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Proportionality help needed

  1. Sep 14, 2005 #1

    DB

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    proportionality help needed plz

    stuck on a proportionality problem...
    1) the pressure exerted by a fluid in a pipe varies inversely as the sixth power of the diameter. what is the multiplicative change (delta X_m) and percentage change (delta X%) in the pressure is the diameter of the pipe decreases by 20%?
    [tex]p\propto \frac{1}{d^6}[/tex]

    [tex]\frac{p_2}{p_1}=\frac{1}{0.2^6}[/tex]

    [tex]\frac{p_2}{p_1}=15625[/tex]

    therefore

    [tex]\frac{15625}{1}\equiv \frac{1}{0.2^6}[/tex]

    so

    [tex]\Delta X_m=15625[/tex]

    and

    [tex]\Delta X_m -1 = \Delta X_{relative}[/tex]

    and

    [tex]\Delta X_{rel.} * 100 = Delta X_%[/tex]

    so

    [tex]15625-1=15624*100=\Delta X_%[/tex]

    [tex]\Delta X_% = 1.5624 * 10^6[/tex]?
    i must of done something wrong...any help appreciated :smile:
     
  2. jcsd
  3. Sep 14, 2005 #2

    DB

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    if u cant see my last three step i got the percentage change as 1.5624*10^6%
     
  4. Sep 14, 2005 #3

    Doc Al

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    Staff: Mentor

    Recheck this step. When the diameter decreases by 20%: [itex]D_2 = 0.8 D_1[/itex]
     
  5. Sep 14, 2005 #4

    DB

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    thanks doc
    shame on me, stupid mistake, but this seems right, the multiplicative change is 3.18 and the percentage change is 218%. that right?
     
  6. Sep 14, 2005 #5

    Doc Al

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    Staff: Mentor

    Sounds good to me.
     
  7. Sep 14, 2005 #6

    DB

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    thanks doc
     
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