A $14-$inch $($nominal$)$ schedule $40$ cast$-$iron pipe is used to convey $12$ million

gallons per day of benzene. The pipeline is $3$ miles long, the pump motor is $39\%$

efficient, and electricity costs $7\mathrm{.}5$ cents per kWh $.$ An arrangement with a $12-$inch

and a $16-$inch line in parallel with the existing $14-$inch line is to be investigated.

$($a$)$ What is the yearly pumping cost for the single pipe?

$($b$)$ What is the yearly pumping cost for the parallel pipe arrangement?

Note: To reduce the workload, please only write questions $($a$)$ and $($b$).$

Use EES unit system

$g_c=32\mathrm{.}2ftlb\frac{m}{l}b\frac{f}{s^2}$

$g=32\mathrm{.}2f\frac{t^2}{s}$

$1$ gallon $=0\mathrm{.}134f{t}^3$

$1$ mile $=5280ft$

Assume:

$=55\mathrm{.}5lb\frac{m}{f}{t}^3$

$=4\mathrm{.}60{10}^{-4}lb\frac{m}{f}\frac{t}{s}$

$=0\mathrm{.}00015ft$

$Pa=Pb$

$Za=Zb$

Consider only major losses for each line, assuming minor losses are negligible.

Moody chart can be used to determine friction factors values.

Use Appendix C to find inner diameter of pipes.