Project Background and Description: Pressure vessels are an integral part of many manufacturing facilities and processing plants, enabling the safe storage of pressurized liquids and gases. If these vessels are not properly designed, constructed, and maintained, failure can occur which is very dangerous. As such, pressure vessel design and analysis are regulated by engineering authorities such as ASME (American Society of Mechanical Engineers). These standards outline critical design parameters such as maximum allowable operating pressure, temperature, safety factors and the required minimum wall thickness. You are an intern at company "XYZ Ltd." and you are asked to evaluate a pressure vessel that is in currently in use at a compressor station. Per the company's internal standards, the following should be evaluated: Part A: The actual wall thickness of the pressure vessel based on the information available Part B: The range of internal operating pressures that the vessel can sustain based on the wall thickness calculated in Part A. This is to be done in accordance with the ASME Boiler and Pressure Vessel Code Section VIII - 2017. The detailed problem requirements, inputs, mathematical model and required outputs are detailed in the following sections. Please read the entire document carefully before beginning to code. Part A - Calculation of Wall Thickness The pressure vessel that is currently in operation at the compressor station is shown in Figure 1. It has a cylindrical middle section and two hemispherical heads. The outer radius (R) is 10 in., and the length of the cylindrical section is 24 in. The wall thickness of the cylindrical section is t, and the wall thickness of the hemispherical heads is 1.5t. Determine t if the weight of the entire pressure vessel is 42.27 lb. The pressure vessel is made of aluminum and has a specific weight of 0.101 lb/in. Use the following mathematical formulation for the total volume (V) to determine t: 4 V = (24 * * 10) + ( * * 10) [ * (10 t) + 24 + - 4 * - * * (10 1.5t)] = 42.27 0.101 R-10 in. 24 in. Figure 1: Sketch of Pressure Vessel Steps for Mathematical Model 1) Solve the polynomial given above for t. Hint: Use the conv and roots functions. Discuss which root is the wall thickness t. [8 mks] 2) Print a statement with the wall thickness of the cylindrical section and the wall thickness of the hemispherical head. [2 mks] Part B - Determination of the Allowable Range for the Internal Pressure Per the ASME Boiler and Pressure Vessel Code 2017 Section 4.3.3, the minimum required thickness of a cylindrical shell (t_cyl) subjected to internal pressure should be determined using the following equation: P t_cyl = R R(exp SE-1) Also, per the ASME Boiler and Pressure Vessel Code-2017 Section 4.3.3, the minimum required thickness of a hemispherical head (t_sph) subjected to internal pressure should be determined using the following equation: t_sph = R (exp [0.5*P] 1) P1 S* E where: R is the outer radius of the vessel (in) P is the internal pressure (psi) S is the material stress value = 20000 psi E is the joint/weld efficiency factor = 1 Company "XYZ Ltd." wants to operate the pressure vessel within a range of 100 to 400 psi. Determine if the pressure vessel can be operated over this entire range based on the ASME code requirements for the minimum wall thickness. Use the actual wall thicknesses calculated in Part A and compare with the minimum calculated values. Steps for Mathematical Model 1) Create an array of evenly spaced values for the desired pressure range from 100 to 400 psi. [1 mks] 2) Calculate the minimum required wall thickness of the cylindrical shell and hemispherical heads over the pressure range defined in Step 1. [3 mks] 3) Compare the minimum calculated values to the wall thickness determined in Part A. What is the allowable pressure range for the entire vessel? [3 mks] 4) On the same figure, plot the minimum required thickness of the cylindrical section vs pressure and the minimum required thickness of the hemispherical head vs pressure. Ensure that the plot: a. Clearly distinguishes the values of the plot for which the real vessel meets the ASME criteria and for which values the vessel fails to meet the ASME criteria. You can use different colours, line types and/or point markers. [3 mks] b. Include title, labels for x and y axes, and a legend. [2 mks] 5) Print a statement with the allowable range for the internal pressure. [1 mk] Note: Loops should not be used in the code for this analysis. Project Rubric All files should be submitted to the D2L Dropbox: one m-file and project report (pdf document described in Table 1). Table 1: Project Rubric Marks [Total = 30] 10 13 Topic Break-down Part A Marks defined in Part A description Part B Commenting and Organization Report Marks defined in Part B description Commenting is well done (not too much or too little) and program is properly thought out and organized. Code is 2 readable and easy to use. 2-4 pages of content which identifies the problem and the methodology used to solve it. Report should include: Abstract, Introduction, Methodology/Matlab Model Description, Presentation of results and Discussion, Conclusion (should include limitations of your code and possible future enhancements), References 5