Fluid flow - Pipe flows. Networks

The study of real fluid dynamics has highlighted the complexity of dealing with such flows, especially when the flows are turbulent, i.e. in almost all industrial cases. Solving these flows by means of local balance equations requires the use of behavioral models and numerical resolution methods. While this type of resolution is rich in information on parameter fields (velocity, pressure, temperature, density, etc.), it is cumbersome to implement and sometimes unnecessary. In fact, engineers do not always need to have absolute knowledge of all these fields at all times, but simply need to know average values for a given space or in a particular zone, for flows which in practice are often permanent, at least on average.

This is particularly true of fluid flows in straight pipelines or pipelines with singularities such as bends, changes in cross-section, valves, etc. In most of these industrial pipelines, fluids flow in a steady or pseudo-permanent state, often with little or no variation in density. This is known as "permanent flow of incompressible fluids in pipes", and is extremely common in a large number of industrial situations, particularly in the energy sector.

This article focuses on the study of the mean flow of these particular types of fluid and, in particular, on head losses. In this study, which corresponds to what is also known as pipe hydraulics, we will first deal with the flow of a fluid in long cylindrical pipes, i.e. those whose length exceeds 30 to 50 times the diameter, and whose considered inlet section is located at a distance of at least 20 times the diameter downstream of any singularity. Head losses determined under such conditions are referred to as regular or distributed. In the second part, the study will focus on flows in singularities or "accidents" existing in pipes (bends, changes in cross-section, branches, valves, etc.). The corresponding head losses are referred to as singular. The final section is devoted to the study of pipe networks and the resolution of related problems.

Although applicable, strictly speaking, only to incompressible fluids in isothermal flow, the results of this article can be extended to compressible fluids provided that, in this case, the pressure variations from one point to another of the pipe under consideration are relatively small (less than about 50%).