Generalized, Dynamic, and Transient-Storage Form of the Preissmann Slot

Abstract

A new formulation of the Preissmann Slot for modeling surcharged (pressurized) one-dimensional (1D) pipe flow is presented. The Dynamic Preissmann Slot (DPS) is derived in a nondimensional form where the slot is treated as transient storage, which is a function of slot cross-sectional area rather than width. The use of transient storage area removes the traditional conceptualization of the slot as a simple rectangular shape of fixed width. The transient storage area and its shape evolve dynamically with the flow. A nondimensional smoothing approach, using a newly defined Preissmann Number, is developed to address issues of instabilities and shocks that have been problems for prior Preissmann Slot models. The new model is tested using a Saint-Venant equation finite-volume solver that has been written as an extension of the Storm Water Management Model (SWMM). Comparison of model results to laboratory data from the literature show that the new approach captures mixed-flow dynamics in transitions from unpressurized to pressurized flow and back again.