Valve closure in graph-theoretical models for slow transient network analysis

A valve closure algorithm is presented for inclusion within a slow transient (rigid water column) pipe network model. The algorithm is specifically formulated for (but not limited to) node-based, graph-theoretical models and is both direct and accurate. It is distinguished from conventional approaches by its direct assignment of the final discharge at closure to zero and subsequent use of the head loss at the closing valve to compute the flow rate in pipes incident to the closing valve. As a result, redistribution of residual flow prior to closure to these incident pipes is not required, leading to a less computationally demanding and more robust algorithm than previously published valve closure procedures. Application of the valve closure algorithm is illustrated in a pipe network, which also nicely demonstrates again the relation between rigid water column and water hammer models.