# Misunderstanding blood pressure and Bernoulli's equation

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I have a question about something from TBR physics.
There was a question that asked to compare the blood pressure in veins in the neck and calves of someone standing up.
The answer was that the pressure would be greater in the calves, and their reasoning used Bernoulli's equation. The vein in the neck is at a higher value in the y direction, therefore, the pressure here would be lower when compared to the calves, which are at a lower y value.

The equation is: k = P + 0.5(row)v^2 + (row)gy

However, I reasoned that the pressure in the neck would be greater, because the blood would have to work against gravity to reach the neck, while it wouldn't need to do so to reach the calves. Thus, the heart would need to pump harder to get an equivalent volume of blood to the neck, the pressure provided would be higher.

I'm getting a little confused by this, could someone clarify for me? Thanks.

However, I reasoned that the pressure in the neck would be greater, because the blood would have to work against gravity to reach the neck, while it wouldn't need to do so to reach the calves. Thus, the heart would need to pump harder to get an equivalent volume of blood to the neck, the pressure provided would be higher.

I'm getting a little confused by this, could someone clarify for me? Thanks.
First, let's clarify that veins bring blood back toward the heart. Arteries pump blood Away from the heart. So, venous blood coming from the neck is actually heading toward the heart, not away from it (you're thinking of arteries!). The veins in the legs have a larger column of fluid above them and more gravitational pull to fight on their way back toward the heart. Hence, the pressure would be greater in the legs.

Hope this helps!

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This problem assumes that the Bernoulli equation for veins in the calves is equal to the Bernoulli equation for veins in the neck. Thus:

Assuming velocity remains constant in this problem, the only terms that can change are height and pressure (since density and gravity remain constant as well). As height in the neck, h2, is higher than h1, pressure needs to compensate, either by increasing P1 or decreasing P2. Either way, P2 is less than P1, and thus pressure is lower in the neck than in the calves.

In terms of your reasoning, we are assuming that the circulatory system is a closed system and blood is an ideal fluid, so the heart propels blood throughout the entire system, regardless of whether it is moving toward or against gravity. I probably don't have the best biological explanation, however Bernoulli's equation should hold for questions like these.

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This problem assumes that the Bernoulli equation for veins in the calves is equal to the Bernoulli equation for veins in the neck. Thus:
View attachment 287963
Assuming velocity remains constant in this problem, the only terms that can change are height and pressure (since density and gravity remain constant as well). As height in the neck, h2, is higher than h1, pressure needs to compensate, either by increasing P1 or decreasing P2. Either way, P2 is less than P1, and thus pressure is lower in the neck than in the calves.

In terms of your reasoning, we are assuming that the circulatory system is a closed system and blood is an ideal fluid, so the heart propels blood throughout the entire system, regardless of whether it is moving toward or against gravity. I probably don't have the best biological explanation, however Bernoulli's equation should hold for questions like these.

Thanks for the response. So what you mean by "assuming that the circulatory is a closed system" is that forces are conserved, and thus, there are no external forces acting on the system (IE, gravity)?

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First, let's clarify that veins bring blood back toward the heart. Arteries pump blood Away from the heart. So, venous blood coming from the neck is actually heading toward the heart, not away from it (you're thinking of arteries!). The veins in the legs have a larger column of fluid above them and more gravitational pull to fight on their way back toward the heart. Hence, the pressure would be greater in the legs.

Hope this helps!

ah whoops, that totally makes sense. Don't even need to consider Bernoulli's equation then in this case.

Thanks for the response. So what you mean by "assuming that the circulatory is a closed system" is that forces are conserved, and thus, there are no external forces acting on the system (IE, gravity)?

Gravity is still at play, so what I mean is that both the fluid moving upward at one side of the system and the fluid moving downward at the other side of the system are both being affected by gravity.

It would initially appear that the heart must pump to overcome a height difference of when moving upward, however, due to gravitational effects, this isn’t the case, as for every unit of fluid pumped vertically upwards, a corresponding unit of fluid drops on the return side of the system.

Basically I am trying to illustrate that gravity is still present obviously, but it shouldn't influence the other variables of the system.

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I believe the answer would be the same even if it were talking about arteries. Stick with Bernoulli on this one, as it can be thought of as a hydraulics problem.