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I'm studying human physiology. And there is a often repeated notion that blood flows "from areas of high pressure to lower pressure". I was wondering why that is so. However there is no real explanation for it. I understand that in a gradient the force points into the direction of low pressure. Further research on the web has just caused more confusion, because there are certain voices saying that it is a true notion and certain voices claiming that this is not true and instead energy arguments should be used. I have read about Poiseuilles law, Bernoullis law and several more and they just seem to contradict eachother in the end.

So my question is: In general, does a fluid always flow from high pressure to low pressure? Strictly related to the human body, does blood (in the "closed" system) always flow from high pressure to low pressure? Why?

It'd be great if somebody could enlighten me. I'm also sure that answering this question would help many others as well, as it is (in my view) a very basic question but very important for anybody trying to learn/understand physiology.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Apr 7, 2023 at 8:28
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    $\begingroup$ I've seen some similar questions from people in biology who are more comfortable with the formality of mathematics - does that apply to you? In biology and physiology (and, really, even in physics in some contexts), people tend to not be so formal with their statements, because the complexity of the systems make it exhausting to do so. You'd never finish a sentence. Instead, it's perfectly reasonable to make a statement about what is typical without qualification, and to revisit any exceptions at a later time. $\endgroup$ Apr 7, 2023 at 17:04
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    $\begingroup$ Alternatively, since you're asking on a Physics site, maybe you're really looking for an explanation of the physics of why there is a flow from high to low pressure, rather than the way the question is posed in the title. Or, you may be applying Bernoulli wrong, as in biology.stackexchange.com/questions/36443/… or biology.stackexchange.com/questions/100136/… $\endgroup$ Apr 7, 2023 at 17:06
  • $\begingroup$ $$\lim {-infty}{infty}cos dz\frac {1+x^2}$$ $\endgroup$ Apr 10, 2023 at 2:52
  • $\begingroup$ The thing is, pressure in the human body is usually highest at the heart and blood flows away from the heart, so while the saying it's incorrect in fluid dynamics, it's, to some extent, correct for them human blood system. $\endgroup$
    – DonQuiKong
    Apr 10, 2023 at 7:26

7 Answers 7

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No. Fluids in general do not flow strictly from points where pressure is high to points where pressure is low. Even in the simplest static case (which is a reasonable first approximation for blood), you need to consider both pressure and potential energy, rather than pressure alone.

Imagine a cylindrical glass of water (or air, it is easier to imagine with a compressible fluid). Hydrostatic pressure increases linearly from zero at surface towards the bottom, yet there is no net movement of fluid from the bottom towards the surface. It is the sum of pressure and potential which needs to be constant, not pressure alone.

If the pressure gradient were somehow made lower than this, that is, (pressure + potential) would be lower at the bottom than at the surface; the fluid will even flow towards the bottom where pressure is higher, until equilibrium is reached again.

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  • $\begingroup$ In your example, the fluid in the glass does not flow from high to low pressure because gravity is acting against it. If gravity suddenly clicked off, the fluid would then move in the direction of low pressure until it was in equilibrium. So it seems to me that the answer is yes, fluid does flow from high pressure to low pressure unless some addition force acts on it. $\endgroup$
    – dev_willis
    Apr 10, 2023 at 16:13
  • $\begingroup$ @dev_willis Sure, many models and theories are much simpler in absence of external forces. In that case you are right. But the question explicitly stated "in general". $\endgroup$ Apr 11, 2023 at 7:23
  • $\begingroup$ "In general" means "what generally happens." It does not mean "taking into account all external forces." In this case, what generally happens is also what always happens: pressure causes movement. By your logic, one could say that gravity does not always pull toward the center of mass because sometimes people jump. $\endgroup$
    – dev_willis
    Apr 13, 2023 at 18:38
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    $\begingroup$ @dev_willis No, that is not correct. Gravity pulls you towards the centre of mass no matter what, even if you jump, use a jetpack or enter orbit. A good analogy here would be stating that "objects always accelerate in the direction of gravitational force", which is obviously false (you can jump or launch a rocket), even though it is true in absence of other forces. $\endgroup$ Apr 14, 2023 at 9:43
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    $\begingroup$ Definitely not. It is a simple counterexample to the exact formulation in the question. $\endgroup$ Apr 14, 2023 at 13:50
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As you pointed out, the force is directed from the regions of high pressure towards the low pressure, and, according to the Newton's second law, this is where the acceleration is directed.

This does not mean that the blood always flow in this direction - e.g., if for some reason it has initial speed in the opposite direction it first needs to slow down, before reversing the direction of motion. Like a stone that we throw up in the air - it first flies against the direction of gravity, but we know how this experiment ends.

Energy arguments is a different way to describe the same situation - that is energy arguments and kinematic/dynamic arguments are not mutually exclusive, but rather complimentary. Retaking the thrown stone analogy - the lowest potential energy of the stone is when it lies on the ground, but it first flies up (reducing its kinetic energy and increasing the potential one) and only then falls. This neglects friction/dissipation, which can be also taken into account, as energy conversion to other forms - here we would go into thermodynamic discussion of internal energy, free energy, entropy, etc. - probably also not uncommon in biological literature.

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    $\begingroup$ Without going through the various dimensionless numbers in detail (but see en.wikipedia.org/wiki/Dimensionless_numbers_in_fluid_mechanics if you're interested), I'd assume that for most biological systems, viscosity & friction with the blood vessel walls is going to dominate free-streaming effects. That means the "blood always flows from high pressure to low pressure" formulation should work in most cases. In the cases where it doesn't work, I'd expect quasi-steady flow, because the heart's pressure pulses would be dominated by the free-streaming... maybe if you're draining a corpse? $\endgroup$ Apr 7, 2023 at 17:30
  • $\begingroup$ Thanks. This is a valuable comment. $\endgroup$
    – Roger V.
    Apr 7, 2023 at 18:03
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The question has been answered already but since the OP mentions the Bernoulli equation it is instructive to see how this equation actually explains flow against pressure.

Bernoulli's equation governs the motion of the fluid in the absence of frictional losses. For incompressible fluid, $$ \frac{v^2}{2} + g z + \frac{P}{\rho} = \text{const.} $$ Consider flow through a blood vessel of varying diameter, below. Constricted-vessel

Velocity is higher in the constriction because the same mass has to flow through a smaller area. Neglecting the gravitational potential, Bernoulli's equation says that the pressure at the constriction is lower than at the edges of the vessel. That is: $$P_A > P_B < P_C$$ From $B$ to $C$ the flow is against the pressure gradient. This is possible because the fluid has enough kinetic energy to overcome the opposing pressure.

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  • $\begingroup$ Is that a lapsus, above the last TeX line? $\endgroup$
    – Peltio
    Apr 9, 2023 at 21:45
  • $\begingroup$ @Peltio The mistake was in the text, not the equation: the pressure in the constriction is lower than in the inlet or outlet, because the velocity is higher in the neck and the sum $v^2/2+P/\rho$ is constant. This is known as the Venturi effect. $\endgroup$
    – Themis
    Apr 9, 2023 at 23:49
  • $\begingroup$ Yes, in the text above the equation. Anyway now it's gone. $\endgroup$
    – Peltio
    Apr 10, 2023 at 5:05
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I don't know much about blood circulation and just give some basics of steady state fluid mechanics. Poiseuille was a physilogist who was interested in the circulation in blood capillaries. In the latter case, it is indeed the difference in pressure which compensates for the forces of viscosity and the circulation must take place from the high pressures towards the low pressures. But other forces may play a role. For example gravity. A fluid flowing from a reservoir is at the top at atmospheric pressure and at the bottom at atmospheric pressure. Gravity replaces the pressure difference. We have the same situation in the Ostwald viscometer.

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  • $\begingroup$ When you say "in the latter case", what cases are you considering and which one do you consider to be "the latter"? $\endgroup$
    – The Photon
    Apr 7, 2023 at 17:20
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    $\begingroup$ In a system for which friction dominates momentum, gravity is basically going to add to the pressure in the lower extremities, per $P = gh\rho$ $\endgroup$ Apr 7, 2023 at 17:23
  • $\begingroup$ English is not my native language. For "in the latter case", I was speaking of the "Hagen-Poiseuille" flow. I think that P=ghρ does not apply for a non static situation. For a vertical Hagen Poiseuille flow, with atmospheric pressure at the top and the bottom, there is no pressure gradient. $\endgroup$ Apr 8, 2023 at 11:42
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A more accurate statement would be that force is directed from high pressure to low pressure. This is accurate because the force density is exactly equal (minus) the gradient of pressure: $$\rho\vec a=-\nabla p$$ where $\rho$ is the density, $\vec a $ the acceleration of the fluid at a point and $\nabla p$ is the higher-dimensional analogue of the derivative. In 3D it is given by $\nabla p=(\frac{d p}{dx},\frac{d p}{dy},\frac{d p}{dz})$. In 1D it is just the derivative: $\nabla p=\frac{d p}{dx}$. The gradient is large in places where the pressure goes from high to low.

So the statement "blood flows from areas of high pressure to areas of low pressure" is as accurate as saying "objects will move in the direction of forces". Gravity points down so things move down, right? Objects often tend to move in roughly the direction of forces that are applied to them, but there are many exceptions to this and the most notable one is probably circular motion. In circular motion the force is directed inwards, while the motion is tangential to the circle. The fluid analogue of circular motion is of course a vortex. Here the fluid spins in a circle and the necessary centripetal force for this motion is provided by a pressure gradient.

So while fluid doesn't necessarily from high to low pressure, in the case of blood inside a body it usually does. When there is a lot of friction in the system, like in the human body, fluid tends to flow from high pressure to low pressure.

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Strictly related to the human body, does blood (in the "closed" system) always flow from high pressure to low pressure? Why?

No. A counter-example in the human body is an aneurysm.

An aneurysm is a pathological widening of an artery. Because the cross-sectional area of the vessel is larger in an aneurysm, the blood must slow down on entering the aneurysm. This means that there is a force in the retrograde direction on entering the aneurysm and therefore a “backwards” pressure gradient.

The pressure in the aneurysm is higher than the pressure in the upstream vessel, so blood flowing into the aneurysm is flowing from a region of low pressure to a region of high pressure. An aneurysm is dangerous precisely because of this. The pressure in the aneurysm can potentially be high enough to rupture the vessel and cause a very large internal bleed.

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Pressure is confusing, because it an abstraction allowing us to talk about fluids in a simplified way. At the lowest level you have cells and molecules with momentum colliding and transferring that momentum in those collisions. In some cases just thinking about high and low pressure is enough to understand how the fluid moves, but in the body it's not hard to think of examples where those abstractions fall short. You've mentioned Poiseuille's Law which is useful for thinking about how blood moves though a vessel, but if you actually try to apply Poiseuille's Law numerically you'll realise immediately, that an artery is elastic, so the diameter is not constant, rather the contraction of muscle around the artery and external pressure means there is an elastance relationship - the diameter changes with the pressure in the vessel, which seems like something that maybe you could ignore, except that blood pressure is pulsatile, it's changing with the beating of the heart. Use Poiseuille's Law as high level abstraction to understand at a high level how fluid moves, but be aware that modelling the movement of fluid in the body is not a finished problem. Clinicians are still researching the best high level abstractions to model what's happening in a patient:

https://cardiothoracicsurgery.biomedcentral.com/articles/10.1186/s13019-023-02134-3

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