For connecting a parent pipe with radius of r0 to many children pipes with radius of ri , the formula of generalized Murray's law is: r o a = 1 1 − X ∑ i = 1 N r i a {\displaystyle r_{o}^{a}={1 \over 1-X}\sum _{i=1}^{N}r_{i}^{a}} , where the X is the ratio of mass variation during mass transfer in the parent pore, the exponent α is dependent on the type of the transfer. For laminar flow α =3; for turbulent flow α =7/3; for molecule or ionic diffusion α =2; etc.