Hydraulic Analysis of Distribution Systems (also known as Hydraulic Network Modeling), is essentially the implementation of a numerical method associated with mesh networks for the resolution of a system of Load (or Piezometric Heads) and Flow equations.

Distribution systems (also known as Aqueducts) are meshed systems or closed networks designed in a redundant manner where water to supply one user can follow various paths to supply any user or any area of ​​the system can be served by more than one pipe simultaneously. The above is in order to provide users with greater reliability of the service and that the breakage and subsequent repair of a section of the system does not necessarily imply the suspension of the service.

This configuration generates an indeterminate system of equations, where generally the known data are the diameters and roughness of the pipes that make up the system, the estimated or projected values ​​of flow demanded by the system and at least the value of a known load boundary (for example the water level in a Reservoir). The final result of the iterative mathematical process (until a minimum numerical convergence predefined by the modeler is reached for the set of equations) is the obtaining of the flows that circulate through the pipes and the different pressures in the nodes of the system.

The mathematical formulation of the analysis of distribution systems is essentially based on two basic (and very old) principles that must be met regardless of the configuration and elements that make up the system or Hydraulic Network, these are:

In practice, the representation and hydraulic analysis of distribution systems or networks is carried out through a "Computational Model" or Hydraulic Model that allows the mathematical solution of the unknowns of the system of equations. This model is not only represented by pipes but also by Storage Tanks, Reservoirs (Reservoirs), Regulation Valves, Pumps, Meters, Accessories, among other elements.

The model variables (some known) are then:

The set of equations made up of head or head and flow equations (generally associated with internal circuits), is represented by a non-linear and indeterminate system of mathematical expressions that requires the adoption of mathematical methodologies of an iterative nature that finally allow the different unknowns of the system to be determined.