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Homework Help: Pressure difference between aorta and aneurysm

  1. Jan 28, 2009 #1
    1. The problem statement, all variables and given/known data
    In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.0cm) enters an aneurysm with a radius of 3.0cm, how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta? The average flow rate through the aorta is 120cm³/s. Assume the blood is nonviscous and the patient is lying down so there is no change in height.

    2. Relevant equations
    Bernoulli's Principle?

    P1 + 1/2pv1² = P2 + 1/2pv2² where:
    P1 = pressure in the aorta?
    P2 = pressure in the aneurysm?
    p = density of blood
    v1 = initial velocity
    v2 = final velocity

    v = flowrate/pi*r²

    3. The attempt at a solution

    Calculated the initial velocity to be 38.19718634cm/s

    So, using Bernoulli's Principle:

    P1 + 1/2pv1² = P2 + 1/2pv2²

    I changed it around a bit:
    P1 - P2 = 1/2pv2² - 1/2pv1²
    ΔP = 1/2pv2² - 1/2pv1²

    and ended up with:
    ΔP = 1/2p(v2² - v1²)

    But, there is no density for blood given, and I'm unsure what to do about that. Did I make a mistake when I modified the formula?

    I am quite confused now. Do I just make up a value for blood density?
  2. jcsd
  3. Jan 28, 2009 #2
    actually, do the 1/2p cancel each other out?

    1/2pv2²-1/2pv1² => v2²-v1²

  4. Jan 28, 2009 #3


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    Science Advisor
    Homework Helper

    Density of blood is rho = 1060 kg/m^3. The rhos do not cancel out.
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