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# Blood flow, pressure, & Bernoulli's

Discussion in 'MCAT Study Question Q&A' started by unsung, May 25, 2008.

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1. ### unsungEstablished Member

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Help me out here. I'm getting confused between osmotic pressure and hydrostatic pressure in capillaries. What's the difference between the two, exactly? Isn't hydrostatic pressure just pressure at a given depth in a static liquid?

Also, EK says that blood flow does not follow Bernoulli's equation (which says pressure is inversely proportional to cross-sectional area)... but I don't see why it doesn't.

Thanks!
2. ### rocuroniumEstablished Member

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In a capillary, the hydrostatic pressure is the pressure that the blood exerts on the capillary walls. This is in the outward direction.

The osmotic pressure is due to the difference in solute concentrations on either side of the capillary wall. This tends to draw fluids inward.

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Very simply, hydrostatic pressure is the pressure of blood against the vessel wall during blood flow. This force causes blood to seep out of the vessel.

I don't have EK, but blood flow in the cardiovascular system definitely does not follow bernoulli's equation.

I won't go into the math of it or an in depth explanation of Bernoulli's equation because it's not MCAT relevant. Therefore, some of the things I will say are gross oversimplifications but do lend a superficial understanding of how this concept applies to the cardiovascular system. Bernoulli's principle basically states that when the velocity of of a fluid through a tube increases, the pressure (more specifically, what is known as the fluid's 'gravitational potential energy') decreases. That is pressure and kinetic energy are 'traded' for one another in an ideal fluid flow system. This is essentially a type of conservation of energy.

Picture the following situation:
You have a tube that abruptly changes radius from a large radius to a small radius and an ideal fluid is flowing from the large radius section to the small radius section. In this situation, the fluid pressure of the fluid in the large radius part of the tube is actually greater than the pressure in the small radius part of the tube. In addition, note that the fluid velocity is higher in the small part of the tube than the large part of the tube.
Bernoulli's principle is basically saying that as a fluid's velocity goes up, it's fluid pressure must go down, and as it's velocity goes down, it's fluid pressure must go up. In essence, this is a form of conservation of energy; the increase in kinetic energy of the fluid going from the large part of the tube to the small part of the tube occurs at the expense of a drop in fluid pressure.

**EDIT: Wikipedia actually explains this decently well. It's a little too in depth for the MCAT, but here ya go: http://en.wikipedia.org/wiki/Bernoulli%27s_principle ** (See Diagram)

Okay so realizing that fact, now think about what is observed to happen in the blood vessels.

As you go from the aorta to the capillaries, The cross-sectional area of the sum of the tubes increases.
1) That is, the cross-sectional area of the capillaries summed together is far greater than the cross-sectional area of the aorta.
2) Also remember that fluid velocity is higher in the aorta than in the capillaries.
3) In addition, blood pressure is observed to decrease from the aorta to the capillaries. That is, pressure decreases as you move toward the veins.

But wait a minute...didn't we just say that Bernoulli's principle states that if the velocity of a fluid were to decrease, that there must be a concurrent increase in the pressure of the fluid? Doesn't that imply that pressure should increase as we move from the aorta (small cross-sectional area) to the capillaries (large cross-sectional area)? Yes, that is Bernoulli's principle. Hmmm...so what's wrong? This means that Bernoulli's principle is not satisfied by the circulatory system!! But why?

It should be noted that Bernoulli's principle only really applies under some very ideal conditions: Non-turbulent flow, laminar flow, incompressible fluids and low mach numbers. The cardiovascular system does not satisfy those requirements save low mach numbers and incompressibility (and even incompressibility is not satisfied at the level of the capillaries for reasons explained below.)

Now if you were talking flow JUST in a large single tube artery, then you could make an approximation with Bernoulli's equation. The cardiovascular system, however is not a laminar flow system, but rather a pulsatile flow system (think beating heart), it also has many imperfect bifurcations (branches) which cause turbulent flow, and also, its has particles in the fluid (Cells, proteins, etc.) which are not a negligible size as the arteries branch off into smaller and smaller tubes. In capillaries, the red blood cells can be the same width as the capillary itself. In those situations, the fluid is no longer incompressible...heck some would argue it's not even really a fluid. Thus, overall, Bernoulli's equation does not hold for the circulatory system!

We can conceptually break the 'equilibrium' between pressure and kinetic energy from Bernoulli's equation into two principles based on cross-sectional area:
**Note that the following argument is not entirely accurate, and is functional only in terms of the cardiovascular system.

1) "As Cross-sectional area increases, fluid velocity decreases"

and

2) "As Cross-sectional area increases, fluid pressure increases."

For the cardiovascular system, the first one is true, and is seen in the continuity equation: A1v1 = A2v2. In other words, as we move from aorta to capillaries, the fluid velocity decreases.

The second part though, is not true. In fact, as we move from aorta (small cross-sectional area, high velocity) to capillaries (large cross-sectional area, low velocity), the pressure decreases. It does not increase! This is contradictory to Bernoulli's principle for ideal fluids.

So you must be very careful when applying Bernoulli's principle to the cardiovascular system. You must keep straight that the cardiovascular system as a whole does not follow the ideal laws of fluid flow!
4. ### rocuroniumEstablished Member

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5. ### engineeredoutLightning Ballseeker

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I just looked some stuff up, and found that the approximate reynolds number is 2000. Not exactly laminar, but not exactly turbulent either. Obviously low mach-numbers. You're saying its due to the pressure from heartbeat that the cv system doesn't behave like it should?

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Heartbeat is one reason...well more specifically, it's the consequence of one of the reasons: Local constrictions along the cardiovasculature immediately make blood flow unideal, because bernoulli's principle only applies to constant flow along a streamline.
Other reason include:
RBCs and other cell types are certainly not of negligible size the smaller you get. Blood really isn't an ideal fluid at the level of capillaries.
The arteries that branch immediately off of the Aorta are Windkessel Vessels
Arteries and veins have an intrinsic elastance and can also constrict and dilate due to smooth muscle contraction
Bifurcations cause local turbulent disturbances (which can be truly turbulent in the local vicinity of the branch point.)

Remember that I said that Bernoulli's principle can be applied (with care) to the larger blood vessels. I believe that the reason an Aneurysm is so dangerous is because the cross-sectional area of the vessel increases, and thus local pressure increases (in accordance with Bernoulli) to further compound the stress on the already stretched wall, eventually leading to rupture.

Hope this helps!
7. ### wizenedoneIndeed...

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So, to summarize:

Bernoulli's principle says that "As velocity increases, pressure decreases."

But in the case of capillaries, "As velocity increases, pressure also increases" or "As velocity decreases, pressure also decreases" for the reasons you mentioned above (not ideal flow, etc)?

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More or less, although velocity always decreases from the arteries to the capillaries, not increases.
9. ### wizenedoneIndeed...

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Ahh..true!

Thanks for clearing it up for all of us.

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blood entering the atrial causes high hydrostatic pressure
once blood is in capillaries low hydrostatic pressure and high osmotic pressure in the veins.
11. ### FarcusNew Member

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but once you enter the vein the pressure is increase back a little although not to the extend of artery. This is due to the Relatively Smaller Girth of the vein in comparison to the capillary.
12. ### HeyeonHeyeon

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Thanks much! Tht was helpful!! So overall one could say that the cardiovascular sys is more likely to follow Poiseuille's Laws?