A practical overview of unsteady pipe flow modeling: from physics to numerical solutions

Various unsteady or transient models have evolved in order to help engineers achieve economy of analysis, design, construction, operation and maintenance. The specific usage of each model is strongly dependent on the level of unsteadiness in the system and on the accuracy, assumptions and limitations of the applied mathematical model and its numerical solution. Although the research literature is quite clear on these issues, there is often much confusion in practice. In this paper, the key practical differences and advantage for the four transient models — water hammer models, rigid water column analysis, quasi-steady analysis and so-called Joukowski approach — are compared and contrasted with respect to three criteria: their physical attributes, the hydraulic predictions they lead to, and the related numerical considerations of stability and accuracy. A useful guideline for determining the degree of unsteadiness is presented and then linked to an appropriate unsteady model.