A redundant fluid network is one for which there are multiple paths for the fluid to flow between two points in the system. A common example is the distribution system for water to urban dwellings.
Water mains follow the street system and are interconnected in the same pattern as are the streets.
Withdrawing water at one location may induce flows in many nearby pipes in the network. Another example is the human circulatory system, which is very redundant with respect to the small blood vessels but not the large ones. A redundant network identifying the nodal points i,j,k and the flow rates and between them. A node i is connected to a few nearby nodes by pipes . The analysis of a network flow requires the determination of the set of nodal head values , ,. . . that will give rise to flows that satisfy equation 9.21 or 9.22 at all nodal points.