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 splits into two branches of radii and , then all three radii should obey the equation If network flow is smooth and leak-free, then systems that obey Murray's law minimize the resistance to flow through the network. For turbulent networks, the law takes the same form but with a different characteristic exponent α.