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In biophysical fluid dynamics, Murray's law is a potential relationship between radii at junctions in a network of fluid-carrying tubular pipes. Its simplest version proposes that whenever a branch of radius r {\displaystyle r} splits into two branches of radii r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} , then all three radii should obey the equation
Murray's law is observed in the vascular and respiratory systems of animals, xylem in plants, and the respiratory system of insects. In principle, Murray's law also applies to biomimetic engineering, but human designs rarely exploit the law.
Murray's law is named after Cecil D. Murray, a physiologist at Bryn Mawr College, who first argued that efficient transport might determine the structure of the human vascular system.