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Math Help - Poiseuille's Law

  1. #1
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    Poiseuille's Law

    R sub 0 - normal radius

    P sub 0 - normal pressure

    R and P are the constricted values.

    Use Poiseuille's Law:
    F(flux- rate of blood past a given point) = (1/8) (pi PR^4/nl)
    to show that P and R are related by the equation:

    (P/Po) = (Ro/R)^4

    note: Deduce that if the radius of an artery is reduced to 3/4 of it's former value, then the pressure is more than tripled.

    I don't even know where to begin with this problem. Like, I can't even get started. What should I do? Help please!
    Last edited by smray7; April 2nd 2011 at 08:28 AM. Reason: correct equation
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  2. #2
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    Quote Originally Posted by smray7 View Post
    R sub 0 - normal radius

    P sub 0 - normal pressure

    R and P are the constricted values.

    Use Poiseuille's Law:
    F(flux- rate of blood past a given point) = (1/8) (pi PR^4/nl)
    to show that P and R are related by the equation:

    (P/Po) = (Ro/R)^4

    note: Deduce that if the radius of an artery is reduced to 3/4 of it's former value, then the pressure is more than tripled.

    I don't even know where to begin with this problem. Like, I can't even get started. What should I do? Help please!
    The question is a little hard to read but I think this is what you are looking for

    \displaystyle F(R,P)=\left( \frac{1}{8}\pi P R^4 \right)

    Now \displaystyle F(R_0,P_0)=\left( \frac{1}{8}\pi P_0 R_0^4 \right)

    and

    \displaystyle F\left( \frac{3}{4}R_0,P\right)=\left( \frac{1}{8}\pi P_0\left( \frac{3}{4}R_0 \right)^4\right)=\left( \frac{1}{8}\pi P_0 \frac{81}{256}R_0^4 \right)

    Now if we take their ratio we get

    \displaystyle \frac{F(R_0,P_0)}{F\left( \frac{3}{4}R_0,P\right)}=\frac{256}{81}> 3
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  3. #3
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    I don't understand how all the work you showed me proves P/Po = (Ro/R)^4.
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by smray7 View Post
    I don't understand how all the work you showed me proves P/Po = (Ro/R)^4.
    What have your tried?

    2nd Hint your are assuming the Volume of blood flowing is constant.

    The volume of blood transported is

    \displaystyle F(R,P)=V=F(R_0,P_0)
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