For the line shown in figure below; material ortho$-$dichlorobenzene $($ODCB$),$ flow rate $10,000k\frac{g}{h},$ temperature $20C,$ pipe material carbon steel.

a$)$ Calculate the line size $($pipe diameter$)[$Unit: $mm]$

b$)$ Calculate the optimum pipe diameter. $[$Unit: $mm]$

DATA : ODCB density at $20C=1306k\frac{g}{m^3}$ : Viscosity $=0$:$9cp$

A$106$ Carbon steel pipe:

$25to200mm,d_i,$ optimum $=0\mathrm{.}664G^{0\mathrm{.}51}{}^{-0\mathrm{.}36}$

$250to600mm,d_i,$ optimum $=0\mathrm{.}534G^{0\mathrm{.}43}{}^{-0\mathrm{.}30}$

$304$ Stainless steel pipe:

$25to200mm,d_i,$ optimum $=0\mathrm{.}550G^{0\mathrm{.}49}{}^{-0\mathrm{.}35}$

$250to600mm,d_i,$ optimum $=0\mathrm{.}465G^{0\mathrm{.}43}{}^{-0\mathrm{.}31}$