Optimum Pipe Sizing is a common issue in process industries. A liquid is contained in a reactor vessel at 115 bar absolute pressure. It is transferred to a storage vessel through a 50 mm internal diameter commercial steel pipe. The storage vessel is nitrogen blanketed and pressure above the liquid surface is kept constant at 1500 N/sq. m gauge. The total run of pipe between the two vessels is 300 m. The miscellaneous losses due to entry and exit losses, fittings, valves, etc., amount to 1200 equivalent pipe diameters. The liquid level in the storage vessel is at an elevation 20 m below the level in the reactor. A turbine is fitted in the pipeline to recover the excess energy that is available, over that required to transfer the liquid from one vessel to the other. The properties of the fluid are: density 895 kg/Cu. m, viscosity 0.76 mNs/

sq. m Any available/assumed cost data can be used

Perform the following tasks:

Present the detailed analysis of the problem at hand, Develop the Objective function and constraint Models Solve the Problem using appropriate optimization technique Perform sensitivity analysis.