Pressure difference between aorta and aneurysm

In summary, the conversation discusses an aortic aneurysm and how it affects blood pressure. Using Bernoulli's Principle, the difference in pressure between the aorta and the aneurysm can be calculated by subtracting the initial and final velocities. However, since the density of blood is not given, the value of 1/2p cannot be calculated. The density of blood is 1060 kg/m^3 and cannot be cancelled out in the equation.
  • #1
dcramps
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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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  • #2
actually, do the 1/2p cancel each other out?1/2pv2²-1/2pv1² => v2²-v1²

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

1. What is the normal pressure difference between the aorta and aneurysm?

The normal pressure difference between the aorta and aneurysm varies depending on the individual and their health. Generally, the pressure in the aorta is around 120/80 mmHg, while an aneurysm may have a lower pressure due to the weakening of the artery walls. It is important to monitor and manage this pressure difference to avoid complications.

2. How does the pressure difference affect the risk of aneurysm rupture?

A higher pressure difference between the aorta and aneurysm can increase the risk of aneurysm rupture. This is because the aneurysm is already weakened and a higher pressure can put more stress on the artery walls, causing it to burst. It is important to keep the pressure difference under control to prevent such complications.

3. Can the pressure difference between the aorta and aneurysm be measured?

Yes, the pressure difference between the aorta and aneurysm can be measured using various imaging techniques such as ultrasound, CT scans, or MRI. These tests can also help in monitoring the pressure difference over time and detecting any changes or abnormalities.

4. What are the symptoms of a high pressure difference between the aorta and aneurysm?

Some common symptoms of a high pressure difference between the aorta and aneurysm include chest or back pain, shortness of breath, dizziness, and a pulsating feeling in the abdomen. However, in some cases, there may be no symptoms at all, making regular check-ups and monitoring even more important.

5. How can the pressure difference between the aorta and aneurysm be managed?

The pressure difference between the aorta and aneurysm can be managed through lifestyle changes such as maintaining a healthy blood pressure, quitting smoking, and exercising regularly. In some cases, medication or surgery may be necessary to control the pressure difference and prevent complications.

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