Fig.B-22
Capacitance defined as the slope of the characteristic curve.
Filling or charging a vessel increases energy of the fluid stored inside
it - in the case of
open vessels filled with liquid,
which are of interest here, it is the position energy which increases with increasing
heigh ot the liquid surface. The energy remains available
for being later released during the discharge process.
This, of course, is commonly used for energy storage and it is obvious that for this
purpose it is useful to work with large level heigth differences to increase
the amount of energy stored in a given amount of liquid. If, on the other hand, the
task is to store as much liquid as possible without exerting to much input work,
it will be useful to keep pressure - and height - levels low, and this is accomplished
with wide vessels. To characterise the process of liquid
Fig.B-23
accumulation in an element
of a hydraulic system, the best way is to plot the accumulation characteristic - the
dependence of the mass of stored fluid upon the
specific energy difference .
It is
also possible to characterise the element by a single scalar quantity, capacitance
. It is defined as the local slope of the accumulation characteristic. For vessels
with complex shape and, as a consequence, nonlinear accumulation characteristic curves this slope determines behaviour for small changes
around a particular state. Particularly simple are prismatic vessels
of constant cross section over their whole height (Fig.B-23), for which the
accumulation characteristic is linear.
Fig.B-24
Their capacitance is therefore a constant. In Fig.B-24 there is a derivation
of the formula used to evaluate the dissipance of a prismatic vessel. Note that -
as might be expected -
Fig.B-25
dissipance increases with increasing cross section
of the vessel. The graphical presentation
- valid for water - in Fig.B-25 may be helpful in providing an idea for
the order of magnitude. There is also in Fig.B-25 an auxiliary scale
for vessel diameter in the case of circular cross section.
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This is page Nr. B09 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS" Any comments and suggestions concerning this text may be mailed to the author
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