Problem $4(25$ pts$)$: A factory has purchased the lower reservoir depicted in problem $3,$ and requires that the discharge rate to the reservoir be increased to $2m{s}^{-1}.$ The utility is considering two options to meet the modified demand. The first option is to replace the old sewer pipeline with a single structural steel pipe of the same length. The second option is to raise the elevation of the upper cistern to increase the pressure head.

a$)(10$ pts$.)$ Evaluate the viability of replacing the pipeline. What diameter structural steel pipe will be required to meet the discharge demand with the current storage tank height? Structural steel pipe is available in diameters between $50cm$ and $500cm$ in increments of $5cm.$

b$)(10$ pts$.)$ Evaluate the viability of adding an elevated pressure thank. What elevation would the cistern tank need to be raised to in order to meet the modified demand with the existing pipeline?

c$)(5$ pts$.)$ The cost of structural steel pipe is $$100+$$${2000}^{**}$ Diameter $(m)$ per $m$ of pipe. The price to raise the height of the water tower is $$2500$ per $m$ elevation gain. Which is the most cost$-$effective option to meet customer demand?