There are many interesting applications of our energy density model to the flow of blood in the human circulatory system. One interesting phenomenon is an aneurysm, a sudden abnormal enlargement of a section of an artery due to a weakening of the arterial wall. If the blood flow rate remains constant through the artery, how does the pressure in the enlarged section (the aneurysm) compare to the pressure in the rest of the artery? Neglect any affects of resistance to flow in your explanation.

Pressure increases due to enlargement

Explanation:

Energy density is just a fancy name for pressure

Pressure is same at the bottom of the cups (same level-Pascal's law)

thus, Air pressure 1 + h1d1g = Air pressure 2 + h2d1g

= Air pressure 3 + (h2-h1)d2g +h1d1g

from the first 2, we get that since h2>h1, AP2<AP1

from the next 2, we get that since d2<d1, AP3>AP2

from first and third, we get that AP1>AP3

thus, finally AP1>AP3>AP2

for fluids flowing in tubes (blood vessel in this case)

P+0.5dv^2 + gh is constant (also called the bernoulli equation

for the same blood vessel, the heights remain same i.e h1=h2

for same flow rate, inc in area decreases the speed at which the blood flows as vA must remain same

hence, P increases due to enlargement

Pressure in enlarged portion is greater than remaining portion of artery.

Explanation:

The Bernoullis equation at front and back side of arterial wall is given by:

the bal will not change its velocity.