The Flowing System Gasdynamics Part 2: Euler momentum conservation equation solution

TL;DR

This paper presents an algebraic solution to the Euler momentum conservation equation for fluid flow in various elements, enabling analysis of non-stationary conditions with time-varying factors.

Contribution

It introduces a novel algebraic method for solving the momentum equation in flowing systems, accounting for dynamic physical factors and extending previous contact interaction models.

Findings

Provides a distribution law of static head along the flow element

Enables description of non-stationary fluid motion under variable conditions

Simplifies the integration of the differential equation for practical applications

Abstract

The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are: pipe, tube, orifice, mouthpiece, diffuser, etc. and its combination. The integration of the differential equation has reduced to distribution law of static head along the length of flowing element and has proved the elementary algebraic solution that introduced in the previous paper by these authors. The received solution allows to describe the motion of fluid medium in non-stationary conditions, under action of any time-varying physical factors: a roughness of streamlined surface, the area of the section of the flowing element, the heat exchange with the streamlined surface, the technical work, the additional weight flow of fluid medium.