Question

1. An aortic aneurysm exists as a bulging out of the aorta walls, where the aorta walls are actually more elastic than normal aorta walls, and deform more in response to the blood pressure in the aorta. If the radius of the aorta is typically 1 cm and the blood flow rate is 100 cm^3 s^-1 , how much would the pressure increase in the aortic aneurysm if the radius of the aneurysm is 3 cm? Assume that the blood vessel is horizontal and ignore the viscous nature of blood

Answer 1

You need to use Poiseuille's law to figure it out:

If you think about it logically, if the flow remains constant and the radius increases, the pressure must decrease.

Poiseuille's law has too many Greek characters for me to type it here (check the link above), but it states that the flow equals pi times the radius of the tube to the fourth power times the pressure, divided by (8 times the viscosity times the length of the tube).

If flow and viscosity remain constant for a given length of aorta, then the pressure will decrease by the difference in the radius to the fourth power.

1^4 = 1
3 ^4 = about 81

So, the pressure in the aneurysm will be about 1/81th that in the aorta, IF the flow remains constant.

I think in real life, the flow decreases and the pressure remains more constant, though. Otherwise, the flow of blood would stop.

See, kids, THIS is why we take physics before going to medical school. There are actually real life applications in the medical world for this stuff.