Water Rigid Column Theory Formulated with Incidence Matrix

Gradually Varied Unsteady Flow Analysis in Pipelines

Abstract

Steady flow analysis in pipe networks, based on assumption that incompressible water and rigid pipe wall is extended to unsteady flow analysis, which can deal with slowly varying transients. A new theory is constructed owing to the incidence matrix providing information on pipe connections, whereas the existing theory is graph-theoretically formulated in the loop analysis using a loop matrix. This leads to a system of nonlinear ordinary differential equations (ODE_s) which can be easily handled without changing the system of ODEs when valves are completely closed. A valve is considered completely closed when the flow rate through a valve becomes less than given small value Δ_q. Thus, it is designed to eliminate an error, Δ_q, in flow rates owing to the incidence matrix