Bernoulli's Principle and Vasodilation/constriction

[SuperSneaky]

So I don't quite understand how Bernoulli's Principle applies to vasculature.

When we vasodilate, we decrease blood pressure. However, according to Bernoulli's, the maximum cross-sectional diameter portion of a pipe experiences the greatest fluid pressure. Can anyone clarify this?

---

Members don't see this ad.

 

[WolfofSDN]

It's hard to apply Bernoulli's principle to the CV system because it is a closed system, which violates the conditions of Bernoulli's principle.

 

[Schenker]

I'll put Bernoulli's principle into words, as it relates to your question.

Bernoulli's equation says that along a single streamline of fluid, as diameter decreases, pressure decreases too.

You seem to be clear on that. Now let's apply it to a section of blood vasculature.

Pick a point in the middle of a vessel; measure the pressure (Pressure1) at that point. Now make the vessel dilate. Then, pick the same point as before and measure the pressure (Pressure2).

Can you use Bernoulli's principle to predict the relationship between Pressure1 and Pressure2? No. Why? Because Pressure1 and Pressure2 don't exist along the same streamline of fluid; though both pressures were measured at the same point in space, the streamline flowing through that point changed over time as the vessel dilated.

In order to use Bernoulli's principle to compare fluid properties at two points in a system, you need to be able to draw a picture of the system as it exists in a single point of time and draw a streamline of water between those two points.

It's hard to apply Bernoulli's principle to the CV system because it is a closed system, which violates the conditions of Bernoulli's principle.

Bernoulli's principle isn't violated by closed systems. You can in fact use it to analyse the cardiovascular system, as long as you are comparing two points along the same streamline. A hypothetical example would be to compare the pressure in an artery that passes into only one arteriole. The arteriole is smaller in diameter than the preceding artery, so pressure will be greater in the artery.

 

[WolfofSDN]

I'll put Bernoulli's principle into words, as it relates to your question.

You seem to be clear on that. Now let's apply it to a section of blood vasculature.

Pick a point in the middle of a vessel; measure the pressure (Pressure1) at that point. Now make the vessel dilate. Then, pick the same point as before and measure the pressure (Pressure2).

Can you use Bernoulli's principle to predict the relationship between Pressure1 and Pressure2? No. Why? Because Pressure1 and Pressure2 don't exist along the same streamline of fluid; though both pressures were measured at the same point in space, the streamline flowing through that point changed over time as the vessel dilated.

In order to use Bernoulli's principle to compare fluid properties at two points in a system, you need to be able to draw a picture of the system as it exists in a single point of time and draw a streamline of water between those two points.



Bernoulli's principle isn't violated by closed systems. You can in fact use it to analyse the cardiovascular system, as long as you are comparing two points along the same streamline. A hypothetical example would be to compare the pressure in an artery that passes into only one arteriole. The arteriole is smaller in diameter than the preceding artery, so pressure will be greater in the artery.

Sorry, I didn't elaborate. By closed system I was implying that energy is not constant.