has a constant density independent of the magnitude of the
applied pressure, but the density of a compressible fluid varies with the applied pressure.
However, a compressible fluid does not exhibit compressibility effects whenever it is used in a system. Suppose
you have a compressible fluid in a system in which pressure does not change significantly. Then, the effects of
compressibility (density changes) do not appear and the compressible fluid behaves like an incompressible
fluid. For example, in the heating and ventilating system of a building, the air flow rates are very low and the
pressure and density changes are also very small. Consequently, air (by definition, a compressible fluid) behaves
WHAT IS A COMPRESSIBLE FLUID?
A compressible fluid is any fluid whose density varies significantly with pressure.
WHEN CAN THE COMPRESSIBILITY OF A FLUID BE IGNORED?
As a general rule of thumb, when V 2 ≪ Δp/Δρ, the compressibility of a fluid is negligible and it behaves like an incompressible
fluid.
Modern Engineering Thermodynamics. DOI: 10.1016/B978-0-12-374996-3.00016-6
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