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Velocity distribution of a newtonian fluid in a circular pipe using finite difference

  1. Sep 7, 2011 #1
    I am to find the velocity distribution where there is non steady flow of a Newtonian fluid in a circular pipe. I did a mass and momentum balance around the system and ended up with the following equation:
    dp/ds = 4 + 1/e*d/de(e*dp/de)

    The derivatives in the equation are partial derivatives

    the values of p,s,e are dimensionless numbers.

    I am to assume that the solution is separable and then use finite difference method to solve for p. This is where i am having problems. What will the equation be after the assumption is made and the equation is simplified.

    I have attempted the question:

    I equated the right hand side = 0:

    4 + 1/e*d/de(e*dp/de) = 0

    and made the partial derivatives total derivatives and then applied the chain rule:

    4 + 1/e*dp/de + d/de(dp/de). Is this correct????????
     
  2. jcsd
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