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solve the task for flows in the network
- Thread starter kardy44
- Start date
D
Deleted member 4993
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If I were to do this problem:Hello, my brother got this assignment and the task is basically the title, to solve x1,2,3,4. To be honest we dont even know how to start so every help would be much appreciated.
View attachment 22863
Thanks in advance
I would write the equations for conservation of mass at points A, B, C & D and solve.
Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about these problems.
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HallsofIvy
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- Jan 27, 2012
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First, do you understand what the chart is showing? What are the values of \(\displaystyle x_1\), \(\displaystyle x_2\), \(\displaystyle x_3\), and \(\displaystyle x_4\) supposed to mean? You call these flows. Can we think of them as the amounts flowing through pipes, perhaps? Or traffic moving down streets? In any case should the amount flowing into an intersection be the same as the amount flowing out? (That is what Subhotosh Kahn is refering to as "conservation of mass".)
For example, look at intersection "A". You have 350 going in and \(\displaystyle x_1\) and \(\displaystyle x_2\) going out. If the amount flowing into an intersection has to be the same as the amoung flowing out then \(\displaystyle x_1+ x_2= 350\). Similarly at intersection "B". You have \(\displaystyle x_1\) flowing in, 100 and \(\displaystyle x_3\) flowing out. If the amount flowing into an intersection has to be the same as the amount flowing out, we must have \(\displaystyle x_1= 100+ x_3\).
Do the same for intersections C and D to get four equations to solve for \(\displaystyle x_1\), \(\displaystyle x_2\), \(\displaystyle x_3\), and \(\displaystyle x_4\).
For example, look at intersection "A". You have 350 going in and \(\displaystyle x_1\) and \(\displaystyle x_2\) going out. If the amount flowing into an intersection has to be the same as the amoung flowing out then \(\displaystyle x_1+ x_2= 350\). Similarly at intersection "B". You have \(\displaystyle x_1\) flowing in, 100 and \(\displaystyle x_3\) flowing out. If the amount flowing into an intersection has to be the same as the amount flowing out, we must have \(\displaystyle x_1= 100+ x_3\).
Do the same for intersections C and D to get four equations to solve for \(\displaystyle x_1\), \(\displaystyle x_2\), \(\displaystyle x_3\), and \(\displaystyle x_4\).
Last edited:
D
Deleted member 4993
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Equation for Node A:Hello, my brother got this assignment and the task is basically the title, to solve x1,2,3,4. To be honest we dont even know how to start so every help would be much appreciated.
View attachment 22863
Thanks in advance
Input = output \(\displaystyle \ \to \ \)350 = x1 + x2 ................................... (1)
Equation for Node B:
Input = output \(\displaystyle \ \to \ \)x1 = x3 + 100 ................................... (2)
Equation for Node C:
Input = output \(\displaystyle \ \to \ \)x3 + x4 = 30 ................................... (3)
Equation for Node D:
Input = output \(\displaystyle \ \to \ \)x2 = x4 + 200 ................................... (4)
Majority of the work is done (setting up the equations). Solve the 4 equations above to calculate the unknowns.