Author(s): Ondrej Urban; Josef Mikulasek

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Keywords: No Keywords

Abstract: Fluid flow in systems where the length exceeds the width multiple times (e.g. piping systems) is preferably modelled using one-dimensional equations. These equations are often derived with the assumption of uniform velocity and pressure profiles, which is not the case in real flows, and therefore correction factors need to be introduced. In this contribution, we consider the general integral equation for Newtonian fluid flow in a pipe and derive exact expressions of correction factors that need to be employed if a simplified form of the governing equation is used. This equation is used in practice in the pressure–time method, a way to determine the flow rate in large hydropower plants. Attention is paid to the so-called penstock factor, which is present in the unsteady term. Using the data from full three-dimensional CFD simulations of unsteady flow in fictious penstocks with elbows, we study the accuracy of the simplified pressure–time method and the effect of different expressions of the penstock factor. The obtained results provide further insight into the applicability of one-dimensional methods.

DOI: https://doi.org/10.1088/1755-1315/1561/1/012022

Year: 2025