Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Is the author integrating constants?

  1. Jul 28, 2016 #1
    Dear Sirs,

    I am currently calculating a velocity profile of an annular flow. Unfortunatelly I am not understanding the following step:

    http://[url=https://postimg.org/image/vl256ffhj/][ATTACH=full]200119[/ATTACH]

    That seems the author had integrated the R constant. And remains the question: why had R been realocated into the ln´s parenthesys?

    Thanks,
    Peter
     
    Last edited by a moderator: May 8, 2017
  2. jcsd
  3. Jul 28, 2016 #2

    marcusl

    User Avatar
    Science Advisor
    Gold Member

    The first term R*r/R is obvious so I assume that your question regards the second term. Make a change of variables u = r/R, so that dr = R du. This R is pulled out in front making R^2, while int{du/u} becomes ln(u) = ln(r/R). There's no integration of constants.
     
  4. Jul 29, 2016 #3

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    No, he integrates rightly over ##r##. How do you come to a different conclusion. Note that
    $$\frac{\mathrm{d}}{\mathrm{d} r} \ln(r/R)=\frac{1}{r}$$.
    Rightly he avoids a dimensionful logarithm by introducing an arbitrary constant. You need initial/boundary conditions anyway to fix the integration constant ##C_2##. So that's the correct general solution of the ODE (2.4-5).
     
  5. Jul 29, 2016 #4

    Ssnow

    User Avatar
    Gold Member

    Hi, before the integration you can multiply and divide by ##R##, one of this remain outside the parentesis so the ##R^2##, after observe that ##\frac{1}{R}\left(\frac{R}{r}\right)## is ##\frac{d}{dr}\ln{\frac{r}{R}}##. Yes, here ##R## is trated as constant and ##C_{2}## is the constant of integration that remains multiplied by the constant term in front of the bracket.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Is the author integrating constants?
  1. Integration constant (Replies: 6)

Loading...