New models for adiabatic and isentropic flow description in tubular friction and adiabatic exponent generalization

Abstract

In practical fluid mechanics, in terms of tube flow description, there is a lack of analytical descriptions and solutions of frictional adiabatic and isentropic flow. This paper explores the connections between the modeling these two flow types and reveals that frictional isentropic flow can be achieved if the heat generated by friction is removed from the flow. This is, in fact, a polytropic flow, which is made isentropic by heat extraction. The study also presents a new description and solution of adiabatic flow, which is not isentropic due to friction, but no heat loss is considered in this work. Adiabatic frictional flow is implemented by extending the application of the adiabatic exponent (k). The adiabatic exponent (k) is naturally used to describe the isentropic or adiabatic state changes of ideal gases. During adiabatic state changes, the entropy of the ideal gas remains unchanged if the state change occurs without internal friction, without internal thermal expansion and without external energy absorption or loss. This means it is no longer an isentropic change of state if there is internal friction in the fluid. The adiabatic change of state without external heat input is therefore not necessarily isentropic. In common terms, a distinction is not always made between adiabatic and isentropic state changes. This paper expands on the use of the adiabatic exponent to describe frictional flows. Further, the paper outlines the possibility of using the exponent k to describe polytropic flows, which, of course, are by no means isentropic, but can be made mathematically so if one can compensate for internal heat generation by external heat extraction.