Given the fact that there is lack of a uniform deduction process in theory and an all-embracing base equation group for existing one-dimensional dynamic models of flow system

the integral and differential conservative equations of quasi one-dimensional compressible transient flow in pipe with variable section were derived by rational modeling based on integral conservative equations in Eulerian type of specification suitable for control volume of continuous fluid media.The expansion work resulted from variation of control volume was taken into account by reserving the variable volume term in energy equation.With two kinds of finite volume grids which are interlaced in discrete space

a finite volume model was established to describe quasi one-dimensional compressible transient pipe flow field.Actions derived from variable volume

variable fluid properties

axial heat conductivity and gravity were considered in the model.This reinforces and clarifies the theoretical foundation for the numerical system of finite element state-variable model

and also improves the scope of application.On the other hand

the model can be further developed to establish flow field models of common components in pipe system in collaboration with throttling model of valve core.