Fig.E-6
In the present textbook, we have already encountered capacitance in chap. [B], which characterises the capability of a hydraulic system element to accumulate (and discharge) fluid during unsteady processes, and dissipance in chap. [D], which characterises steady state behaviour. Here we shall learn about the third and last one, inertance. In previous chapter [D] we have also learned about steady charactersitics of pipeline system elements. They are dependences between the mass flow rate passing through the element and the specific energy drop across the
Fig.E-7
element . If the flow varies with time, however, fluid inertia causes the energetic drop to be higher that what is found from the characteristic curve (or what is evaluated from dissipance which characterises this curve): the drop increases (or, if the flow rate diminishes, decreases) by an amount , Fig.E-6, which does not depend upon the flow rate but it is, instead, proportional to the rate of its change in time, . The proportionality constant in this relation is the inertance (from latin "inertia" meaning apathy, indifference, indolence). This quantity characterises globally all inertial effects in a given element. According to the definition in Fig.E-6 it may be
Fig.E-8
evaluated from experimental data even in situation where, because of too complicated charater of internal flow, we are unable to compute it. For a simple constant-cross-section pipe, with the usual assumption of one-dimensionality = / may be differentiated to:

- so that, according to the resultant relation in Fig.E-1, the expression for is:

... so that the resultant expression for inertance is
... Fig.E-7.
This results is presented in form of diagrams in Figs. E-8 and E-9, which may be used for rought estimate of magnitiude. In Fig. E-8, it is possible to read for a given cross sectional area on the horizontal axis (or from the diameter on the auxiliary scale) the value of inertance per unit length for three most important fluids.
Fig.E-9

For air, Fig.E-9 makes possible direct reading of the value of inertance. Note, in particular, the usual decimal orders of . Shaded area in Fig.E-9 represents the region of common / ratios. Practical experience shows that values in Fig.E-8 and Fig.E-9 correspond will with real unsteady behaviour in the low-frequency range (up to tens Hz). At higher frquencies inertance often ceases to be constant and becomes frequency dependent.
Practical application of the inertance concept is the subject of chapter [G].


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This is page Nr. E04 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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