Stream Tube Theory

Abstract

The preceding considerations, that covered the derivation of the integral form of the basic equations of fluid mechanics, can also be used advantageously to derive simplified equations applicable to so-called flow filaments or also called stream tubes. The latter can be applied to solve some flow problems. For this purpose, one starts the considerations from flow lines that are introduced as lines of a flow which, at a certain point in time, possess the direction of the flow at each point of the flow field. One can imagine a so-called flow filament to be built up from a bundle of such flow lines and one can make a subdivision of the entire flow field into a multitude of flow filaments. Furthermore, it is possible to bundle flow filaments to obtain stream tube, as indicated in Fig. 9.1. For the suggested approach, one has to consider the properties of flows applied to flow lines, filaments and stream tubes because this concept can only be employed advantageously when the flow quantities assigned to each area of the flow filament can be considered to be constant over the crosssection of the flow filament. This makes it necessary occasionally to choose the cross-sectional area of a flow filament sufficiently small that, for the considered problem, the assumption of uniform state and flow quantities over the cross-sectional area of the flow filament can be fulfilled sufficiently precisely.