Heavy fuel oil, initially semisolid at $15^{\circ} \mathrm{C}$ is to be heated and pumped through a $15 \mathrm{~cm}$ diameter (inside) pipe at the rate of $20000 \mathrm{~kg} / \mathrm{h}$. The pipe line is 1500 long and efficiently lagged. The cost of power for pumping is Rs. 1.0

per kwh used with 50 per cent efficiency, while the cost of steam heat is Rs.40.0 per million kilocalorie. On the basis of the following data, calculate the economic (optimum) pumping temperature.

Data: Specific heat of oil $=0.5 \mathrm{kcal} / \mathrm{kg}^{0} \mathrm{C}$; Density of oil $=950 \mathrm{~kg} / \mathrm{m}^{3}$

$H_{f s}=\frac{2 f v^{2} L}{g c D}$ where $f=4 \times \operatorname{Re}^{-0.2}, \operatorname{Re}=$ Reynolds Number

Oil viscosity $(\mathrm{kg} / \mathrm{m} . \mathrm{sec}) \mu=\frac{1.0}{d T}$

Where $d T$ is the rise in oil temperature over $15^{\circ} \mathrm{C}$