Pipeline Systems

Pipeline circuits are the most common application of Hydraulics and Fluid Mechanics in civil and industrial engineering. The liquid is conveyed into pipes of various diameters and roughness, usually in the presence of special components such as valves, curves, elbows, fittings. In most cases the problems can be solved by applying the energy balance in terms of Bernoulli’s extended theorem with additional energy losses. Energy losses belong to the category of concentrated and distributed losses, both proportional to the velocity head (at least in turbulent conditions) with a coefficient that depends on the type of the special component, on the roughness of the duct and on the Reynolds number. In particular, the distributed energy losses are calculated with the Darcy formula where the friction factor is calculated with the Moody chart or, in case of turbulent flow, with the Colebrook–White equation, an equation in implicit form of the friction factor, the relative roughness and the number of Reynolds The Colebrook–White equation in the general case has no analytical solution, and a numerical procedure is required, if necessary with iterations.