Basics of Fluid Mechanics, 2014a

378 CHAPTER 11. COMPRESSIBLE FLOW ONE DIMENSIONAL
as external flow.
These processes include situations not expected to have a compressible flow, such
as manufacturing process such as the die casting, injection molding. The die casting
process is a process in which liquid metal, mostly aluminum, is injected into a mold
to obtain a near final shape. The air is displaced by the liquid metal in a very rapid
manner, in a matter of milliseconds, therefore the compressibility has to be taken into
account.
Clearly, mechanical or aero engineers are not the only ones who have to deal with
some aspects of compressible flow. Even manufacturing engineers have to deal with
many situations where the compressibility or compressible flow understating is essential
for adequate design. Another example, control engineers who are using pneumatic
systems must consider compressible flow aspects of the substances used. The compressible
flow unique phenomena also appear in zoology (bird fly), geological systems,
biological system (human body) etc. These systems require consideration of the unique
phenomena of compressible flow.
In this Chapter, a greater emphasis is on the internal flow while the external flow
is treated to some extend in the next Chapter. It is recognized that the basic fluid
mechanics class has a limited time devoted to these topics. Additional information
(such as historical background) can be found in “Fundamentals of Compressible Flow”
by the same author on Potto Project web site.
11.3 Speed of Sound
Most of compressible flow occurs at relative
high velocity as compere to the speed
of sound. Hence, the speed of sound has
to discussed initially. Outside the ideal
gas, limited other situations will be discussed.
11.3.1 Introduction
dU
Sound
Wave
P+dP
ρ+dρ
ρ P c
Fig. -11.1. A very slow moving piston in a still
gas.
People had recognized for several hundred years that sound is a variation of pressure.
What is the speed of the small disturbance travel in a “quiet” medium? This velocity
is referred to as the speed of sound and is discussed first.
To answer this question consider a
piston moving from the left to the right
at a relatively small velocity (see Figure
11.1). The information that the piston is
moving passes thorough a single “pressure
pulse.” It is assumed that if the velocity
of the piston is infinitesimally small, the
pulse will be infinitesimally small. Thus,
the pressure and density can be assumed
dU
C.V.
c−dU
P+dP
ρ+dρ
Fig. -11.2. Stationary sound wave and gas
moves relative to the pulse.
ρ P c