Blood Vessels do they NOT follow Bernoulli's principle?

[lollol]

According to bernoullli, assuming ideal flow, if you increase the area of a tube... vessel in this case, pressure increases as well

however, high blood pressure is caused by constriction of arteries... so is blood flow just not ideal then?

 

[olgranpappy]

must be.

Indeed, as opposed to a perfect fluid in a perfect pipe, it seems that blood will not just flow freely through veins... that's the point of your heart; you need something to push the blood.

Tho, I'd like to hear someone else's opinion on this as well.

 

[russ_watters]

According to bernoullli, assuming ideal flow, if you increase the area of a tube... vessel in this case, pressure increases as well

however, high blood pressure is caused by constriction of arteries... so is blood flow just not ideal then?

You are mixing up two different issues there. The venturi effect holds for constant flow along a streamline, the total pressure is constant. But if you take a pipe with a certain flow and add a restriction to it, you will need to increase the pressure to generate the same flow.

 

[FredGarvin]

Like Russ mentioned...at the point of restriction, the pressure will be lower. However, go upstream of that restriction and you will find the increased backpressure the system needs to maintain the same flowrate.

 

[lollol]

Can you guys look at this question... I'm told not to mix Bernoulli with blood pressure blood vessels... but:

From Berkeley Review Physics:

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:

A) smaller pressure on the surrounding arterial wall, b/c the flow velocity increases

B) greater pressure on the surrounding arterial wall, b/c the flow velocity increases

Answer: A) Explanation is... "will the pressure increase or decrease when the blood velocity increases? it should decrease (from bernoulli's equation)".

To use or not to use Bernoulli on blood vessel questions... that is the question

 

[russ_watters]

We didn't say not to mix Bernoulli with blood vessel pressure. What we're saying is that you are just applying it incorrectly. So let me try again:

Bernoulli's principle states that the total pressure along a streamline is constant. That means that neglecting friction, if blood flows through a restriction, its pressure inside the restriction will be lower than just before or after the restriction.

But this does not imply that adding a restriction to a blood vessel will reduce the pressure in it. Adding a restriction causes the overall pressure loss in the vessel to increase, which causes the heart to have to apply more pressure to keep the flow constant.

Consider a valve in a pipe loop with a pump. With the valve all the way open, the pressure on either side of the valve is roughly the same as the pressure inside the valve. If you close the valve halfway, the velocity inside the valve is greater than on either side, so the pressure is lower inside than on either side of the valve. But closing the valve also adds a restriction to the flow, which increases the pressure upstream of the valve and reduces the flow of the system. You can use Bernoulli's equation to calculate the new flow based on the new pressure by comparing the new streamline (total pressure) to the old streamline.

Your heart works exactly the same way.

 

[lollol]

I see what you're saying...

so you're saying... DETERMINE whether the blood pressure is a "response" or not.

If it is not a response, a narrowing of the blood vessel actually causes a decrease in pressure immediately.

But because of the heart, to maintain flow, pressure will be increased.

So in problem I posted above, we were supposed to assume the immediate effect of a blood vessel size decrease... and not what the response was?

 

[denverdoc]

That would be my take--it is a crummy question that can actually get a more thoughtful testtaker in trouble, on account of the rise seen in blood pressure when vessels constrict.
To use an electrcal circuit analogy, the cardiovascular systen tries to maintain constant current--cardiac output in other words and so if resistance rises, so too will pressure. But in this case the question seems to focus on purely hemodynamic pronciples in an isolated artery.

 

[Doc Al]

I see what you're saying...

so you're saying... DETERMINE whether the blood pressure is a "response" or not.

If it is not a response, a narrowing of the blood vessel actually causes a decrease in pressure immediately.

But because of the heart, to maintain flow, pressure will be increased.

So in problem I posted above, we were supposed to assume the immediate effect of a blood vessel size decrease... and not what the response was?

I don't see this as having anything to do with "immediate effect" or "response".

They just want you to apply Bernoulli to the assumed streamline flow through an artery (as Russ explained). If some segment is narrower for any reason, you can deduce that the static pressure in that segment is less compared to the pressure in a non-narrowed segment of the same streamline flow. (This does not mean that narrowing a blood vessel decreases blood pressure! You are not doing a "before and after" comparison. Nor are you comparing clean arteries to clogged ones.)


They are just asking a simple physics question, not the more interesting (and important) question of "What happens to blood pressure when arteries narrow?". (I agree with denverdoc that the question can be misleading if you think too much.)

 

[Dale]

According to bernoullli, assuming ideal flow, if you increase the area of a tube... vessel in this case, pressure increases as well

however, high blood pressure is caused by constriction of arteries... so is blood flow just not ideal then?

There is nothing magical about blood. Blood flow does indeed follow Bernoulli's principles in the larger vessels*. An aneurysm (http://en.wikipedia.org/wiki/Aneurysm) is a dangerous vascular malformation precisely because the cross sectional area of the vessel increases, the pressure increases, and the risk of rupture increases.

Chronic hypertension has many causes and the constriction of arteries is a relatively small long-term effect. In fact chronic hypertension is generally more related to kidneys than the blood vessels. The constriction of arteries has a dramatic short-term effect on blood pressure by changing the total volume of the vasculature. This is used by the body to maintain core blood flow and pressure when in a state of shock after significant blood loss.

*EDIT: in cappillaries, where the size of the blood cells is large relative to the vessel, blood flow cannot really be analyzed quite the same way since it is no longer a homogenous fluid with a single viscosity. As long as the size of the cells is small compared to the diameter of the vessel Bernoulli holds.

 

[Doc Al]

Great example, DaleSpam!

 

[FredGarvin]

Good thing you threw in the edit at the end. Very small blood vessels are a tough thing for people to model because blood is very non-Newtonian.

 

[russ_watters]

You are not doing a "before and after" comparison. Nor are you comparing clean arteries to clogged ones.

That, I think, is the best way to make the point: Bernoulli's principle itself is not a "before and after" comparison, it is a description of the flow in a pipe at one point in time. You can use the implications of that principle to make predictions about different scenarios (such as adding restrictions to a pipe), but that is more complicated than looking at the scenario described in Bernoulli's principle itself.

 

[denverdoc]

There is nothing magical about blood. Blood flow does indeed follow Bernoulli's principles in the larger vessels*. An aneurysm (http://en.wikipedia.org/wiki/Aneurysm) is a dangerous vascular malformation precisely because the cross sectional area of the vessel increases, the pressure increases, and the risk of rupture increases.

Chronic hypertension has many causes and the constriction of arteries is a relatively small long-term effect. In fact chronic hypertension is generally more related to kidneys than the blood vessels. The constriction of arteries has a dramatic short-term effect on blood pressure by changing the total volume of the vasculature. This is used by the body to maintain core blood flow and pressure when in a state of shock after significant blood loss.

*EDIT: in cappillaries, where the size of the blood cells is large relative to the vessel, blood flow cannot really be analyzed quite the same way since it is no longer a homogenous fluid with a single viscosity. As long as the size of the cells is small compared to the diameter of the vessel Bernoulli holds.

The piece neglected so far is the compliance of the vessels and the effect of LaPlaces law-T=P*R When a vessel begins to balloon the increasing radius, pressure and thinning of muscle leads to a rupture, not some increase in pressure alone based on Bernoulli's.

 

[Q_Goest]

Hi lollol,
I don’t disagree with anything here, but it all has to be taken in context with some understanding of Bernoulli’s and frictional flow losses which I don’t see anyone mentioning.

Bernoulli’s is only an idealized equation which doesn’t account for frictional flow losses. If you apply Bernoulli’s to a system such as arteries where the blood is going around in a circular route, there would be no need for a heart to pump the blood – the blood would just continue flowing by itself. Needless to say, something’s wrong with an equation that predicts perpetual motion.

According to bernoullli, assuming ideal flow, if you increase the area of a tube... vessel in this case, pressure increases as well

Note that this assumes:
1. The static pressure (sometimes called stagnation pressure) and velocity (or flow rate) at some location is constant between the two cases being compared.
2. The flow then enters a section of the arteries where the cross sectional area increases. Bernoulli’s alone would predict an increase in static wall pressure for the larger cross section. (This is not entirely true - see assumption 3.)
3. No frictional losses (ie: permanent pressure loss as predicted for example by the Darcy-Weisbach equation).

In a real blood vessel, or any pipe, assumption 1 is questionable as it depends on the entire system. If a restriction in the system is changed, then because there are other real considerations that go beyond what Bernoulli predicts, the system flow rate and pressure at any point can vary between the two cases. This is true for a variety of reasons. Note that assumption 3 is simply not true regardless and this is one source of error. Also, the heart, like many pump designs, will have some kind of variation with flow depending on the pressure difference between the inlet of the heart (pump) and outlet. This is what Russ is talking about when he says that Bernoulli’s is not a before and after comparison.

The pressure between the inlet and outlet of the heart can be increased by real restrictions throughout the system of arteries and blood vessels. But note here that Bernoulli’s equation alone doesn’t account for any permanent pressure drop. Bernoulli’s alone would say that, if the flow area of the artery going into the heart is the same as the flow area of the artery coming out of the heart, the pressure at those two locations will be the same. Reality simply isn’t like that.

Restrictions in the blood vessels due to clogging of arteries for example, increases the overall resistance to flow. In the real case which isn’t predicted by Bernoulli’s, this restriction to flow means that if the heart is to maintain a constant flow, the pressure the heart must generate will be higher when there is more resistance to flow.

Bernoulli’s isn’t wrong, it just doesn’t account for permanent pressure losses in any fluid system. Sometimes, neglecting this pressure loss is acceptable and leads to fairly accurate results, such as flow through a converging/diverging nozzle. Other times, neglecting permanent pressure losses leads to a total misunderstanding of what is happening as in the case of flow through a network of pipes or arteries. If you want to correctly model nature, you also need to take into account any permanent pressure losses in such a system. These permanent losses aren't predicted by Bernoulli's.

 

[croghan27]

snip
*EDIT: in cappillaries, where the size of the blood cells is large relative to the vessel, blood flow cannot really be analyzed quite the same way since it is no longer a homogenous fluid with a single viscosity. As long as the size of the cells is small compared to the diameter of the vessel Bernoulli holds.

Does this hold true for a slurry, a mixture of a fluid and a solid? Is there something like a partial pressure that operates in a lumpy mixture -

* I know partial pressure refers to pressure in constitutent gases - but the solids in a slurry must influence the Bernoulli actions (is that proper?) of that slurry somehow. My experience is with a coke slurry in oil refineries, but it should work with porridge or the situation discussed here with the blood, just as well.

 

[Dale]

On the capillary or even the arteriole scale that is a good description of blood, as a slurry.

I don't know of any variant of Bernoulli's principle that would work for a slurry. The problem with trying to derive such an equation is that the solid chunks interrupt the streamlines and so the basic assumption of the principle is questionable.