Pressure difference between aorta and aneurysm

AI Thread Summary
In an aortic aneurysm, a bulge occurs due to weakened aortic walls, leading to a pressure difference between the aorta and the aneurysm. The discussion centers around applying Bernoulli's Principle to calculate this pressure difference, ΔP, using the flow rate and radii of the aorta and aneurysm. The initial velocity of blood flow was calculated to be approximately 38.2 cm/s, but confusion arose regarding the density of blood, which is necessary for the calculations. It was clarified that the density of blood is 1060 kg/m³ and that the density terms do not cancel out in the equation. The key takeaway is that accurate values for density are essential for determining the pressure difference in this scenario.
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Homework Statement


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.

Homework 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

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?
 
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actually, do the 1/2p cancel each other out?1/2pv2²-1/2pv1² => v2²-v1²

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

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