The purpose of this paper is to describe the equations which govern the flow of compressible fluids through pipes. Particular emphasis is placed on those used within the natural gas industry in hopes that engineers within that industry can make knowledgeable decisions on how to model pipes. Its thesis is that all practical equations were created to solve intense numerical problems and have been made obsolete by advancing computing technology. It further discusses a new flow formula proposed by the GERG Research project 1.19 A NOTE CONCERNING UNITS These equations have generally been published in the English system of units. Where appropriate, alternate equations in metric units have been included, with the names of the metric units being shown in italic type. Since the Pole, Spitzglass, and Weymouth equations are included only for historical completeness, only their original published form is presented.
During the almost two centuries that the natural gas industry has been in existence there has always been a need for workable equations to relate the flow of gas through a pipe to the properties of both the pipe and the gas and to the operating conditions such as pressure and temperature. The usefulness of such equations is obvious: systems must be designed and operated with full knowledge of what pressures will result from required flow rates. The purpose of this paper is to describe the ways that this has been accomplished and to provide some practical insight into what the current practice should be. Since nearly every text on fluid mechanics, and they are legion, contains some derivation of the fundamental equation governing one dimensional, compressible fluid flow, it is not necessary to repeat that derivation here. Excellent derivations are presented in the Hyman, Stoner, and Karnitz paper, the Gibson paper (the best), and the Finch and Ko paper referenced in the bibliography. Essentially one begins with the partial differential equations of motion along with the equation of state and then starts assuming and integrating.
A key component of the above flow equation is the equation of state that describes the volume that a given mass of a given gas will occupy at a given pressure and temperature. For an ideal gas the equation of state is well known, simple, and can be derived in a number of ways from first principles; for a real gas it becomes quite complex, depending on molecular size and shape, and inter-molecular forces. The deviation from ideality is usually expressed as the ratio between the real volume and the ideal volume; hence the intuitive term "supercompressibility", denoted by "z", implying that the real gas can be compressed more that its ideal counterpart.