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Fig.D-13
This schematic illustration presents general shapes of pipe characteristics -
the dependences between the overal difference of available specific energy
between the pipe ends upon the mass flow rate.
For laminar flow, as might be evaluated by inserting the Hagen-Poiseuille law, the
dependence upon
velocity (and, hence, flow rate) is linear. For the turbulent flow
calculated by the Blasius formula, the energetic drop is proportional
to 1.75th power of flow rate. The two characteristics have a common
intersection point which - very roughly - corresponds to the
critical value of
Reynolds number.
The important conclusion from this results is that not only Nature
tends to increase entropy
by introducing the frictional loss mechanism, but if there are available alternatives,
Nature always select the one which results in fastest rate of entropy growth.
Here we can see that of the
two available characteristics, the one is actually followed (laminar for
low Reynolds numbers, turbulent for large Reynolds numbers) which leads to larger
dissipation of ordered motion energy.
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