$(10$ points$)$ Water is flowing through a $10$ m long tube with a $15$ mm diameter at a flow rate of $2\mathrm{.}5k\frac{g}{s}.$

The inlet mean temperature is $333$ K and the outlet mean temperature is $375$ K $.$ Determine the mean temperature at a location of $4\mathrm{.}5$ m from the inlet.

Properties for water: $c_p=4210\frac{J}{k}gK$

Reminder: $P=DL=(0\mathrm{.}015)(10)$

$D=0\mathrm{.}471$

$L=10m$

$D=15mm=0\mathrm{.}015m$

${}_{}=2\mathrm{.}5k\frac{g}{s}=2\mathrm{.}5$

$m^{}=0\mathrm{.}01k\frac{g}{s}$

$T_i=333k$

$T_0=325k$