An aspect of the 'hydraulics' of the unsteady motions of a fluid

Problems involving unsteady fluid flows in ducts of complex shape are commonly solved with the aid of a one-dimensional approximating scheme where the flow characteristics to be determined are the mean cross-sectional values of the flow parameters. The parameters of one-dimensional flow on either side of a sharp bend or at a bifurcation must then be linked by certain relations. In the case of steady motions, these (well-known) relations are defined in terms of hydraulic resistance coefficients. For unsteady motions, the problem of obtaining such relations is far more complex. Possible approaches to the solution of the latter problem are examined.