Computational Methods in Engineering

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ENGR 328 Final Project Due: 05/09/2019 @ 11:59 pm Choose one of the problems below. For the chosen problem write out the relevant equations and associated diagrams needed to determine those equations. Write out the equivalent linear system. Given the assembled linear system and MatLab, solve the silmultaneous equations using Gauss elimination or LU decomposition with pivoting. Check your answers using the backslah operator. Submit a pdf including your written equations and linear system as well as your MatLab script used to solve the linear system. Problem 1. Steady-state analysis of a system of reactors: A conservative substance (one that does not increase or decrease due to chemical transformations) is exchanged through several reactors as shown below. The flow rates into, out of, and between reactors are given: Q1 = 2, Q2 = 5, Q3 = 10, Q4 = 1, Q5 = 4, Q6 = 11, Q7 = 7, Q8 = 9, Q9 = 3, Q10 = 15, Q11 = 6 (m3 / min). The input flow rates and concentrations are also given: Q01 = 13, c01 = 10, Q05 = 12, c05 = 20. Solve for the concentrations: c1, c2, c3, c4, c5, and c6 (mg / m3) in each reactor. Problem 2. Statically determinate trusses: The truss system below has a fixed connection on the bottom left and a roller connection on the bottom right. Pins connect the trusses at points A, B, C, and D. The exterior force acting at B is horizontal to the ground and the force at D is at a 45 degree angle to the horizontal. Assuming a static situation, solve for the forces in each truss: AB, AC, AD, BC, and CD. Problem 3. Currents and voltages in a resistor circuit: Given the diagram below and using Kirchhoff’s rules, determine the current in each branch of the circuit. The resistances are: R1 = 50, R2 = 100, R3 = 150, R4 = 100, R5 = 200, R6 = 50, R7 = 100, R8 = 150. The voltage sources are: V1 = 200 and V2 = 100. Problem 4. Stead-state displacements in a mass-spring system: Consider the mass-spring system shown below. The system is released and allowed to come to rest under the effects of gravity. The springs are linear and follow Hooke’s law. The masses are: M1 = 2, M2 = 1.5, M3 = 1.5, M4 = 3, M5 = 2, and M6 = 1. The stiffness of the springs are: K1 = 10, K2 = 5, K3 = 5, K4 = 15, K5 = 10, and K6 = 12. Assume all masses can only move vertically and that M2 and M3 are held vertically even. Determine the displacement of each mass.
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