[SOLUTION] A Food Manufacturing Company

CPE Pressure Vessels Limited Company manufacturers pressure vessel for oil, gas, petrochemical, nuclear and water industries as shown in Figure 3 (length L, diameter 2R, hemispherical ends). As a design engineer of the CPE company you have been asked to design a pressure vessel for the food manufacturing industry. The main objective of the work is to select a suitable material for the outer wall of the pressure vessel. When the pressure vessel is fully assembled it resemble as a cylindrical shape having an external pressure, p. The design of the outer wall of the cylindrical pressure tank and the selected material should resist the external pressure. The radius of the pressure tank is 10 m. The outer wall containing the pressure, p should not fail either by yielding or by fast fracture. The size of the possible largest crack contained in the outer wall is ac.Figure 3: Pressure vessel for the food manufacturing companyMost of the pressure vessels are made of high strength alloy steel, and they are heavy. You are asked to explore the potential of alternative materials for lighter pressure vessels, recognizing there must be a trade-off between mass and cost – if it is too expensive, the manufacturing company will not want it even if it is lighterMaterials properties that are available for ranking materials are: density (?); Yield strength (?y); Critical stress intensity factor or fracture toughness of the material (????????????). The volume of material can be evaluated with respect to the surface area and the thickness of the cylindrical outer wall.You will need to decide your own dimensions, extra constraints and find out the equations for yielding and fast fracture of the pressure vessel. In order to translate the right material selection for the food processing application into a real engineering problem you need to answer the following questions:(a) Translation of problem indicating function, objective, constraints and free variables? You need to provide a clear definition to the problem.(6 marks)(b) Derive the performance material index for failure and select materially graphically. Discuss the implication of two performance index for the selection of one material.(10 marks)(c) Explain and justify with supporting evidence (both numerical and graphically) what would happen to the performance index if both the ends of the pressure vessel are closed.