Another possibility is to specify a characterisation quantity which
Fig.D-21
determines the characteristic curve. This is a similar idea to the use of resistance to characterise the steady-state behaviour of an element of an electric circuit. Basic behaviour of electric elements is linear (Ohm's law .. there are, of course, many exceptions) - so that their characteristic is a straight line passing through the origin, fully described by resistance
= the slope of the line. In the present case of hydraulic and pneumatic elements, the basic behaviour is quadratic.
Fig.D-22 Characteristics in logarithmic co-ordinates: as is shown here on the
example of characteristic of the orifice from Fig.D-20, in logarithmic co-ordinates
typical characteristics of hydraulic and pneumatic devices transform into straight
lines with slope +2. Note the broken lines of constant dissipated power. With dif-
ferent magnitudes of dissipance Q, these straight lines are placed at different posi-
tions (so that there is different specific-energy drop and different dissipated power
at the same mass flow rate) but remain parallel.
The parabola of Fig.D-20 is described by the quadratic dissipance , the coefficient in Fig.D-21. Since the energetic drop across an element (Fig.D-19) is basically the energy converted into heat, , the expression from Fig.D-2 may be inserted into Fig.D-21. Expressing velocity from Fig.A-20 leads to

and when this is compared with Fig.D-21, the resultant expression for the dissipance is

The difference between the two approaches: The fact that value of the coefficient is equal for geometrically similar devices may be used with advantage in experimental determination of the

Fig.D-23 An experimental verification of the fact that dissipance
value of an element (here an orifice with rounded upstream inlet)
is sufficiently constant to be useful as a characterisation scalar quantity
which determines in a unique manner the element behaviour. Very exact
measurements would reveal that at different states of fluid (in this case
air at different temperatures and magnitudes of barometric pressure)
there are different values of dissipance - and that small but unavoidable
friction loss component decreases the value with increasing flow rate.
As documented here, this is all indistinguishable in the usual scatter
caused by common experimental errors.
local loss using a scaled down (or, in the case of small devices, scaled up) laboratory models. On the other hand, a smaller geometrically similar device restricts fluid flow much more - its dissipance is larger, being inversely proportional to square of cross-sectional area , a fact not at all reflected in . Note also that specification of for an alement with different or variable internal cross sections is meaningful only together with an information for which was the coefficient evaluated. No such additional information is required when we specify . Value also includes an information about the used fluid - this may be an advantage but also a disadvantage if fluid specific volume changes (not really very common, but possible situation). Note also that dissipation coefficient , not dependent upon fluid properties, may be found in experiments using some completely different fluid than one inteded for actual operations.


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This is page Nr. D10 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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