THESIS
2023
1 online resource (x, 92 pages) : color illustrations
Abstract
A rapid change in the rate of flow in a closed conduit is accompanied by spatial and temporal changes in mass, momentum, energy and entropy. Conventional water-hammer models consist of the one-dimensional mass and momentum equations. This thesis undertakes a rigorous derivation of the one-dimensional set of equations that govern the changes in mass, momentum, energy and entropy. In addition, the equations of classical thermodynamics are averaged over the pipe cross-sectional area. The coupling of mass, momentum, energy, entropy and averaged thermodynamics relations leads to an entropy inequality that depends on the wall shear stress and the velocity profile. This inequality provides a powerful framework for the examination of steady and unsteady friction models, where positive entropy g...[
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A rapid change in the rate of flow in a closed conduit is accompanied by spatial and temporal changes in mass, momentum, energy and entropy. Conventional water-hammer models consist of the one-dimensional mass and momentum equations. This thesis undertakes a rigorous derivation of the one-dimensional set of equations that govern the changes in mass, momentum, energy and entropy. In addition, the equations of classical thermodynamics are averaged over the pipe cross-sectional area. The coupling of mass, momentum, energy, entropy and averaged thermodynamics relations leads to an entropy inequality that depends on the wall shear stress and the velocity profile. This inequality provides a powerful framework for the examination of steady and unsteady friction models, where positive entropy generation indicates the friction models being used is physically correct since it obeys the second law of thermodynamics. A range of steady and unsteady wall friction relations, such as the Darcy-Weisbach, Zielke, Vardy-Brown, Brunone, and Pezzinga, are assessed so as to delineate the ones that are entropy satisfying from the ones that are not.
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