Beacuse of the difficulties associated with evaluation and measurement so small thermal effects a usage became common to express the magnitude of the loss (- conversion into disordered motion) as a percentage of kinetic energy (- energy of ordered motions), from which thermal energy is generated by the conversion.
The percentage is specified by the coefficient of dissipance - alco called loss coefficient or coefficient of resistance against the flow or coefficient of drag .. note that it is equivalent to coefficient of drag as defined in flow past bodies.
Fig.D-2 Coefficient used to express the extent of kinetic energy conversion into thermal energy.

Practical aspects make it important to discriminate between two sorts of "losses", as shown in Fig.D-3. In spite of the fact that in most cases the both sorts are present simultaneously, it is useful to treat them separately because they behave differently.
Fig.D-3

Although kinetic energy becomes converted into the thermal one, it cannot arbitrarily decrease (or undergo other changes). Its variations are determined in a unique manner by the variations of cross sections - according to the Castelli Theorem. As a result, the energetic conversions are almost always more complicated. The decrease of caused by the conversion into must be made up by other components of energy.


- this loss is usually small when compared with local loss. However, it increases with length of the investigated pipeline element and may become very large in very long pipelines. As shown in Fig.D-4, for a pipe with constant cross-section it is particularly evident that more complex energetic changes must take place than a simple . Velocity (because of = constant) and therefore also the kinetic energy in this case simply cannot vary. If there is, as is the case in Fig.D-4, also = 0 , there are actually only two variable terms in the equation, pressure energy and thermal energy.

Fig.D-4 Friction loss in a horizontal constant cross section pipe: Castelli Theorem dictates that for constant cross section there is invariant velocity - and hence also invariant kinetic energy. If conversion of some kinetic energy into heat takes place, the decrease must be immediately compensated for by changes in another energy component: because the pipe is horizontal (an there are, therefore, no changes in position energy), the only possible chance is decrease in pressure energy.

For evaluation of frictional loss, the Weisbach formula is used, a shown in Fig.D-04. Apart from the ratio / - which fully determines the geometry, there is the friction loss coefficient . It depends upon character of flow and upon fricitonal properties of the particular fluid. The latter are determined by quantity named viscosity .


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This is page Nr. D02 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

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