Flow in branch pipe 2

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Homework Statement


in the previous therad
https://www.physicsforums.com/threads/flow-in-branch-pipe.866194/
(post #14) , i was told that water can flow in one direction only in a netwrok of pipes .
However , in the notes uploaded here , the author stated that when P is below surface of B , then water must be out of B and Q1 + Q2 = Q3 ?
I4r4Jk1.jpg

Homework Equations




The Attempt at a Solution


IMO , it should be Q2 = Q1 + Q3 , since i was told that water can only flow in 1 direction , am i right ? [/B]
 

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  • #3
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I would not have set this problem up the way that they have set it up. I would have written the following 3 equations:

$$\frac{p_A}{\rho g}+z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_B}{\rho g}+z_B+\frac{fL_1v_2^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_C}{\rho g}+z_C+\frac{fL_1v_3^2}{gd_1}$$
So,
$$z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}\tag{1}$$
$$\frac{p_D}{\rho g}+z_D=z_B+\frac{fL_1v_2^2}{gd_1}\tag{2}$$
$$\frac{p_D}{\rho g}+z_D=z_C+\frac{fL_1v_3^2}{gd_1}\tag{3}$$

What would Eqn. 2 have to look like if the flow were from B to D, rather than from D to B?
 
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  • #4
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I would not have set this problem up the way that they have set it up. I would have written the following 3 equations:

$$\frac{p_A}{\rho g}+z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_B}{\rho g}+z_B+\frac{fL_1v_2^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_C}{\rho g}+z_C+\frac{fL_1v_3^2}{gd_1}$$
So,
$$z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}\tag{1}$$
$$\frac{p_D}{\rho g}+z_D=z_B+\frac{fL_1v_2^2}{gd_1}\tag{2}$$
$$\frac{p_D}{\rho g}+z_D=z_C+\frac{fL_1v_3^2}{gd_1}\tag{3}$$

What would Eqn. 2 have to look like if the flow were from B to D, rather than from D to B?
if the flow were from B to D ,
PB / ρg + zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) ,
as PB = 0 ,so ,
zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) , am i right ?
am i right ?
 
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  • #5
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is the author wrong ? how could Q1 + Q2 = Q3 ? how could the water flow in different direction ?
in the previous thread , i was told that 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 , so the water can only flow out from A , and into B and C..
https://www.physicsforums.com/threads/flow-in-branch-pipe.866194/
 
  • #6
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if the flow were from B to D ,
PB / ρg + zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) ,
as PB = 0 ,so ,
zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) , am i right ?
am i right ?
Yes. Now, see if there is a possible solution for this case.
 
  • #7
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Yes. Now, see if there is a possible solution for this case.
what do you mean ?
 
  • #9
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This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
IMO , that is not feasible , since i was told that water can only flow in 1 direction
 
  • #10
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IMO , that is not feasible , since i was told that water can only flow in 1 direction
If that's the case, then when you solve the equations, you will not get a real solution. Why don't you try solving it and see what you get. Who told you that silly thing anyway?
 
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  • #12
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If that's the case, then when you solve the equations, you will not get a real solution. Why don't you try solving it and see what you get. Who told you that silly thing anyway?
so , the statement of water can only flowing in 1 direction is incorrect ?
 
  • #13
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anyone can clarify ?
 
  • #14
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This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
how to know that if the equations have solutions ?
 
  • #16
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how to know that if the equations have solutions ?
Solve them and see if the solution is real or complex.
 

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