Stationary flow distribution in hydraulic circuits

The analysis of stationary and nonstationary flow distributions in multiloop hydraulic systems with lumped, regulated, and distributed parameters and in heterogeneous systems was given in (Gorban et al., 2001, 2006 Kaganovich et al., 1997). In the concluding section of Section 5 the abundant capabilities of the flow MEIS are illustrated by the simplest example of stationary isothermal flow distribution of incompressible fluid in the three-loop circuit. It is shown how the degrees of order (laminar or turbulent modes) on the branches of this circuit are determined from calculation of the final equilibrium. 

The model of final equilibrium (13)-(17) for the assumed conditions has the form find 

The dimension of 7 is not indicated because of its dependence on the value (3. 

It should also be noted that the Prigogine theorem on the minimum entropy production is applicable to the circuit as a whole and for its individual branches (open subsystems). Actually, the maximum amount of entropy is formed in the environment owing to heat transfer to it from the hydraulic circuit. In the circuit itself the energy imparted to the fluid is entirely spent on its motion along the branches, i.e., on performance of effective work, and the entropy production at given conditions of interaction with the environment takes its minimal value equal to zero. The minimality of AS/ was shown in (Gorban et al., 2001, 2006). 

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