The exterior differential form representation of the quasi-one-dimensional flow equations

A new formulation of analyzing unsteady quasi-one-dimensional flows is presented. The usual basic equations of the flows are reformed to a system of Pfaffian forms. The disturbances propagating along the characteristic lines make their explicit appearance in the equations. The governing equations of the disturbance functions are derived from the basic equations by the exterior differentiation. These governing equations clarify the mutual interaction between the disturbances and the interference with the variation of the cross-section of ducts. This work is useful to study the wave motion and the shock propagation in ducts with variable cross-section.