# Homework Help: Flow in branch pipe

1. Apr 9, 2016

### foo9008

1. The problem statement, all variables and given/known data
the author stated that Q1= Q2 + Q3 , that's means the water flowing from reservoir A to B and C ....

2. Relevant equations

3. The attempt at a solution
why cant Q1 + Q2 = Q3 ??? which means water flow from reservoir A and B to C ?

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2. Apr 9, 2016

### SteamKing

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

3. Apr 9, 2016

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4. Apr 9, 2016

### SteamKing

Staff Emeritus
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?

5. Apr 9, 2016

### foo9008

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. Apr 9, 2016

### SteamKing

Staff Emeritus
Now, do you want to take another try at answering the question you posed in the OP?

7. Apr 9, 2016

### foo9008

i still dont 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. Apr 9, 2016

### SteamKing

Staff Emeritus
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.

9. Apr 9, 2016

### foo9008

since ZA and ZB > ZC , why cant 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. Apr 9, 2016

### foo9008

why it is not possible for water from B to flow to junction D ? how to know that ?

11. Apr 10, 2016

### foo9008

deleted

Last edited: Apr 10, 2016
12. Apr 10, 2016

### foo9008

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 cant water from reservoir 2 flow out ? which means Q1 +Q2 = Q3 ?

13. Apr 11, 2016

### foo9008

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. Apr 11, 2016

### SteamKing

Staff Emeritus
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.

15. Apr 11, 2016

### foo9008

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. Apr 11, 2016

### SteamKing

Staff Emeritus
Unless something weird is going on, water generally flows in only one direction at a time within a pipe.

17. May 4, 2016

### foo9008

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

Last edited: May 4, 2016
18. May 4, 2016

### foo9008

Can anyone explain??

19. May 4, 2016

### foo9008

can anyone explain why the iteration stop at v1 = 1.82 , where f(x) = -0.03 , shouldnt the iteration stop at f(x) = 0 ?

20. May 4, 2016

### SteamKing

Staff Emeritus
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. May 4, 2016

### foo9008

so , f(v1) = -0.0005 is accurate enough for exercises?

22. May 5, 2016

### SteamKing

Staff Emeritus
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.