Kitchen water at $10C$ flows over a $10-cm-$diameter pipe with a velocity of $1\mathrm{.}5\frac{m}{s}.$ Geothermal water enters the pipe at $90C$ at a rate of $1\mathrm{.}25k\frac{g}{s}.$ For calculation purposes, the surface temperature of the pipe may be assumed to be $70C.$ If the geothermal water is to leave the pipe at $50C,$ determine the required length of the pipe in meter $(m).$

$($For both water streams, use $k=0\mathrm{.}631\frac{W}{m}*K,Pr=4\mathrm{.}32,v=0\mathrm{.}658{10}^{-6}\frac{m^2}{s},$ and $c_p=4179\frac{J}{k}g*K).$

The required length of the pipe is $$ m$.$