PROBLEM STATEMENT $($Design optimization problem$)$

When installing a pump, several critical factors must be considered, including the alignment

of the pump and the driving motor, the flexibility of the connected equipment, the

foundation fitting, and the protection of the pump from interference that can affect its

service limits$.$ Centrifugal pumps are often used to intermittently transport water.

Deficiencies in the pipe$-$pump design performance can lead to poor system efficiency and

potential damage from cavitation. The complete design of the pipe system should include

considerations such as the pipe layout, pipe elevation, distance between pipe stations,

pumping flows, and pump locations. In this specific pipe pump system, water at $35C($with

a density of $994k\frac{g}{m^3}$ and vapor pressure of $1\mathrm{.}7$ kPa $)$ flows through $7\mathrm{.}5$ cm diameter suction

and deliver pipe