(a) Derive the equations to be solved for the unknown flow rates and write the system as an angmented matrix. (b) By reducing the augmented matrix in part (a) to reduced row-echelon form, determine the unkuown flow rates in the pipe network. Indicate which row operations you have used.
(a) Derive the equations to be solved for the unknown flow rates and write the system as an angmented matrix. (b) By reducing the augmented matrix in part (a) to reduced row-echelon form, determine the unkuown flow rates in the pipe network. Indicate which row operations you have used.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider a network of pipes at an oil refinery. The diagram below shows the flow rates and
direction of flow of hydrocarbons in each pipe, with unknown flow rates 1, 12, 3; 1 *5 and ag
(all r, 2 0).
200
150
200
25
X5
175
(a) Derive the equations to be solved for the unknown flow rates and write the system as an
augmented matrix.
(b) By reducing the augmented matrix in part (a) to reduced row-echelon form, determine the
unknown flow rates in the pipe network. Indicate which row operations you have used.
(c) Suppose that two of the pipes become blocked so that r3 = 0 and x, = 0. Determine the
flow rates in the remaining pipes. Justify your answer.
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