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Pressure along the pipe

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data
    In this notes , i was told that there is an increase in pressure along the inner wall

    2. Relevant equations


    3. The attempt at a solution
    IMO , it should be there is increase in pressure at the outer wall , as we can see , the outer wall is longer , so the water would flow slower, resulting in the increases in pressure , am i right ?
     

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  3. Apr 20, 2016 #2

    BvU

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    If the outer wall is longer, then the stuff has to move faster there, isn't it ?

    Cf river bends: on the outer edge sand is being eroded, on the inner sand is being deposited. That's how you get meandering.
     
  4. Apr 20, 2016 #3
    i still dont understand , can you explain further?
     
  5. Apr 21, 2016 #4

    BvU

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    It's this assumption you want to reconsider.
    I don't know if the context is for laminar flow or for turbulent flow. The latter is easiest to imagine: radial pressure profile flat in the straight sections. To make the longer path for the outer turn the liquid has to flow faster. And on the inside the shorter path necessitates a slower flow. So there is a pressure profile (Bernoulli) in the 45 degree plane (lower right to top left in your picture) : higher pressure on the inside to lower pressure at the outer point. The guide vanes can prevent the liquid from responding to that pressure difference with an outward flow (so in an undesired drection) by 'pushing' it in the right direction (f = dp/dt).
     
  6. Apr 21, 2016 #5
    do you mean if the flow is turbulent , the water at the outer region of pipe(longer) is flowing faster , why is it so ?
     
  7. Apr 21, 2016 #6

    BvU

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    On the lower left of the picture, planes of equal pressure are horizontal. On the right vertical. They have to change orientation but are reluctant to do so (inertia).

    upload_2016-4-21_10-43-4.png

    On the inside, the liquid has to 'brake': it wants to flow faster but is held up. So pressure is rising.
    On the outside the pressure drops to accelerate the liquid.
    Velocity profile follows (Bernoulli)

    I've only drawn a few blue arrows to suggest this.
    In the horizontal direction something similar happens
     
  8. Apr 21, 2016 #7
    whaty do you mean by On the inside, the liquid has to 'brake': it wants to flow faster but is held up.??? how can the liquid be held up ?
     
  9. Apr 21, 2016 #8

    BvU

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    Hehe, you ask good questions. I'll have to look up a few things that I seem to have imagined wrongly... (what I wrote is contradicted by figure 2..., but I do like figure 3, at least if my interpretation is right...)
     
  10. Apr 21, 2016 #9
    ok , let me know if you have found out the new explaination .
     
  11. Apr 22, 2016 #10
    hi , do you have any idea about the question that i asked earlier?
     
  12. Apr 22, 2016 #11

    haruspex

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    I didn't reply to this thread originally because it made no sense to me either. I was hoping someone more expert might explain it. Anyway, here's my inexpert 2c.
    One problem with the "has to go faster" argument is that there is no obvious reason why it has to keep up.
    The referenced text mentions centrifugal forces. The argument from that, surely, is that a net radially inward force must exist, which implies higher pressure on the outside. Since that implies the outside flow would slow down into the bend (relative to the inside flow, at least) it suggests the creation of a counterclockwise eddy.
     
  13. Apr 22, 2016 #12
    so , the notes is wrong ? the pressure at the outer wall should higher than the inner wall ?
     
  14. Apr 22, 2016 #13

    haruspex

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    That's how I see it, but, as I wrote, I do not consider myself expert in hydrodynamics.
     
  15. Apr 22, 2016 #14

    BvU

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    I looked at the link in post #8 with interest, and also at ref.1 therein (*).
    Clearly, even my interpretation of fig. 3 was wrong ands the pressure at outer wall is higher -- and consequently (?) the velocity is lower. So the first paragraph of your notes is disproved and my defence was ill-advised.

    I still think
    that this is not a cause-effect relation, but that's only as a physicist (and obviously I'm not a fluid flow expert :frown:).

    Some aspects of this elbow flow are counter-intuitive, others make sense. Thank you for bringing it up in this critical manner !

    (*)
    I particularly like the (page 14)
    and it would be interesting to check (by calculation or from experiment) the claim in your notes that the insertion of guide vanes eases the situation and reduces the pressure drop. My bet is that it does.
     
  16. Apr 22, 2016 #15

    haruspex

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    This strikes me as essentially the same as the mention of centripetal acceleration in the text cited in the OP. It may be that the claim there that the pressure is therefore greatest on the inside of the bend is simply a typo.
    Again, that is consistent with the centripetal acceleration view. The vanes can supply the centripetal force locally, instead of the entire force having to be transmitted from the outside of the elbow.

    I found the velocity map on page 13 particularly interesting. It shows that the flows follow two counter-rotating helices around the curve.
     
  17. Apr 22, 2016 #16
    Ok, since this is not an cause and effect relationship , why the pressure at the outer wall of pipe is higher?
     
  18. Apr 24, 2016 #17
    can you explain, why the pressure at the outer wall of pipe is higher?
     
  19. Apr 24, 2016 #18

    haruspex

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    Do you understand that a centripetal force is needed to get the flow around the elbow?
     
  20. Apr 24, 2016 #19
    Yes
     
  21. Apr 24, 2016 #20

    haruspex

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    So where will that force come from?
     
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