{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:42:06Z","timestamp":1760211726650,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2016,8,5]],"date-time":"2016-08-05T00:00:00Z","timestamp":1470355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Hess\u2013Murray law is a correlation between the radii of successive branchings in bi\/trifurcated vessels in biological tissues. First proposed by the Swiss physiologist and Nobel laureate Walter Rudolf Hess in his 1914 doctoral thesis and published in 1917, the law was \u201crediscovered\u201d by the American physiologist Cecil Dunmore Murray in 1926. The law is based on the assumption that blood or lymph circulation in living organisms is governed by a \u201cwork minimization\u201d principle that\u2014under a certain set of specified conditions\u2014leads to an \u201coptimal branching ratio\u201d of        r  i + 1      r i    =  1   2 3    = 0.7937    . This \u201ccubic root of 2\u201d correlation underwent extensive theoretical and experimental reassessment in the second half of the 20th century, and the results indicate that\u2014under a well-defined series of conditions\u2014the 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. Recent comparisons with numerical investigations of branched flows led to similar conclusions. More recently, the Hess\u2013Murray law came back into the limelight when it was taken as a founding paradigm of the Constructal Law, a theory that employs physical intuition and mathematical reasoning to derive \u201coptimal paths\u201d for the transport of matter and energy between a source and a sink, regardless of the mode of transportation (continuous, like in convection and conduction, or discrete, like in the transportation of goods and people). This paper examines the foundation of the law and argues that both for natural flows and for engineering designs, a minimization of the irreversibility under physically sound boundary conditions leads to somewhat different results. It is also shown that, in the light of an exergy-based resource analysis, an amended version of the Hess\u2013Murray law may still hold an important position in engineering and biological sciences.<\/jats:p>","DOI":"10.3390\/e18080283","type":"journal-article","created":{"date-parts":[[2016,8,5]],"date-time":"2016-08-05T10:10:24Z","timestamp":1470391824000},"page":"283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Critical Reassessment of the Hess\u2013Murray Law"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2220-1762","authenticated-orcid":false,"given":"Enrico","family":"Sciubba","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, University of Roma Sapienza, 00185 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1007\/BF02301268","article-title":"Eine mechanisch bedingte Gesetzm\u00e4\u00dfigkeit im Bau des Blutgef\u00e4\u00dfsystems","volume":"16","author":"Hess","year":"1903","journal-title":"Archiv f\u00fcr Entwicklungsmechanik der Organismen"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/BF01681580","article-title":"\u00dcber die periphere Regulierung der Blutzirkulation","volume":"168","author":"Hess","year":"1917","journal-title":"Pfl\u00fcger\u2019s Archiv f\u00fcr die Gesamte Physiologie des Menschen und der Tiere"},{"key":"ref_3","first-page":"164","article-title":"Hydraulic investigations, subservient to an intended Croonian lecture on the motion of the blood","volume":"98","author":"Young","year":"1808","journal-title":"Philos. 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