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Relating portions of Poiseille's Law to concepts of pressure/radius

  1. Jul 7, 2011 #1
    1. The problem statement, all variables and given/known data
    High blood pressure results from constriction of arteries. To maintain a normal flow rate (flux), the heart has to pump harder, thus increasing the blood pressure. Use Poiseille's Law to show that if R0 and P0 are normal value sof the radius and pressure in an artery and the constricted values are R and P, then for the flux to remain constant, P and R are related by the equation

    P/P0 = (R0/R)^4

    Deduce that if the radius of an artery is reduced to three-fourths of its former value, then the pressure is more than tripled.


    2. Relevant equations
    P/P0 = (R0/R)^4

    and what I know of Poiseille's Law

    F = ((pi)(P)(R^4))/((8)(n)(l))

    Where R=volume, P=pressure, l=length of blood vessel, F=flux, and n=viscosity of blood

    3. The attempt at a solution
    Firstly, I've worded and formatted the question exactly as listed. I did this because I'm a little confused at what it's even asking me to do. Does it read like there are two parts; 1) Proving P and R are related by the given equation and 2) deducing the given specific relationship between a change in radius and a change in volume?

    I really don't know where to start. I don't want the answer given to me but any hints on how to get started and what they're really asking me for would be greatly appreciated.
     
  2. jcsd
  3. Jul 7, 2011 #2

    lanedance

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    so the initial radius R0 and pressure P0 give a flux F
    [tex] F = \frac{\pi P_0 R_0^4}{8nl} [/tex]

    we assume at a new reduced radius R, we can find a pressure P which gives the same flux F
    [tex] F = \frac{\pi P R^4}{8nl} [/tex]

    now equate the RHS of each and rearrange to get P/P0
     
  4. Jul 7, 2011 #3
    Thank you for your reply Lanedance. The way you worded it makes much more sense. However, I'm not sure what you mean by RHS.

    Two instances of the equivilant of F will result in all known variables to cancel out on both sides leaving the variables we're working with. Now I see how they derive the first equation I listed. Now if I plug in some reasonable values I can solve for the unknown.

    I guess I'm mostly confused because this now seems like a rather simple algebra problem and this is a calculus II class.

    EDIT: Also, would you recommend I place reasonable values for R and P in and solve or should I leave it as is with all the variables?
     
    Last edited: Jul 7, 2011
  5. Jul 7, 2011 #4

    lanedance

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    yeah it looks like algebra mainly to me

    RHS - right hand side

    personally i always prefer to leave the variables in until the last step or as late as possible. I find it more flexible & more audiatble

    the question asks you to subsititute in [itex] R = \frac{3}{4}R_0[/itex]
     
  6. Jul 8, 2011 #5
    Awesome, after inserting the 3/4 and adjusting all to the RHS I essentially came down to 256/81=P/4000 (4000=P0, the value I picked as a common P value; used in a previous example).

    Then I simply said 256/81 > 3 and did a little explaining.

    Thank you for your help!
     
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