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Thread: Homer's Blood Pressure problem

  1. #1

    Homer's Blood Pressure problem

    I need help with approaching this huge word problem!

    Homer's blood pressure


    The volume of blood that passes through a cross-section of an artery (of radius R, with pressure difference P) per unit time is given by the formula

    ( is the length of the artery and is viscosity of the blood - both are assumed constant). F is often called the flux. High blood pressure results from constriction of the arteries. As the radius of the arteries shrinks, the blood pressure needs to increase to maintain a constant flux. Suppose and are the initial radius and the initial pressure. Then the flux is . If the pressure and radius at some other time are P and R, then the flux is . Using the fact that flux must remain constant, determine an expression for P in terms of R, , and . As the years go by, the diameter of Homer's arteries is given by , where t is the number of years from the present.
    1. What is Homer's blood pressure in terms of his original blood pressure 10 years from now?
    2. Homer's doctor would like to perform angioplasty to enlarge the arteries when his blood pressure has doubled. When will this happen?

  2. #2
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    Quote Originally Posted by AquaMan View Post
    I need help with approaching this huge word problem!

    Homer's blood pressure


    The volume of blood that passes through a cross-section of an artery (of radius R, with pressure difference P) per unit time is given by the formula

    ( is the length of the artery and is viscosity of the blood - both are assumed constant). F is often called the flux. High blood pressure results from constriction of the arteries. As the radius of the arteries shrinks, the blood pressure needs to increase to maintain a constant flux. Suppose and are the initial radius and the initial pressure. Then the flux is . If the pressure and radius at some other time are P and R, then the flux is . Using the fact that flux must remain constant, determine an expression for P in terms of R, , and . As the years go by, the diameter of Homer's arteries is given by , where t is the number of years from the present.
    1. What is Homer's blood pressure in terms of his original blood pressure 10 years from now?
    2. Homer's doctor would like to perform angioplasty to enlarge the arteries when his blood pressure has doubled. When will this happen?
    What are your thoughts?

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  3. #3
    My thought for the first part is to solve the F= equation for P(pressure difference).

  4. #4
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    Quote Originally Posted by AquaMan View Post
    My thought for the first part is to solve the F= equation for P(pressure difference).
    It is given to you:

    [tex]F \ = \ \dfrac{\pi*P*r^4}{8\eta * l}[/tex]

    Where are you stuck?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  5. #5
    Quote Originally Posted by Subhotosh Khan View Post
    It is given to you:

    [tex]F \ = \ \dfrac{\pi*P*r^4}{8\eta * l}[/tex]

    Where are you stuck?



    So once I solve that and get it to be P=something

    then where do I go from here?

  6. #6
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    Quote Originally Posted by AquaMan View Post
    So once I solve that and get it to be P=something

    then where do I go from here?
    No!

    Read the question carefully. F is constant over time - R is function of time. That makes P a function of time.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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