Apart from property of elements of a system, which is called dissipance and was used on previous several pages to characterise the elements in steady state situations, in unsteady states become important also capacitance and inertance . The variations of state parameters in time are described by differential equations. Typical for hydromechanical processes is nonlinearity of the equations, caused by the quadratic term (the one with the constant ). The consequence of the nonlinearity is practical impossibility of applying the Laplace transform approach, which is the standard solution method in corresponding problems of linear dynamics. Very often only numerical solutions are possible; here, however, we shall concentrate attention on simple cases (with only two characterisation quantities - which indicates that the equations are of first order) where an analytical solution is available. Solution consists of two parts: a part representing transitional process of adjusting to changed conditions, and a part representing response to input variations. It is useful to start the discussion with concentrating on responses to sudden (step) changes. Such changes are, of course, just mathematical models of real processes (which cannot, in reality, admit infinitely fast variations of state parameters) - but they provide a good approximations to several practical processes - and they are rather simple because there is the transitional process alone to be considered.
Dimensionless values ... are here used for expressing both differential equations as well as their solutions. Nondimensionalisation is not necessary in principle, but it brings the advantages of the formulas being incomparably more simple and universally valid.
We use:
... relative energetic drop
... relative time
... relative time
These ratios are formed by relating the dimensional value to some suitably chosen characteristic value,
... relative mass flow rate, and ... relative specific energy difference.



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This is page Nr. G11 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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