Water-Hammer Analysis of Distribution Systems

Complex networks containing multiple pumping stations, reservoirs, zones separated by pressure reducers, and outlets to local grids, are analyzed for steady-state conditions and for transient conditions. For 32K digital computer storage several thousand pipes may be handled for steady-state calculations and several hundred pipes for transient calculations. All solutions are junction oriented satisfying continuity at each junction together with the appropriate steady-state resistance equations or the algebraic water-hammer equations. An indexing system is used which describes the relation of each junction to its adjacent pipes and junctions. For steady-state, heads are assumed at each junction and linearized adjustments to heads are made at each junction, in turn, for many times, until all head and flow relations are satisfied to the required accuracy. Transient heads and flows are calculated at each junction, starting at time zero with steady-state conditions and repeated at each junction for fixed time increments. A computer program (Michigan Algorithmic Decoder) is presented, as well as examples of a valve closing rapidly and a pipe rupture.