Pipe flow in networks

A water distribution network is a web of pipes, valves, tanks and pumps that must deliver enough water at enough pressure to every consumer at peak demand, and keep flowing during fires and breakdowns. Looped networks, in which every point can be fed from two directions, are more reliable than branched, tree-like ones.

Pipe sizing rests on head loss. As water flows, friction with the pipe wall uses up energy. The Darcy–Weisbach equation is the theoretically sound method, using a friction factor from the Moody diagram or Colebrook equation. In water supply practice, the empirical Hazen–Williams formula is widely used, with a coefficient C that depends on pipe material and age; new smooth pipes have high C, old corroded pipes much lower.

In a looped network, the flows must satisfy two rules: at each junction, flow in equals flow out; around each loop, the head losses add up to zero. The classic Hardy Cross method corrects assumed loop flows by successive approximation; today network software solves the whole set of equations together and also runs extended-period simulations over the daily demand cycle.

Design keeps minimum residual pressures at the farthest and highest points, limits velocities to avoid both sediment deposition and high surge, and checks fire-flow cases. India's CPHEEO manual gives recommended C values, pressures and design periods.