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Force Analysis: Circular Pipe

  1. Feb 15, 2016 #1
    "Consider a fully developed laminar flow in a circular pipe, perform force analysis on an element of the real fluid."

    I've just started this type of question, and I'm a bit confused about where to go from here:

    I've managed to do a force balance horizontally to show that the partial derivative of pressure with respect to x should be zero (which is obvious anyway?), but I have no idea what to do with the vertical force balance and what the question is really asking me to do.

    Thanks in advance!
  2. jcsd
  3. Feb 15, 2016 #2
    Are you assuming that the pipe is horizontal or vertical?
  4. Feb 19, 2016 #3
    The pipe is horizontal in the diagram, sorry should have mentioned that.
  5. Feb 19, 2016 #4
    Is x the direction along the pipe axis?
  6. Feb 19, 2016 #5
    Yes, along the pipe axis.
  7. Feb 19, 2016 #6
    What was your rationale for saying that the partial derivative of the pressure with respect to x is zero?
  8. Feb 20, 2016 #7
    I did a force balance on the horizontal and it came out with that, which I believe is correct?

    I have no idea about the vertical force balance though.
  9. Feb 20, 2016 #8
    It is not correct. How are you supposed to be doing this: (a) using shell momentum balances or (b) using the Navier Stokes equations?

    What forces are acting horizontally on the fluid, besides the pressures.
  10. Feb 22, 2016 #9
    I haven't heard of either of these methods, and upon looking them up they don't look familiar to me either.

    I forgot about the viscous force acting on the fluid element I think. Would I represent this using Stoke's Law or some other way? If using Stoke's law would the radius be the pipe radius or the fluid element's radius?

  11. Feb 22, 2016 #10
    Are you currently taking a course in Fluid Mechanics? What textbook are you using? Have you ever heard of the book Transport Phenomena by Bird, Stewart, and Lightfoot? Are you familiar with the following concepts: stress tensor, Newton's law of viscosity?

    Stokes Law would not be appropriate for this problem.
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