Ok, so I have these two phenomena that seem to be quite well documented as true, and yet also seem to be mutually exclusive:
The faster a fluid moves across a surface, the lower the pressure exerted on that surface. This is demonstrated by airplane wings and props, helicopter rotors, etc.
“Blood pressure” is the reading of the pressure exerted against the walls of the blood vessels. Increased blood pressure is the result of the blood, for whatever reason (exertion, cholesterol buildup, etc.) moving more quickly through the blood vessels.
So, if fluid moving faster reduces pressure on the surface across which it moves, how does faster blood movement increase blood pressure?
This has to be a simple case of a little knowledge being a dangerous thing. In my search through the archives, I came across this thread, indicating that I don’t know nearly as much about fluid dynamics as I thought I did (you’d think that a BS in Chem Eng would be of SOME use in everyday life!).
Not exactly. The way I think of it, at such low speeds, Bernoulli’s Law is not the main factor. When blood vessels become constricted (e.g., plaque builds up), the cross-sectional area is decreased. However, the more important effect is that the blood vessels’ elasticity is decreased, so that, while the difference in pressure is not so great, the effect of the pressure is (i.e., the blood vessels don’t bend as much [they are less flexible] and thus are more likely to break. The Bernoulli equation factors in somewhere, too, so if that is your only question see Cecil’s column on the subject (sort of).
Hmmm…
Not exactly the issue I had in mind for the blood vessel part of it.
Any factor causing the increase in fluid velocity of blood will result in an increase in blood pressure. An increase in heart rate (from exertion, anxiety, whatever) will increase blood pressure temporarily. For that matter, the systolic blood pressure (the higher bp number) is the pressure on the walls of the blood vessels while the blood is being pumped, while the diastolic (the lower number) is the pressure while the ventricle is at rest (blood is pretty much stationary in the arteries).
So, I’m assuming that I’m applying Bernoulli’s law incorrectly for the blood pressure. I’m pretty sure that somehow Bernoulli is supposed to describe blood pressure accurately, since that’s what the equation was developed for in the first place, only later to be ripped off for use in aero- and hydrodynamics
Bernoulli’s Law, while real, is only an extremely minor component of lift in all man-made aircraft. Angle-of-Attack (AKA deflection) is what actually causes the vast majority of the lift in any heavier than air aircraft. If Bernoulli’s Law was the major force giving airplanes lift then none would be able to fly inverted but we know that is not the case.
Bernoulli’s Law is probably the most exaggerated force in all of physics. We have debated this in Great Debates several times and it is a shame that Bernoulli’s Law is given such an important pace in aerodynamics theory.
Yep, one thread discussing that was the one I linked in the OP.
My issue, though, is that it does, in fact, exist, and that it seems incompatible with the measurement of blood pressure.
I’ll take your word for it that the angle of attack, etc, etc, plays a larger part in aircraft lift. I was one of the people referenced in the thread that got their info on Bernoulli’s law directly from an undergrad-level fluids textbook, and has gone around thinking that it was the definitive answer to all fluid dynamic problems.
The thing is, though, that it is an accurate equation, to the extent that it describes fluid flow (in the same way that Newtonian physics is accurate, but only tells part of the story). My confusion lies in the seeming contradiction of higher fluid velocity reducing surface pressure in the aircraft scenario, and decreasing it in the blood scenario.
Well, first of all, fluids behave differently in enclosed cylinders than when allowed to stream freely.
The primary result of fluid being forced through a constricted vessel is that its velocity will increase (think about a garden hose with a restricting output), but the overall volume of flow stays the same.
For example, if you put a bucket in front of two hoses, and you restrict the nozzle of one, then assuming a constant volume pump both hoses will still fill the bucket at the same time, but one will do so with much faster water flow (but of lower volume).
In addition, for a constant-volume pump to keep working with a restricted hose, it will have to apply more force, and the stress on the walls of the hose will be higher.
So a restricted artery will make the heart work harder, and put more stress on the walls of the artery.
The short answer is that Bernoulli’s relation is only true in certain situations. It’s not the Final Word on fluid mechanics, by any means.
It can be derived from the Navier-Stokes and continuity relations, which are the more complete equations concerning fluid flow. Certain assumptions have to be made when arriving at Bernoulli, and some of them are pretty strong. Basically, Bernoulli’s relation talks about conservation of total energy along a streamline, and trying to extend it to other situations is probably going to cause problems.
Regarding blood flow, I believe it goes like this. Your body basically needs a given blood flow rate at any time, dependent on a number of things like what you’re doing, etc. Say your blood vessels are constricted - the required flow rate (call it Q) will still be the same.
So, we need the same Q through blood vessels of a smaller diameter. This means that the average speed of the fluid must, of necessity, be higher - the same amount of stuff through a smaller amount of space. That’s why the flow speed must be higher through constricted blood vessels.
As for why that means higher blood pressure at the same time - the only way to manage this is by having the heart pump harder - creating more pressure to achieve the same flow rate. IIRC, the pressure drop through a smooth pipe goes inversely with the *fourth power of the diameter: dp/dx ~ 1/D[sup]4[/sup] (for a constant Q). It’s obviously not that simple for pulsating flow like in blood vessels, but it’s the same idea: in a smaller tube you have to pump harder to get the same flow rate.
