Compresibility Flow

Assuming incompressible flow simplifies the math,
but introduces error. Always know how much
Flow of gases in pipe systems is
commonplace in chemical-process plants. Unfortunately, the
design and analysis of gas-flow
systems are considerably more
complicated than for liquid (incompressible) flow, due mainly to pressureinduced variations in the gas-stream
density and velocity. Here, wereview
practical principles and present some
key equations governing gas flow, and
assess several assumptions and rules
of thumb that engineers sometimes
apply in order to simplify gas-flow
analysis and calculations.

Compressible, incompressible

In a broad sense, the appropriate term
for gas flow is compressible flow. In a
stricter sense, however, such flow can
be categorized as eitherincompressible or compressible, depending on the
amount of pressure change the gas undergoes, as well as on other conditions.
Accurately calculating truly compressible flow in pipe systems, especially in branching networks, is a formidable task. Accordingly, engineers
often apply rules of thumb to a given
design situation involving gas flow, to
decide whether the use of (simpler)incompressible-flow calculations can be
justified. Such rules of thumb are helpful, but they can lead one astray when
used without a full understanding of the
underlying assumptions.
Sometimes, the case is clear-cut. For
instance, if the engineer is designing
a near-atmospheric-pressure ventilation system, with pressure drops
measured in inches of water, incompressible-flow methods are perfectlysuitable. Conversely, for design or
specification of a pressure-relief system that is certain to experience high

velocities, compressible-flow methods
will clearly be required. In practice,
many gas systems fall between these
extremes, and it is difficult to assess
the error that will result from using
incompressible methods.
A major purpose of this article is to
offer guidelines forassessing the importance of compressibility effects in a
given case. First, however, we set out
relevant equations, and discuss some
key aspects of gas-flow behavior.1

The underlying equations

Incompressible flow: An apt starting point for discussing gas flow is
an equation more usually applied to
liquids, the Darcy-Weisbach equation
(see Nomenclature box, next page):
(1)
where f is theMoody friction factor,
generally a function of Reynolds number and pipe roughness. This equation
assumes that the density, , is constant.
The density of a liquid is a very
weak function of pressure (hence the
substance is virtually incompressible),
and density changes due to pressure
are ignored in practice. The density
varies more significantly with temperature. In systems involving heattransfer, the density can be based on
the arithmetic average, or, better, the
log mean temperature. When the appropriate density is used, Equation (1)
can be used on a large majority of liquid pipe-flow systems, and for gas flow
1. The quantitative compressible- and incompressible-flow results in this article were obtained
using, respectively, AFT Arrow and AFT Fathom.
Both are commerciallyavailable software for pipe
system modeling. A simplified but highly useful
utility program, Compressible Flow Estimator
(CFE), was developed specifically for this article,
and was used in several cases.

when compressibility can be ignored.
Compressible flow: Equation (1) is
not strictly applicable to compressible flow because, as already noted,
the density and velocity change along
thepipe. Sometimes, engineers apply
Equation (1) to gas flow by taking the
average density and velocity. But, because the variation of each of these
parameters along a pipe is nonlinear,
the arithmetic averages will be incorrect. The difficult question — How
seriously incorrect? — is discussed in
detail later in this article.
Individual length of pipe: More strictly
applicable than Equation...