Page 157 - 48Fundamentals of Compressible Fluid Mechanics

The gas flow throw a long tube has a applicability in situations which occurs in a
relatively long distance and where heat transfer is relatively rapid so that the tem-
perature can be treated, for engineering purposes, as a constant. This model is To put discussion when the
“relatively fast” means.
applicable when a natural gas (or other gases) flows for a large distance. Such sit-
uations are common in large cities in U.S.A. where natural gas is used for heating.
It is more predominate (more applicable) in situations where the gas is pumped for
a length of kilometers.
The high speed of the gas is obtained or explained by the combination of
heat transfer and the friction to the flow. For a long pipe, the pressure difference
reduces the density of the gas. For instance, in a perfect gas, the density is inverse
of the pressure (it has to be kept in mind that the gas undergoes a isothermal
process.). To maintain conservation of mass, the velocity increases inversely to
the pressure. At critical point the velocity reaches the speed of sound at the exit
1
and hence the flow will be chocked .
8.1 The Control Volume Analysis/Governing equations

Figure 8.1 describes the flow of gas from the left to the right. The heat transfer up
stream (or down stream) is assumed to be negligible. Hence, the energy equation
can be written as following:

(8.1)

1 This explanation is not correct as it will shown later on. Close to the critical point (about, , the

heat transfer, is relatively high and the isothermal flow model is not valid anymore. Therefore, the study
of the isothermal flow above this point is academic discussion only.
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