  Negative head loss coefficients in branched junctions, has been controversial
for long. Herwig et al. showed, that the cause is a diffusive shear work
exchange. Based on their work, a new junction internal model is described,
while the conventional head loss is named external. The latter is obtained
experimentally, while the first cannot. This fact seems to push back reaching a
practical solution. Conventionally two head `loss' coefficients are required.
However the internal model needs three: two `pure' head loss coefficients and a
work coefficient. Based on previous works, the paper shows that the missing
equation comes from the Minimum Energy Dissipation Principle (MinEDP). The
characteristic differential equation of a T-junction is discovered, which
relates the two `pure' head loss coefficients. A particular case is presented
to illustrate how to obtain the internal model from the external one by using
it. The results are applied to empirical and numerical data from the same
branched junction; Zhu's measurements (external) and Herwig's CFD computations
(internal), respectively. Finally, an example illustrates how powerful this new
method is to analyse a new, recently published, exhaust return duct.
