About using the minimum energy dissipation to find the steady-state flow distribution in networks

[EN] The incorrect analysis of the flow distribution through HVACduct-networks has an economical and environmental impact.The existence ofnegativehead loss coefficients at branched junc-tions poses a difficulty. However the dissipated energy is inher-ently positive and simplifies the solution. The paper exploresthe use of a variational method based on the minimization of thedissipated mechanical energy to find the actual steady-state flowdistribution through a network. To our knowledge, Robert Nivenwas the first to propose/explore this idea but unfortunately dis-carded the method. The paper begins with a short explanation,afterwards extends previous outcomes [1] and ends with an ex-ample