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Flow in branch pipe 2

  1. Apr 29, 2016 #1
    1. The problem statement, all variables and given/known data
    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
    2. Relevant equations


    3. 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 ?
     

    Attached Files:

  2. jcsd
  3. Apr 29, 2016 #2
  4. Apr 29, 2016 #3
    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?
     
  5. Apr 29, 2016 #4
    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 ?
     
    Last edited: Apr 29, 2016
  6. Apr 29, 2016 #5
    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/
     
  7. Apr 29, 2016 #6
    Yes. Now, see if there is a possible solution for this case.
     
  8. Apr 29, 2016 #7
    what do you mean ?
     
  9. Apr 29, 2016 #8
    This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
     
  10. Apr 29, 2016 #9
    IMO , that is not feasible , since i was told that water can only flow in 1 direction
     
  11. Apr 29, 2016 #10
    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?
     
  12. Apr 29, 2016 #11
  13. Apr 29, 2016 #12
    so , the statement of water can only flowing in 1 direction is incorrect ?
     
  14. Apr 29, 2016 #13
    anyone can clarify ?
     
  15. Apr 30, 2016 #14
    how to know that if the equations have solutions ?
     
  16. Apr 30, 2016 #15
    What direction would it be if D1 were equal to zero?
     
  17. Apr 30, 2016 #16
    Solve them and see if the solution is real or complex.
     
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