The object of interest in previous chapters were mainly passive elements of a pipeline system - devices or pipe segments in which fluid energy is simply conserved - apart from the "loss" due to dissipation. For generality, the basic equation was already written with the nonzero right-hand term,
which represents work performed by outside means, which increases the fluid energy. In the present chapter, the most important and most often encoutered mechanism of acting upon the fluid is discussed. It is the mechanism employed in radial pumps - and radial turbines, in which it is fluid which performs work so that its energy decreases.
Fig.F-1 The subject of the present chapter: relative flow inside a moving pipe.
This mechanism in used in tubes or cavities which move with some carry-away velocity relative to absolute motionless reference space - while fluid flows through them. Fluid velocity relative to tube walls is .. this is the same symbol as we used for velocity so far. The reason for it is that on Earth surface, no perfect motionless state is achievable (rotation of Earth, its orbit around Sun, motion relative to stars,...) and all cases treated so far were actually relative motions. This fact could be, however, neglected: this is because the carry-away motion has some influence on the governing equations only if the carry-away motion is an accelerated one, or if the carry-away velocities of the inlet and the outlet are different. In the case of Earth motion, the differences in velocities (e.g. due to differences in the distance from the Earth axis in the case of its rotation) are negligible.
If the carry away velocities of a tube inlet and outlet differ, fluid in the tube has in these places different magnitude
of the kinetic energy of the carry-away motion , the specific value of which is . The difference in energy is, of course, equal to the performed outside work (which it is necessary to perform to get the tube moving) .
If all the terms of the energy conservation equation (- Bernoullis' Theorem) are put together with the new term added in the present chapter, the most general form resuts as follows:


Going to another page: click
This is page Nr. F01 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

WWW server administrators: Jiri Kvarda, Zdenek Maruna ...... Contact: webmaster@vc.cvut.cz
Last change : 25.03.1997