Variational Theories in Hydrodynamics and Hydraulics

Abstract

Hydrodynamic and hydraulic theories have been developed along two parallel approaches, i.e., the vectorial and variational approaches. Most classical hydraulic theories are based on vectorial approaches. The variational approach is a scalar approach based on the maximization of entropy, minimization of energy, or minimization of energy dissipation rate. A review of variational theories and hypotheses shows that fundamental theories in hydrodynamics and hydraulics derived from vectorial approaches can also be independently derived from variational approaches. A comparison of different variational theories indicates that they are consistent with each other provided that the concepts of entropy and energy are properly defined and correctly applied.