Recent comparisons with numerical investigations of branched flows led to similar conclusions. This “cubic root of 2” correlation underwent extensive theoretical and experimental reassessment in the second half of the 20th century, and the results indicate that-under a well-defined series of conditions-the law is sufficiently accurate for the smallest vessels ( r of the order of fractions of millimeter) but fails for the larger ones moreover, it cannot be successfully extended to turbulent flows. The law is based on the assumption that blood or lymph circulation in living organisms is governed by a “work minimization” principle that-under a certain set of specified conditions-leads to an “optimal branching ratio” of r i + 1 r i = 1 2 3 = 0.7937. First proposed by the Swiss physiologist and Nobel laureate Walter Rudolf Hess in his 1914 doctoral thesis and published in 1917, the law was “rediscovered” by the American physiologist Cecil Dunmore Murray in 1926. The Hess–Murray law is a correlation between the radii of successive branchings in bi/trifurcated vessels in biological tissues.
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