Graph‐Theoretical Model for Slow Transient Analysis of Pipe Networks

Abstract

A method, based on a rigid water column model, for analyzing slow transients in pipe networks is graph‐theoretically formulated using incidence matrices. The formulation is made to facilitate its implementation on digital computers, thus leading to a more refined analysis of slowly changing transient conditions occurring in complicated pipelines. This approach is more advantageous than the loop method for slow transients, particularly with respect to analyzing problems occurring when valves are shut off. The paper presents a derivation of appropriate ordinary differential equations (ODEs) of the first order, numerical methods of integrating stiff ODEs, and a technique for correcting discharges in pipes to conserve mass continuity. Numerical results obtained using rigid versus elastic water column models are compared.