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Assuming incompressible flow simplifies the math, but introduces error. Always know how much
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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 pressure-induced variations in the gasstream density and velocity. Here, we review 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 either incompressible 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 perfectly suitable. 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 for assessing 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 the Moody friction factor, generally a function of Reynolds number and pipe roughness. This equation assumes that the density, p, is constant.
The density of a liquid is...