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Integration task

  1. Oct 16, 2014 #1
    Hi everyone!
    I would like to ask you for help with one of the tasks from my assignment. The rest of the assignment is done including some simple integration but I struggle with this one:

    Task
    "The total load capacity for a circular hydrostatic bearing is given as

    ##W=\int_0^{R_o} p_r(2πr dr) + \int_{R_o}^R p(2πr dr) ##

    By expressing the radial pressure in terms of the recess pressure, and by step by step argument, show that:

    ##W={\frac{π}{2}}{\frac{R^2-R_o^2}{2ln(R/R_o)}}p_r ## "

    I think that radial pressure in terms of recess pressure is:

    ##p=p_r{\frac{ln(R/r)}{ln(R/R_o)}} ##

    I really cannot get my head around it. Shall I just substitute above equation for 'p'? Then I would get:

    ##W=\int_0^{R_o} p_r(2πr dr) + \int_{R_o}^R{\frac{p_r2πrdrln(R/r)}{ln(R/R_o)}} ##

    Do I have to then sort both integrals and just add them up together?
     
  2. jcsd
  3. Oct 16, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes. That is exactly what the formula says.

    BTW: I think the given answer is too small by a factor of 2.
     
  4. Oct 17, 2014 #3
    Here is first part:

    ##\int_R_o^0 ##
     
  5. Oct 17, 2014 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Are you saying that your equation in the original post is wrong?
     
  6. Oct 17, 2014 #5

    Mark44

    Staff: Mentor

    Is this what you meant to write?
    $$\int_{R_0}^0$$
    The LaTeX script for the above is \int_{R_0}^0. If a limit of integration is more than one character, you need to put it in braces - { }.
     
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