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Chemical/Bio Engineering
Perform the same computation as in Sec. 12.1, but change
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To calculate: The concentration of the fluid flow rate through the remaining reactors if the value of the following flow changes to
Answer to Problem 1P
Solution: The concentrations
Explanation of Solution
Given Information:
Flow rates are provided as follows:
Also,
Formula used:
Write system of linear equations in matrix form.
And,
The term
Calculation:
Consider the figure provided in the section 12.1.
Here, Q is the flow rate in cubic meter per minute and c is the concentration in milligrams cubic per meter.
For reactor 1, mass flow rate in is expressed as follows,
Mass flow out rate is,
Provided system is in the steady state. Therefore, mass flow rate will be constant.
So,
Substitute the values of the flow rates.
Substitute the known values from the diagram.
For reactor 2, the mass flow rate in is,
The mass flow rate out is,
The system is in steady state flow therefore, the mass flow in and out is same.
Substitute the values of mass flow rates.
Substitute the values of rates of flows from the figure.
For reactor 3, mass flow rate in is,
The mass flow rate out is,
The system is in steady state flow therefore, the mass flow in and out is same.
Substitute the mass flow rate in the above expression.
Substitute the values of the flow rate from the figure.
For reactor 4, mass flow rate in is,
The mass flow out rate is,
The system is in steady state. Therefore, the mass flow rate in and out will be same.
Substitute the mass flow rate values in the above expression.
Substitute the value of the flow rate from the diagram in the above equation.
For reactor 5, the mass flow rate in is,
The mass flow rate out is,
The system is in steady state therefore, the mass flow rate in and out is same.
Substitute the mass flow rate into the expression.
Substitute the value of flow rate into the above expression.
Write all the system of equations to express in a linear system of equations.
Write the above equations in the matrix
Here, coefficient matrix A is,
Column matrix X is,
Column matrix D is,
Use MATLAB to solve the matrix system
The result is obtained as follows:
Hence,
Hence, the concentrations
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Chapter 12 Solutions
Numerical Methods for Engineers
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