- caused by sudden change of area or flow direction, is usually of dominant magnitude (when compared with friction losses) in a typical hydraulic or pneumatic system - or, generally speaking, in a fluid distribution pipeline system in a machine. Friction losses become dominant if there are long (hundreds of meters or perhaps kilometers) pipes, which are typical for fluid transport over long distances.
Fig.D-17

The reason for treating local losses apart is, however, not their magnitude but their different behaviour. They are usually caused by dissipation of kinetic energy of jets and wall jets generated inside the investigated device by flow separation from sharp or strongly curved walls. Let us recall (Fig. D-3) that
Fig.D-18 Local
losses result from dissipation of fluid jets and wall jets similarly as in the submerged jet case Fig.C-25. If it were possible to determine the jet cross section area, it would be possible to calculate jet velocity and thus the dissipated kinetic energy. This, however, is seldom possible - - especially for separation from curved surface (as shown here in the case of bend).

their typical property is constancy of the loss (drag) coefficient , independence upon Reynolds number . It should be said that strictly speaking this is just an idealisation: in most practical cases there is also some inevitable, even if small friction loss component, which may become non-negligible at small Reynolds numbers where it manifests itself by a variation of the loss coefficient. As a rough guide, such variations may be neglected if Reynolds number - calculated from inlet diameter or diameter of the smallest cross section in the element and the corresponding velocity in the same cross section -is larger than .

Characteristics and dissipance
Apart from the characterisation by the value of the loss coefficient, there are other ways how to describe behaviour of an element of a pipeline system.
Fig.D-19
Schematic example of a typical characteristic
(the dependence of the specific energy difference
across the element on the mass flow rate that is
passing through it).
Especially if the task is to connect several elements and design from them a system (mode details about such a task are in chap. [G]), the characterisation by is not convenient. This is beacuse elements of equal shape but different size have the same value - and yet in a system they behave, of course differently. The most comprehensive description of behaviour is presentation of a characteristic - the dependence between the mass flow rate passing through the element and the specific-energy difference between its inlet and outlet terminals - Fig.D-20. Elements with purely local losses possess very simple characteristic: it is the quadratic parabola - Fig.D-19 . The fact is documented on a practical example of measured characteristic in Fig.D-19a. Of course, there are elements with more complicated behaviour, which is reflected in the more complex shape of their characteristics.

Fig.D-20 Above: Schematic representation of a typical
hydraulic or pneumatic element. There are
two terminals: one of them the input
terminal, the other the output
terminal. Because of the incom-
pressibility assumption there is
no accumulation of fluid inside the
element. As a result, input and output
flow rates are equal. There is just one
measurable difference in fluid specific
energy: the difference between the input
and the output.



Fig.D-19a Left: Practical example of an experimentally determined characteristic of a device exhibiting an almost purely local character of the loss.


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This is page Nr. D09 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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