Question $3.$ A countercurrent double pipe heat exchanger is used to cool an organic liquid from $80C$ to $65C.$ The flow rate of the organic liquid is $3500k\frac{g}{h}r.$ Water at $15C$ and $3000k\frac{g}{h}r$ is available for the cooling. The heat exchanger is constructed by placing a $5\mathrm{.}0cm$ tube around a copper tube with $2\mathrm{.}54cm$ outside diameter and $2\mathrm{.}22cm$ inside diameter. Water flows through the copper tube. There is also appreciable thermal resistance due to scale formation on the outside surface of the copper tube $)=(2{10}^{-3}{m}^2\frac{K}{W}.$ Assume the following physical properties are valid for the organic liquid at its average temperature:

$=860k\frac{g}{m^3}$;$,=1\mathrm{.}7{10}^{-3}kg*\frac{m}{s}$;$,k=0\mathrm{.}14\frac{W}{m}K$;$,c_p=1600\frac{J}{k}gK.$

a$)$ Calculate the length of the heat exchanger assuming viscosity correction factor is $1.$

b$)$ Estimate the pressure drop for the tube side using the inside heat transfer coefficient calculated in part $a.$

Answer: $22\mathrm{.}7m,58\mathrm{.}7$kPa