This paper discusses the current understanding of aspects of the physics of fluid flow in pipelines relevant to pipeline flow simulations. Topics include fluid properties, the laminar/turbulent transition, friction (including methods of drag reduction), energy flow and dissipation, and the effect of more than one phase in the pipeline. Practical issues are described in terms of fundamental physics, as contrasted with an empirical approach.


Flow through tubes was the subject of some of the earliest attempts to understand the physics of fluid flow. Reynolds' original experiments on turbulence were done with ink streams in water flowing in tubes. Steady-state axial laminar flow in a cylinder is one of the few fluid flow problems for which an exact solution of the fundamental flow equations can be found. Flow in pipelines is usually analyzed by numerical simulations based on a special case of the Navier-Stokes equations for fluid flow, in which the viscous stresses are consolidated into a friction force term based partly on physics and partly on empirical results. The Navier-Stokes equations are essentially expressions of the conservation of mass and momentum. Only in recent years has the flow and dissipation of energy been added to such simulations. There remain substantial shortcomings in the understanding of the laminar-turbulent transition and in the definition and effect of varying fluid properties. The understanding of pipeline hydraulic operations involves forces, motion, and energy transformations, which are the elements of what we call the physics of pipeline flow. Our objective in this paper is to present a review of the current state of this understanding, including some of its history, and calling attention to notable deficiencies.

Who cares about the Physics?

It is possible to design, build, and operate a pipeline using rules of thumb and practical experience, with no reference to the underlying fundamentals. We believe this approach is fraught with hazard, because pipelines and their modes of operation vary a great deal. The physics does not vary, although there are some things not well understood. Knowing what isn't understood is also useful. So, pipeliners should care about the physics.

Fluid Properties - Liquids vs. Gases

An unfortunate, in our opinion, development in the practice of pipeline simulation has been a tendency to treat gas and liquid pipelines separately, even though the flow equations and the numerical methods are the same. With an appropriate equation of state and minor adjustments in time and distance steps, a good simulator can be used for either gases or liquids. Devices, on the other hand, especially pumps, compressors, and throttling valves, behave differently for liquids and gases. Liquids and gases have different macroscopic properties arising from the fundamental differences in the two types of fluid. It is a strength of the pipe flow equations, which are essentially expressions of the conservation of the fundamental quantities, mass, momentum, and energy, that the same equations and methods work for both.

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