Restrictions Applied When Solving One-Dimensional Hydrodynamic Equations

Abstract

As it is known, “Long waves in open channel are called unsteady flow, for which the characteristic linear dimension along the length “L” is much greater than the maximum depth “h”. The hydrodynamic theory of long waves is called the shallow water theory. In mathematical modeling of long waves, as a rule, do not use the full three-dimensional hydrodynamic equations, but apply simplified equations averaged over depth (planned equations) or over the cross section of the channel (one-dimensional equations). With such averaging, it is necessary to apply some hypotheses, the most important of which is the hypothesis of pressure distribution over the depth of the flow. In the article was justified the possibility of using planned and one-dimensional equations of hydrodynamics in the modeling of long waves. Discusses the main provisions adopted in the derivation of the hydrodynamic equations, consisting of the scalar flow continuity equation based on the law of conservation of mass and the vector energy equation on the law of conservation of momentum and defines main hypotheses which were used in solving them.