Gaussian Elimination - Pipes in a Steady-State Configuration - Chemical Flowing - Engineering Assignment Help

Assignment Task:

Gaussian Elimination 

The diagram below shows five mixing vessels connected by pipes in a steady-state  configuration. Water is pumped through the pipes at the steady rates shown in the  diagram. The incoming water contains a chemical, the amount of which is specified by  its concentration c (mg/m3). 

The principle of conservation of mass states that  

mass of chemical flowing in = mass of chemical flowing out 

where the mass flow rate of the chemical is obtained by multiplying the volume flow rate  of the water by the concentration of the chemical. 

First, obtain the equations for the concentrations of the chemical, ci, inside the vessels  following the example discussed in class. Then, use Gaussian elimination to determine  the unknown concentrations ci. 

Answer the following questions as a check for the values of the concentrations that you  calculate: 

1. Can the concentration within the system ever be higher than the maximum concentration going in? Explain. 

2. Can the concentration within the system ever be lower than the minimum  concentration going in? Explain. 

3. How does the concentration of one of the vessels compare to its nearest  neighbors? Explain. 

4. What is the concentration of the outflow? This can be determined independently  of using Gaussian elimination. 

Submit: 

1. The answers to the four questions above,  

2. The set of 5 equations in 5 unknowns in matrix form, and  

3. Your answers for the unknowns.

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