Water distribution network is system with the follwing physical elements
- the water distribution pipes,
- the storage tanks,
- the flow and pressure control parts
- the various outflow components (hose connections, hydrants, etc
The boundaries of the systems are the points of inflow and outflow of water. A simple schematic representation of the system is shown below
The mathematical model of water distribution networks consists of:
- Branches, representing pipeline segments with length L, diameter D, pressure class PN, and roughness coefficient ks. The water flow in each branch is considered constant (there are no other points of entry and exit of water from the branch except its ends).
- Nodes. At the ends of each branch are nodes that correspond to points at which is possible to have
(i) inflow or outflow of water,
(ii) convergence or divergence of pipelines,
(iii) change in the characteristics of the pipelines (D, PN, ks).
The state variables within the system are:
- the discharge Q
- the pressure p
- the water quality variables.
The mathematical principles that govern the operation of the hydraulic model are:
- the continuity equations at the nodes, and
- the energy conservation equations in loops (the Darcy – Weisbach equation is used to calculate energy losses in industries.
From these relations emerges a non-linear system of equations, the solution of which gives the unknown quantities (the state variables). The standard practice is to consider that the characteristics of the branch (length, diameter, roughness coefficient), the level of each tank, the heights of the nodes and the inlet and outlet discharged as known. The unknown values resulting from the solution are the benefits to the branches and the pressure to the nodes.
The construction and solution of the system of equations that arise in the models is very easy with the use of appropriate software such as EPANET
Simulation of water quality
In network water quality simulation models, the following parameters are usually studied:
- the concentration of residual chlorine.
- chlorination by-products (eg trihalomethanes).
- the age of the water.
- the percentage of water from the various inputs to the network when there are multiple power sources
- the concentration of chemicals used as tracers to study the hydraulic operation and regulate the network model.
The values of these parameters are calculated at each position of the network as they change over time. The implementation of the quality model must be preceded by the solution of the hydraulic model and the initial and limit quality conditions of the system must be determined.
The mathematical relationships that govern the operation of the quality model are:
- the transport and reaction equations of the chemical component in the industries,
- the mixing equations of the component in nodes and tanks,
- and the kinetics of the reaction of the component with water and the walls of the pipes