How to transform this diagram into a $Ax=b$
Could you please help me to write this model into an $Ax=b$ system
differential-equations systems-of-equations
edited Dec 7 at 12:37
Harry Peter
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
add a comment |
Could you please help me to write this model into an $Ax=b$ system
differential-equations systems-of-equations
edited Dec 7 at 12:37
Harry Peter
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17
add a comment |
Could you please help me to write this model into an $Ax=b$ system
differential-equations systems-of-equations
edited Dec 7 at 12:37
Harry Peter
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
Could you please help me to write this model into an $Ax=b$ system
differential-equations systems-of-equations
differential-equations systems-of-equations
edited Dec 7 at 12:37
Harry Peter
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
edited Dec 7 at 12:37
Harry Peter
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
edited Dec 7 at 12:37
Harry Peter
5,44111439
edited Dec 7 at 12:37
Harry Peter
5,44111439
edited Dec 7 at 12:37
Harry Peter
5,44111439
5,44111439
asked Nov 29 at 18:04
Ahmed
1,251512
asked Nov 29 at 18:04
Ahmed
1,251512
asked Nov 29 at 18:04
Ahmed
1,251512
1,251512
What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17
add a comment |
What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17
What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17
add a comment |
1 Answer
1
active
oldest
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Let's call the concentrations in the four tanks as $c_1,c_2,c_3,c_4$. If volume $v$ leaves from tank $i$ in one minute, the quantity of sulfur that leaves is $vc_i$. What does steady state means? It means that the concentration and volumes in the tank do not change. If you look at your picture, you see that for each tank, the volume of oil going in is the same as the volume of oil going out. That means that the quantity of sulfur going in is the same as the quantity of sulfur going out. I use the convention that tank 1 is top left, 2 is top center, 3 is top right, and 4 is bottom.
The sulfur going into tank 1 is coming from the top well and from tank four, and it is going out to tank 2 (via two routes), tank 3, and tanker. The total volume coming in is $5m^3/min+3m^3/min$, equal to the volume going out $(3+1+1+3)m^3/min$
The sulfur going in and out is $$5 XYZ+3 c_4 =8 c_1$$
You need to do this for all tanks. For example, in tank 4: $$1c_3+2ZYX=3c_4$$
Move all terms with $c_i$ to the left side, and all constants to the right side of the equal signs. Now you have the system of equations.
Note that the concentration of sulfur going to the tanker is $c_1$, and to the pipeline is $c_3$
answered Nov 29 at 19:42
Andrei
10.9k21025
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
Let's call the concentrations in the four tanks as $c_1,c_2,c_3,c_4$. If volume $v$ leaves from tank $i$ in one minute, the quantity of sulfur that leaves is $vc_i$. What does steady state means? It means that the concentration and volumes in the tank do not change. If you look at your picture, you see that for each tank, the volume of oil going in is the same as the volume of oil going out. That means that the quantity of sulfur going in is the same as the quantity of sulfur going out. I use the convention that tank 1 is top left, 2 is top center, 3 is top right, and 4 is bottom.
The sulfur going into tank 1 is coming from the top well and from tank four, and it is going out to tank 2 (via two routes), tank 3, and tanker. The total volume coming in is $5m^3/min+3m^3/min$, equal to the volume going out $(3+1+1+3)m^3/min$
The sulfur going in and out is $$5 XYZ+3 c_4 =8 c_1$$
You need to do this for all tanks. For example, in tank 4: $$1c_3+2ZYX=3c_4$$
Move all terms with $c_i$ to the left side, and all constants to the right side of the equal signs. Now you have the system of equations.
Note that the concentration of sulfur going to the tanker is $c_1$, and to the pipeline is $c_3$
answered Nov 29 at 19:42
Andrei
10.9k21025
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
add a comment |
Let's call the concentrations in the four tanks as $c_1,c_2,c_3,c_4$. If volume $v$ leaves from tank $i$ in one minute, the quantity of sulfur that leaves is $vc_i$. What does steady state means? It means that the concentration and volumes in the tank do not change. If you look at your picture, you see that for each tank, the volume of oil going in is the same as the volume of oil going out. That means that the quantity of sulfur going in is the same as the quantity of sulfur going out. I use the convention that tank 1 is top left, 2 is top center, 3 is top right, and 4 is bottom.
The sulfur going into tank 1 is coming from the top well and from tank four, and it is going out to tank 2 (via two routes), tank 3, and tanker. The total volume coming in is $5m^3/min+3m^3/min$, equal to the volume going out $(3+1+1+3)m^3/min$
The sulfur going in and out is $$5 XYZ+3 c_4 =8 c_1$$
You need to do this for all tanks. For example, in tank 4: $$1c_3+2ZYX=3c_4$$
Move all terms with $c_i$ to the left side, and all constants to the right side of the equal signs. Now you have the system of equations.
Note that the concentration of sulfur going to the tanker is $c_1$, and to the pipeline is $c_3$
answered Nov 29 at 19:42
Andrei
10.9k21025
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
add a comment |
Let's call the concentrations in the four tanks as $c_1,c_2,c_3,c_4$. If volume $v$ leaves from tank $i$ in one minute, the quantity of sulfur that leaves is $vc_i$. What does steady state means? It means that the concentration and volumes in the tank do not change. If you look at your picture, you see that for each tank, the volume of oil going in is the same as the volume of oil going out. That means that the quantity of sulfur going in is the same as the quantity of sulfur going out. I use the convention that tank 1 is top left, 2 is top center, 3 is top right, and 4 is bottom.
The sulfur going into tank 1 is coming from the top well and from tank four, and it is going out to tank 2 (via two routes), tank 3, and tanker. The total volume coming in is $5m^3/min+3m^3/min$, equal to the volume going out $(3+1+1+3)m^3/min$
The sulfur going in and out is $$5 XYZ+3 c_4 =8 c_1$$
You need to do this for all tanks. For example, in tank 4: $$1c_3+2ZYX=3c_4$$
Move all terms with $c_i$ to the left side, and all constants to the right side of the equal signs. Now you have the system of equations.
Note that the concentration of sulfur going to the tanker is $c_1$, and to the pipeline is $c_3$
answered Nov 29 at 19:42
Andrei
10.9k21025
Let's call the concentrations in the four tanks as $c_1,c_2,c_3,c_4$. If volume $v$ leaves from tank $i$ in one minute, the quantity of sulfur that leaves is $vc_i$. What does steady state means? It means that the concentration and volumes in the tank do not change. If you look at your picture, you see that for each tank, the volume of oil going in is the same as the volume of oil going out. That means that the quantity of sulfur going in is the same as the quantity of sulfur going out. I use the convention that tank 1 is top left, 2 is top center, 3 is top right, and 4 is bottom.
The sulfur going into tank 1 is coming from the top well and from tank four, and it is going out to tank 2 (via two routes), tank 3, and tanker. The total volume coming in is $5m^3/min+3m^3/min$, equal to the volume going out $(3+1+1+3)m^3/min$
The sulfur going in and out is $$5 XYZ+3 c_4 =8 c_1$$
You need to do this for all tanks. For example, in tank 4: $$1c_3+2ZYX=3c_4$$
Move all terms with $c_i$ to the left side, and all constants to the right side of the equal signs. Now you have the system of equations.
Note that the concentration of sulfur going to the tanker is $c_1$, and to the pipeline is $c_3$
answered Nov 29 at 19:42
Andrei
10.9k21025
answered Nov 29 at 19:42
Andrei
10.9k21025
answered Nov 29 at 19:42
Andrei
10.9k21025
answered Nov 29 at 19:42
Andrei
10.9k21025
10.9k21025
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
add a comment |
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
Thanks a lot for your full help
– Ahmed
Nov 30 at 8:36
add a comment |
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What have you tried so far?
– Viktor Glombik
Nov 29 at 18:13
I have a very little idea about these things. I am a numerical analysist. I know that we have to take care of the arrows when they are in and out, but I don't know how.
– Ahmed
Nov 29 at 18:17