Blood flow, atherosclerosis

[arc5005]

When blood flows through an artery, it exerts pressure on the surrounding arterial wall. Compared to a section of healthy artery of equal size, a narrowed section of diseased artery experiences a pressure on the surrounding arterial wall that is:

A. greater, because the flow velocity decreases.
B. greater, because the flow velocity increases.
C. smaller, because the flow velocity decreases.
D. smaller, because the flow velocity increases.



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D) smaller, because the flow velocity increases.

This is a qualitative type of question, and you have two concepts to consider: the local pressure and the blood flow velocity. Consider first the concept you understand the best. For example, will blood-flow speed increase or decrease when blood traverses a narrow region of an artery? It should flow faster (from the cintinuity equation). This rules out choices A & C. Next, will the pressure increase or decrease when the blood velocity increases? It should decrease (from Bernoulli's equation). These two equations are the most important flow equations.

You may have incorrectly assumed that the pressure should increase because of the "high blood pressure" associated with atherosclerosis. The heart of one afflicted with atherosclerosis pumps with a greater pressure to keep the blood volumetric flow rate at healthy levels, increasing the total pressure throughout the arteries. However, the pressure is lower in an unhealthy section of an artery than it is in a nearby healthy section because of the increased flow speed. This comparison was the thrust of this question. As an aside, the lower pressure in the narrowing artery can be low enough to do more than offset the increased pumping pressure of the heart, making the arterial pressure lower than that in a healthy individual's artery.


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Could someone help me understand this part: Next, will the pressure increase or decrease when the blood velocity increases? It should decrease (from Bernoulli's equation).

Can anyone show me how to derive this from the equation, please?

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[AdaptPrep]

Could someone help me understand this part: Next, will the pressure increase or decrease when the blood velocity increases? It should decrease (from Bernoulli's equation).
Can anyone show me how to derive this from the equation, please?

Hi, arc5005.

As you know, Bernoulli's Equation is:
P1 + (1/2)(rho)(v1^2) + (rho)(g)(h1) = P2 + (1/2)(rho)(v2^2) + (rho)(g)(h2)
where rho is density of blood

The (rho)(g)(h1) and (rho)(g)(h2) terms can cancel out since they are not changing (same height).

This leaves:
P1 + (1/2)(rho)(v1^2) = P2 + (1/2)(rho)(v2^2)

For me, it helps to remove the (1/2)(rho) from both sides as well since the density is the same and 1/2 is like a constant (mathematically, that is a no-no, but we do not need a value, so it works here):
P1 + v1^2 = P2 + v2^2

Since v2 (velocity of the blood in the narrow portion) is larger due to fluid continuity, what must happen to P2 to keep the right-hand side of the equation equal to the left-hand side of the equation? P2 must decrease.

I hope that helps.

Good luck!