In an aortic aneurysm, a bulge forms where the walls of the aorta are

Question

In an aortic aneurysm, a bulge forms where the walls of the aorta are

weakened. If blood flowing through the aorta (radius 1.0 cm) enters an aneurysm with a radius of 2.5 cm, 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 120 cm3/s. Assume the blood is nonviscous and the patient is lying down so there is no change in height.
A. 150 kPa B. 75Pa C. 75 kPa D. 62 Pa E. 750 Pa

So I thought I was on the right track, I found the area of both the normal blood vessel, and where the aneurysm is using A=pi*r^2 for A1= 3.142 and A2= 19.63, then I used rate flow=A1v1=A2v2 to find the velocity in both. I got v1= 38.20 and v2= 6.116.

I know I should somehow use Bernoulli's equation, or I think I should, but I have no idea what to do now.

Any help would be appreciated!

Thanks

Answer 1

The dimensions of your velocities are cm/s and you have used the continuity equation correctly to get the two velocities.

You are correct that the Bernoulli equation is what you need to compute the pressure difference. It is only valid if viscous effects can be neglected, which is OK over such a short distance. With no difference in height,
(p2 - p1) = (1/2)(density)(V1^2 - V2^2)
Use 1.06 g/cm^3 for the density of blood.

p2 - p1 = (0.5)(1.06)[38.2^2 - 6.1^2] = 746 dyne/cm^2 (round to 750)
= 7.5*10^4 Pa = 75 kPa

That is quite high, about 3/4 atmosphere. No wonder people die of ruptured aneurysyms

Answer 2

.. for showing your own work. We encourage students to do that here, but very few do.

Answer 3

thanks!

but when i checked the conversion online, 750 dyne converts to 75 Pa, not 75kPa, which conversion is correct?

Is there a reason you have a different conversion, that I'm not seeing?

Answer 4

1 Pascal = 1 N/m^2

= 10^5 dyne/10^4 cm^2
= 10 dyne/cm^2

You are quite right. My conversion was wrong.

Answer 5

thank you so much!

Have a good night

Answer 6

You're on the right track! Bernoulli's equation can indeed help you determine the difference in pressure between the normal blood vessel and the aneurysm. Bernoulli's equation relates the pressure, velocity, and height of a fluid at two different points in a system.

The equation is given as:

P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2

Where:
P1 and P2 are the pressures at points 1 and 2,
v1 and v2 are the velocities at points 1 and 2,
ρ is the density of the fluid (blood in this case),
g is the acceleration due to gravity, and
h1 and h2 are the heights at points 1 and 2 (since the patient is lying down, h1 and h2 are equal and can be ignored).

We can assume that the pressures at both points are atmospheric pressure since the question asks for the pressure difference. Therefore, P1 and P2 can be set equal to zero.

Plugging in the known values:
v1 = 38.20 cm/s
v2 = 6.116 cm/s
ρ is the density of blood (approximately 1.06 g/cm³)

Now we can solve for the pressure difference, ΔP:

(1/2)ρv1^2 - (1/2)ρv2^2 = ΔP

Plug in the values and convert units as needed:

(1/2)(1.06 g/cm³)(38.20 cm/s)^2 - (1/2)(1.06 g/cm³)(6.116 cm/s)^2 = ΔP

= (1/2)(1.06 × 10³ kg/m³)(0.3820 m/s)^2 - (1/2)(1.06 × 10³ kg/m³)(0.06116 m/s)^2 = ΔP

Now, calculate this expression to get the pressure difference ΔP in Pascals (Pa). You can use a calculator for this step.

Once you have ΔP in Pa, you can convert it to kilopascals (kPa) by dividing by 1000.

Finally, compare the calculated ΔP to the answer choices given and choose the option that matches the value.

I hope this step-by-step explanation helps you find the correct answer!