System Dynamics Approach to Pipe Network Analysis

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Abstract
A method of analysis based on rigid water column theory for slow transients and steady‐state flows in pipe networks is described. A graph theoretic formulation yields a system of ordinary differential equations of the first order that describes the dynamic behavior of the network. A definite Liapunov function of quadratic form to prove asymptotical stability of the network at the steady state is derived from Tellegen's Theorem in electrical circuit theory; this function gives a unique and precise criterion for the attainment of the steady state by the system. The time integration can be performed directly by using, for example, the Runge‐Kutta method without involving any iterative procedure. Simulations of slow transients and dynamic relaxation processes to solve the steady‐state flow problem are shown in terms of small networks.

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