How Does the Q1=Q2+Q3 Concept Explain Flow in Branch Pipes?

[foo9008]

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 ?

 

[SteamKing]

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.

 

[foo9008]

We don't know why, becuz you didn't include the figure which the problem refers to.

 

[SteamKing]

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?

 

[foo9008]

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

 

[SteamKing]

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?

 

[foo9008]

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 ...

 

[SteamKing]

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, Z_A > Z_B and Z_A > Z_C. When Z_A 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.

 

[foo9008]

No, you're not looking at the diagram closely enough.

In the diagram, Z_A > Z_B and Z_A > Z_C. When Z_A 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 Z_A and Z_B > Z_C , 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 ?

 

[foo9008]

No, you're not looking at the diagram closely enough.

In the diagram, Z_A > Z_B and Z_A > Z_C. When Z_A 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 ?

 

[foo9008]

deleted

 

[foo9008]

No, you're not looking at the diagram closely enough.

In the diagram, Z_A > Z_B and Z_A > Z_C. When Z_A 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 ?

 

[foo9008]

No, you're not looking at the diagram closely enough.

In the diagram, Z_A > Z_B and Z_A > Z_C. When Z_A 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

 

[SteamKing]

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.

 

[foo9008]

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 ?

 

[SteamKing]

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.

 

[foo9008]

No, you're not looking at the diagram closely enough.

In the diagram, Z_A > Z_B and Z_A > Z_C. When Z_A 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

 

[foo9008]

Can anyone explain??

 

[foo9008]

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 ?

 

[SteamKing]

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.

 

[foo9008]

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?

 

[SteamKing]

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.