Understanding Flow in Branch Pipes: Exploring Q1=Q2+Q3 Concept

In summary: It is not possible because if Q1 = Q2 + Q3, then the water flowing out of A would be equal to the water flowing out of B + the water flowing out of C. However, this is not the case in the diagram.
  • #1
foo9008
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4

Homework Statement


the author stated that Q1= Q2 + Q3 , that's means the water flowing from reservoir A to B and C ...

Homework Equations

The Attempt at a Solution


why can't Q1 + Q2 = Q3 ? which means water flow from reservoir A and B to C ?
 

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  • #2
foo9008 said:

Homework Statement


the author stated that Q1= Q2 + Q3 , that's means the water flowing from reservoir A to B and C ...

Homework Equations

The Attempt at a Solution


why can't Q1 + Q2 = Q3 ? which means water flow from reservoir A and B to C ?
We don't know why, becuz you didn't include the figure which the problem refers to. :frown: o_O
 
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  • #3
SteamKing said:
We don't know why, becuz you didn't include the figure which the problem refers to. :frown: o_O
 

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  • #4
foo9008 said:

Homework Statement


the author stated that Q1= Q2 + Q3 , that's means the water flowing from reservoir A to B and C ...

Homework Equations

The Attempt at a Solution


why can't Q1 + Q2 = Q3 ? which means water flow from reservoir A and B to C ?
Look at the diagram for this problem.

Concentrate real hard.

Now, ask yourself what is the difference between Q1 + Q2 = Q3 and Q1 = Q2 + Q3?
 
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  • #5
SteamKing said:
Look at the diagram for this problem.

Concentrate real hard.

Now, ask yourself what is the difference between Q1 + Q2 = Q3 and Q1 = Q2 + Q3?
Q1 + Q2 = Q3 means the water flow from reservoir 1 and 2 = reservoir 3 ... Q1 = Q2 + Q3 means the water flow from reservoir 1 = reservoir 3 + 2
 
  • #6
foo9008 said:
Q1 + Q2 = Q3 means the water flow from reservoir 1 and 2 = reservoir 3 ... Q1 = Q2 + Q3 means the water flow from reservoir 1 = reservoir 3 + 2
Now, do you want to take another try at answering the question you posed in the OP?
 
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  • #7
SteamKing said:
Now, do you want to take another try at answering the question you posed in the OP?
i still don't understand why can the water flow from reservoir A and B = reservoir C , which means (Q1 + Q2 = Q3 ) since the water can flow from high to low level , reservoir 1 and 2 are higher than 3 ...
 
  • #8
foo9008 said:
i still don't understand why can the water flow from reservoir A and B = reservoir C , which means (Q1 + Q2 = Q3 ) since the water can flow from high to low level , reservoir 1 and 2 are higher than 3 ...
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
 
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  • #9
SteamKing said:
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
since ZA and ZB > ZC , why can't the water flow rate from A and B equal to C ? I'm confused...

btw , Q1 = Q2 + Q3 means the water flowing out from A equal to water flowing out from B + water flowing from C ?
Or the water flowing out from A is equal to( the water flow from A to B + water flow from A to C )

i assume Q1 = Q2 + Q3 means the water flowing out from A equal to water flowing out from B + water flowing from C ? am i right ?
 
  • #10
SteamKing said:
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
why it is not possible for water from B to flow to junction D ? how to know that ?
 
  • #11
deleted
 
Last edited:
  • #12
SteamKing said:
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
since the reservoir B is higher than junction D , the water can flow from B to D , am i right ?

reservoir 2 also higher than reservoir 3 , why can't water from reservoir 2 flow out ? which means Q1 +Q2 = Q3 ?
 
  • #13
SteamKing said:
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
i know that the ZA is the highest , so the water would flow out ...But , at junction D , water from reservoir B will also flow out to junction D , am i right ? since B is higher than D
 
  • #14
foo9008 said:
i know that the ZA is the highest , so the water would flow out ...But , at junction D , water from reservoir B will also flow out to junction D , am i right ? since B is higher than D
But, in order for water from Res. B to flow to the split at D, it must flow against the pressure in the line created by the flow from Res. A.

You can't look at these flows in isolation. You must look at the entire network system.
 
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  • #15
SteamKing said:
But, in order for water from Res. B to flow to the split at D, it must flow against the pressure in the line created by the flow from Res. A.

You can't look at these flows in isolation. You must look at the entire network system.
tat's why the water can flow in different direction in a pipe, right ? or the water from 2 different source just can flow in a single direction only ? just like the case above ?
 
  • #16
foo9008 said:
tat's why the water can flow in different direction in a pipe, right ? or the water from 2 different source just can flow in a single direction only ? just like the case above ?
Unless something weird is going on, water generally flows in only one direction at a time within a pipe.
 
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  • #17
SteamKing said:
No, you're not looking at the diagram closely enough.

In the diagram, ZA > ZB and ZA > ZC. When ZA is higher, there will be flow out of Reservoir A.

The pipe leading out of Reservoir A splits at point D. By continuity, the flow into the split at D from Reservoir A must equal the flow out of the split into Reservoir B and Reservoir C.

Mathematically, Q1 = Q2 + Q3, which is the continuity equation written for the split at D.

How much flow occurs depends on other factors.
How could the water from A goes to C ? The water has to pass thru d before it can reach C , right? At junction D, its lower than C.. how could the water from low level flow to higher level?? @SteamKing
 
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  • #18
Can anyone explain??
 
  • #19
can anyone explain why the iteration stop at v1 = 1.82 , where f(x) = -0.03 , shouldn't the iteration stop at f(x) = 0 ?
 
  • #20
foo9008 said:
can anyone explain why the iteration stop at v1 = 1.82 , where f(x) = -0.03 , shouldn't the iteration stop at f(x) = 0 ?
It's not clear what you are talking about here.

If you look at 138.jpg, middle of the page, v1 = 1.82 m/s and f(v1) = -0.0005. That seems to be zero for all practical purposes.

The only way to reduce -0.0005 toward zero is to add more digits to v1, which may already be at the limit of its precision, given the accuracy of the original data provided in the problem statement.
 
  • #21
SteamKing said:
It's not clear what you are talking about here.

If you look at 138.jpg, middle of the page, v1 = 1.82 m/s and f(v1) = -0.0005. That seems to be zero for all practical purposes.

The only way to reduce -0.0005 toward zero is to add more digits to v1, which may already be at the limit of its precision, given the accuracy of the original data provided in the problem statement.
so , f(v1) = -0.0005 is accurate enough for exercises?
 
  • #22
foo9008 said:
so , f(v1) = -0.0005 is accurate enough for exercises?
It's accurate enough for most things.

You are free, however, to keep grinding away at these calculations, adding more zeroes to f(v1), but you are not going to come up with a completely different answer than v1 = 1.82 m/s.
 
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1. What is the Q1=Q2+Q3 concept in branch pipes?

The Q1=Q2+Q3 concept in branch pipes is a mathematical equation used to understand the flow of fluids in a branching pipeline system. It states that the total flow rate in the main pipe (Q1) is equal to the sum of the flow rates in the two branch pipes (Q2 and Q3). This concept is based on the principle of conservation of mass and is commonly used in fluid mechanics and hydraulics.

2. How does the Q1=Q2+Q3 concept help in understanding flow in branch pipes?

The Q1=Q2+Q3 concept helps in understanding the distribution of flow in a branching pipeline system. By using this equation, we can determine the flow rates in the branch pipes based on the known flow rate in the main pipe. It also allows us to predict the overall flow rate and pressure changes in the system, which is crucial for designing and optimizing pipelines.

3. What factors affect the application of the Q1=Q2+Q3 concept in branch pipes?

The Q1=Q2+Q3 concept is based on certain assumptions, such as the fluid being incompressible, the pipes being of uniform diameter, and the flow being steady. Any deviations from these assumptions, such as changes in fluid density, pipe diameter, or unsteady flow, can affect the accuracy of the concept. Additionally, the presence of valves, fittings, and other obstructions in the pipeline can also impact the flow distribution and invalidate the Q1=Q2+Q3 equation.

4. How is the Q1=Q2+Q3 concept applied in real-world situations?

The Q1=Q2+Q3 concept is widely used in various industries, including water distribution, oil and gas pipelines, and chemical processing. It is applied during the design and operation of branching pipeline systems to ensure efficient and balanced flow distribution. Engineers also use this concept to troubleshoot flow issues and optimize the performance of existing pipelines.

5. Are there any limitations to the Q1=Q2+Q3 concept in branch pipes?

While the Q1=Q2+Q3 concept is a useful tool for understanding flow in branch pipes, it has some limitations. As mentioned earlier, the accuracy of the concept depends on certain assumptions and can be affected by various factors in real-world situations. It is essential to consider these limitations and use the concept in conjunction with other methods for a more comprehensive understanding of flow in branching pipeline systems.

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