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Fluid mechanics - submerged triangular surfaces

  1. Apr 28, 2012 #1
    Hi, i am having difficulty with a question because i cannot seem to get the right answer. i dont think i am far off i just know i go wrong somwhere and if you could point that out it would be great. the question is attatched. for the first part i find the equations of the lines of the two sides starting from d. then subtract them to find w (=Xright-Xleft). using double integration i find the area by
    A=∫∫dA where limits firstly are X=Xright, X=Xleft and then S=h and S=0. My problem is on part C i cannot get the correct answer which means i have gone somewhere wrong further up, most likely at either the limits im using or for S or finding w. I am meant to use double integration for these questions and Sc=As|o /A and ***|c= ***|o - A*Sc^2.
    Any comments are appreciated, thanks
     

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  2. jcsd
  3. Apr 28, 2012 #2

    tiny-tim

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    Welcome to PF!

    Hi TimIgoe90! Welcome to PF! :smile:
    fine so far :smile:
    yup, your limits can't both be between fixed numbers

    if your S limits are from 0 to h, then your x limits will be functions of S

    (= the left- and right-most coordinates of that strip in the diagram, of height dh :wink:)
     
  4. Apr 28, 2012 #3
    I am sorry not sure i understand. i have found w to be = Xright-Xleft by finding the equation of the lines in terms of S and functions of S. so w= [(b-d)*s/ λh]+[d*s/h]. from my notes i am told that my limits for x should be xleft and xright, which when integrating A=∫∫dA it would give me A=∫wds....what two limits of s would i then need to integrate it? sorry if you already answered but i wasnt sure. thanks
     
  5. Apr 28, 2012 #4

    tiny-tim

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    the limits of S are 0 to h
     
  6. Apr 28, 2012 #5
    thats what i thought it was. but i cannot seem to get the correct answer for part C. im not sure where i am going wrong, my answer is close to the required one, so i dont think i am too far off.
     
  7. Apr 28, 2012 #6

    tiny-tim

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    if you want us to check your work, you'll have to show us :smile:
     
  8. Apr 28, 2012 #7
    That is my working out. Much appreciated
     

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  9. Apr 28, 2012 #8

    tiny-tim

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    it's a little difficult to read, but i think your answer for A is wrong,

    you seem to have lost a 1/λ somewhere :confused:
     
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