Fig.G-3 Interference - an important phenomenon limiting the applicability of system approach. If there are two resistors or other restrictive elements (in the shown example there are two sharp pipe bends) close to each other, they interfere mutally so that - depending upon ther spatial orientation and separation, as shown in the diagram - the resultat drag coefficient may be either larger (case a) or smaller (case b) than simple sum of a single bend.
For economy (and, in fact, even the very manageability of the task - as there is going to be a huge number of such investigated cross section in a typical real system) it is necessary to limit the number of data required for characterisation of an element of a system to the very minimum. For elements of a fluid system having two terminals (one inlet and one outlet - this, of course, is the most often encountered case of elements .. cf. Fig.A-7) the minimum necessary number are two state parameters. One of them is the drop of specific energy [J/kg] of fluid between the two terminals, the other is the mass flow rate [kg/s] passing through the element. These two state parameters are analogous to voltage drop and current intensity used for specification of state in an electric system - Fig.G-2. Historically, other state parameters for fluid systems were in use (note again Fig.G-2) and sometimes their use may be still encountered encountered. Their inadequacy is due to the fact that - in contrast to mass and energy - there is no "law of pressure conservation" or "law of volume conservation" upon which the solution of systems could be based.

BASIC RELATIONS used in system solution
There are, in principle, no other relations available then the Castelli (mass conservation) theorem and Bernoullis' (energy conservation) theorem. Here, however, they are used in a different form, suitable for
Fig.G-4
working with the state parameter. The mass conservation law is used as relation for flows entering a system node (Fig.G-4), while the energy conservation law is used in the form of a relation for energetic differences (drops) in a loop of a system.
Fig.G-5

















They are often referred to as the first and second Kirhhoff laws and are to be applied at each node and loop taken one after another. In a computer solution, it may be useful to apply them in matrix form, together with some suitable characterisation of the system topology - such as Poincare's councidence matrix. This will be not necessary in the present treatment, since we shall discuss only basic cases with usually just a single loop and very small number of elements.
Gustav Robert Kirchhoff
Born: 12 March 1824 in Konigsberg, Prussia
Died: 17 Oct 1887 in Berlin, Germany
The Kirchhoff laws, first announced 1854
were originally intended for computations
of electric circuits. The analogical behaviour
of hydraulic and pneumatic systems was dis-
covered much later.

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This is page Nr. G02 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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