A liquid flows through a heated circular pipe at the rate of $0\mathrm{.}5k\frac{g}{m}in.$ It enters the pipe at a temperature of $10C$ and exits at $30C.$ The inside diameter of the pipe is $2\mathrm{.}5$ cm $.$ The tube wall temperature is constant at $90C.$ The relevant properties for the liquid are: specific heat $=4\mathrm{.}1819k\frac{J}{k}gK,$ thermal conductivity $=0\mathrm{.}598\frac{W}{m}K,$ density $=998\mathrm{.}2k\frac{g}{m^3},$ kinematic viscosity $=10\mathrm{.}04{10}^{-7}\frac{m^2}{s},$ and Prandtl number $=7\mathrm{.}01.$ The appropriate Nusselt number for the heat transfer is expressed as:

$=0\mathrm{.}664(Pr{)}^{-\frac{1}{6}}\sqrt[\phantom{2}]{(\frac{\text{P}\text{e}\text{D}}{L})}$

where Pe is Peclet number, D is pipe inside diameter, L is length of pipe and Pr is Prandtl number. Calculate the length of the pipe.