Revisiting fundamental equations of fluid flow

TL;DR

This paper reexamines the fundamental equations of fluid flow, clarifies the relationship between momentum and energy conservation, and simplifies energy conservation for incompressible Newtonian fluids.

Contribution

It provides a new perspective on the connection between momentum and energy conservation and simplifies the energy conservation equation for specific fluid types.

Findings

Momentum conservation and energy conservation are fundamentally the same concept.

Traditional energy conservation formulas may conflate Lagrangian and Eulerian perspectives.

Simplified energy conservation applies to incompressible Newtonian fluids.

Abstract

The study rederives the fundamental equations of fluid flow and examines the inherent relationship between momentum conservation and mechanical energy conservation. It is shown that the material derivative of velocity is to depict the acceleration of fluid particles in Eulerian perspective, and momentum conservation and mechanical energy conservation are the same concept termed in different descriptions. According to the study, the traditional formula for energy conservation of fluid fails to distinguish the difference between physical quantities described in Lagrangian and Eulerian perspectives. The study simplifies the energy conservation of incompressible Newtonian fluid to be internal energy conservation.