Difficult time understanding Pressure in blood vessels vs physics/chem

[arc5005]

SO I thought I had this down, and then this question came up:

The lowest blood pressure would be in which of the following:

1) Heart
2) Arteries
3) Capillaries
4) Arterioles

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Intuitively, I'm like ohhhh, okay it's definitely capillaries. Then, I second guess myself and I'm like oh wait, based on Bernoulli's principle -- if the speed is higher, then that means pressure is lower. And then I'm here thinking in my head, well the blood is moving faster in the arteries for sure, like right? Then I'm like, oh well since blood flow is like much slower in the capillaries than the arteries, then that means the arteries have a lower pressure, because the velocity is faster... and there I am in a loop of confusion, unsure whether pressure is higher in the arteries or in the capillaries.

Is there a better way to get this concept nailed down -- So I don't confuse this? Because based on Bernoulli's principle, smaller diameter = higher velocity = lower pressure, while larger diameter = lower velocity = higher pressure --> which applying that concept, arteries are thicker, so they have a higher pressure... but they don't have a lower velocity, so is this due to internal resistance? Do I then need to somehow look at this in regards to Pousille's Law?

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[Lawpy]

It’s important to realize Bernoulli’s equation works in very specific and ideal circumstances. The equation has a lot of important assumptions and works well in theory because energy isn’t conserved in reality due to the presence of frictional forces.

When we try to use Bernoulli’s equation to describe blood flow, it helps to restrict focus only on one vessel and ignore other contributing factors. Unfortunately, for this problem, there are a lot of factors in play that complicates the use of Bernoulli’s equation. In fact, take a look at this chart:

There isn’t a clean relationship between blood velocity and blood pressure like you might expect from using Bernoulli’s equation. That’s because there are external forces present in the system. The heart provides a strong external force and contributes to the aorta and arteries being a high pressure, high flow rate and high velocity system. Blood vessels also contribute frictional forces to resist blood flow.

Capillaries are tiny but there are a lot of them and they are arranged in parallel. If we think of capillaries to be like resistors in parallel, the total resistance in capillaries decreases. The blood flow rate also decreases due to increased total cross sectional area (which also results in decreased velocity). And because blood pressure = flow rate * resistance, blood pressure in capillaries also decreases.

I would think of blood pressure as the force per area needed to stop the blood from going forward. And the pressure term in Bernoulli’s equation as the pressure exerted by the blood on the walls of a blood vessel. These two pressures are related but the relationship isn’t clean when there are multiple vessels.

It helps to use Bernoulli’s equation for a single blood vessel to help understand what’s going on.

How does Bernoulli’s Principle apply to the cardiovascular system?

 

[Lawpy]

Here is another explanation from an old discussion: Blood flow, pressure, & Bernoulli's

Also, Poiseuille’s law can generally be applied to understand blood flow since it works for nonideal fluids, such as blood. Continuity equation and pressure = flow * resistance can also be used. Things become complicated and risk oversimplification when you’re using an ideal and restricted model like Bernoulli’s equation to discuss a complicated realistic scenario such as blood circulation.

 

[arc5005]

Here is another explanation from an old discussion: Blood flow, pressure, & Bernoulli's

Also, Poiseuille’s law can generally be applied to understand blood flow since it works for nonideal fluids, such as blood. Continuity equation and pressure = flow * resistance can also be used. Things become complicated and risk oversimplification when you’re using an ideal and restricted model like Bernoulli’s equation to discuss a complicated realistic scenario such as blood circulation.

thank you so much

 

[whitecoater]

If one capillary receives blood from exactly one artery, the hydrostatic pressure exerted on the wall of this capillary will be lower due to Bernoulli's Principle.

If there are more than one capillaries receiving blood from the same one artery, the hydrostatic pressure exerted on each wall of individual capillaries will be lower due to larger area impacted by the same force (think same amount of blood from one balloon is now divided into more than one balloon, yielding less pressure per balloon as per LaPlace's Law). In addition, lower oncotic pressure and more vessel wall elasticity (or less resistance, as per Poiseuille's Law) capillaries vs those at arteries, will lower the pressure even more.