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The physics of blood pressure drop

by Lys0some
Tags: blood, physics, pressure
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Lys0some
#1
Jun25-14, 07:40 PM
P: 3
Hello everybody. I have seen many people asking questions on this forum about the reason to why blood pressure drops as you get farther from the heart.

But honestly, not a single answer satisfied me. My major is physiology, so it's quite funny that I still don't know this "trivial" detail. What is the physics behind the drop in blood pressure?

Because I was not satisfied with any of the answers, such as, capillaries have smaller diameters (because diameter shouldn't make a difference in pressure unless you're fitting in the same volume), the blood "losing energy" as it travels across the long resistance journey (because that just doesn't make sense), the arteries are closest to the pump (that's a cool answer, but doesn't explain anything), velocity drops in capillaries (cool, but shouldn't that increase pressure according to Bernoulli's principle? Besides, blood travels faster in veins), because capillaries have higher resistance (well the total cross sectional area of capillaries is actually greater than arteries and greater than veins), etc. So, I decided to come up with my own explanation and I hope someone corrects me if I am wrong.

The only way I could make sense out of this is by this reason, imagine a long tube that gets wider in the middle, then back to normal diameter at the end, and a pump at one end of it. When the pump pumps the fluid through, the initial part of the tube is facing a large volume of fluid in front of it that is spread along a long distance, as you proceed through the tube, there is progressively less fluid in front of you. So if we consider the pressure a result of a force at one of the end of the tube and another at the other end, then the weaker the force (impedance) in front of you, the less pressure you would experience. As you have less fluid in front of you, you have less mass to push against a resistant tube, so your pressure drops. The further you move, not only you have less volume of fluid to push, but also less resistance in series, since whatever is left of the tube is getting shorter and shorter. The only issue with this explanation, is that the circulatory system is a closed loop. But again, during diastole, the right atrium pressure is pretty much almost zero (3-8 mmHg), so we can almost assume the tube is open at one end letting with a waterfall of blood pouring in the heart.

So can anyone please point out issues in my explanation?

Thanks
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Student100
#2
Jun25-14, 10:08 PM
Student100's Avatar
P: 528
Quote Quote by Lys0some View Post
Hello everybody. I have seen many people asking questions on this forum about the reason to why blood pressure drops as you get farther from the heart.

But honestly, not a single answer satisfied me. My major is physiology, so it's quite funny that I still don't know this "trivial" detail. What is the physics behind the drop in blood pressure?

Because I was not satisfied with any of the answers, such as, capillaries have smaller diameters (because diameter shouldn't make a difference in pressure unless you're fitting in the same volume), the blood "losing energy" as it travels across the long resistance journey (because that just doesn't make sense), the arteries are closest to the pump (that's a cool answer, but doesn't explain anything), velocity drops in capillaries (cool, but shouldn't that increase pressure according to Bernoulli's principle? Besides, blood travels faster in veins), because capillaries have higher resistance (well the total cross sectional area of capillaries is actually greater than arteries and greater than veins), etc. So, I decided to come up with my own explanation and I hope someone corrects me if I am wrong.

The only way I could make sense out of this is by this reason, imagine a long tube that gets wider in the middle, then back to normal diameter at the end, and a pump at one end of it. When the pump pumps the fluid through, the initial part of the tube is facing a large volume of fluid in front of it that is spread along a long distance, as you proceed through the tube, there is progressively less fluid in front of you. So if we consider the pressure a result of a force at one of the end of the tube and another at the other end, then the weaker the force (impedance) in front of you, the less pressure you would experience. As you have less fluid in front of you, you have less mass to push against a resistant tube, so your pressure drops. The further you move, not only you have less volume of fluid to push, but also less resistance in series, since whatever is left of the tube is getting shorter and shorter. The only issue with this explanation, is that the circulatory system is a closed loop. But again, during diastole, the right atrium pressure is pretty much almost zero (3-8 mmHg), so we can almost assume the tube is open at one end letting with a waterfall of blood pouring in the heart.

So can anyone please point out issues in my explanation?

Thanks
I'm almost certain the answer is friction, and speculating isn't really kosher on these forums.

http://faculty.weber.edu/nokazaki/Hu...20pressure.ppt
Lys0some
#3
Jun26-14, 08:10 AM
P: 3
Quote Quote by Student100 View Post
I'm almost certain the answer is friction, and speculating isn't really kosher on these forums.

http://faculty.weber.edu/nokazaki/Hu...20pressure.ppt
Well can you explain how friction reduces blood pressure? I mean, axial friction can only slow down the blood, which would locally increase blood pressure. Blood velocity is slower in the capillaries than the arteries, yet the pressure is lower. Blood velocity is faster in the veins than capillaries, yet blood pressure is lower. So velocity is not the main determinant of blood pressure. Total cross-sectional area is highest in capillaries, but blood pressure decreases progressively, so that is not the cause either. Total resistance is likely low in the capillaries, because they add in parallel.

And I am not speculating, I am making an educated guess. As if the rest of the answers make sense anyway.

bigfooted
#4
Jun26-14, 05:15 PM
P: 285
The physics of blood pressure drop

The basics of pressure losses are explained by simple fluid dynamics. It is a shame that they did not go into it in at least some detail during your studies.

Let's first ignore all the difficult things (non-Newtonian flow, flexible walls, etc) and consider the flow through a simple pipe with solid walls.
The Bernoulli equation states that the total pressure is constant only when there are no frictional losses.
If there is viscosity, you will have pressure losses. The total pressure will go down. if the pipe diameter stays constant, velocity will not change (because of conservation of momentum) and therefore the static pressure will go down.
In the simplest case, laminar flow, the pressure loss is given by:
[itex]\Delta P = \frac{64}{Re}\frac{L}{D}\frac{1}{2}\rho V^2[/itex]
with
D=diameter of pipe
L=length of pipe
[itex]\rho[/itex]=density
V=velocity
Re=Reynolds number [itex]Re=\frac{\rho V L}{\mu}[/itex]
(the derivation of the pressure loss equation is in most basic thermodynamics textbooks, e.g. Cengel - thermodynamics)

The internal energy goes down because static pressure goes down.
The pressure loss is per unit length of pipe, so the more distance you travel, the lower the total pressure and the more internal energy you have lost (to friction at the walls, which is converted in the end to heat.).
If the diameter is smaller, the pressure loss is larger per unit length, so you lose more per meter in the capillaries than in the arteries.

Note that blood flow is actually quite special. In the capillaries, the blood cells are larger than the diameter of the capillaries, and you cannot speak about continuum fluid dynamics anymore, so Bernoulli's equation is not valid.
256bits
#5
Jun26-14, 05:18 PM
P: 1,411
You are not well versed in Bernouilli and fluid flow, so the inappropriate application of the principles is understandable.

The heart is a pumping station and the fluid is the blood. There is no difference here from any other engineeered system such as the water distribution in your city, which in many ways is very similar, in that a large pipe exits the pump, and a network of smaller pipes direct the flow to sections of the city, to smaller pipes that lead to a neighborhood, and even smaller pipes to the home. One difference is that the blood flow is a closed sytem.

In both cases, the water distribution network and the circulatory system, there is what is called continuity - ie what goes in must come out. The pump moves all of the fluid. The pressure at the pump is determined by the system and network of pipes, which is fixed, and the amount of fluid one wishes to pump, which is a variable.

Bernouilli is an energy equation. It says that total head at a pipe location is equal to the sum of the static pressure head, the velocity pressure head, and the elevation pressure head. With a horizontal pipe, the elevation head does not change from one location to the next. If the pipe size changes to a smaller diameter, then the static pressure drops and the velocity head increases( the fluid is moving more quickly ), simply due to the fact that the same amount of fluid, through continuity, is moving through both sections of ONE pipe, and the energies have to be equal at both locations.

This is not the same as splitting the larger pipe into several other pipes of usually smaller diameter. Here, through continuity the flow also has to split. So what was good for calculating the Bernoiulli's at different sections of one pipe, which is easy, one has to take the Bernoulli's of each individual smaller pipe, add them together. The energy of the fluid flow of ALL the smaller pipes has to be equal to that of the larger pipe. If there are a lot of branches the static pressure AND the velocity of the fluid can drop in each smaller branch.

The network of pipes and branches has a resistance to fluid flow. This results in what is called head loss. This is why a pump connected through some pipes back to itself has to be continiously pumping. If there was no such thing as head loss then one could start the pump up to get the fluif flowing, and then shut the pump off and the fluid should keep on moving forever. In the real world in which we live head loss manifests itself as a rise in temperature of the fluid and pipe, and a drop in the static pressure. The pump has to keep on supplying energy.

In the capillaries, there is little static pressure left over from the head loss and little velocity head. Contractions of the muscles aid in the movement of the blood back to the heart and you can think of them as a whole series of pumps along the veinous network. Valves prevent the back flow of the blood as it moves towards the heart.

Questions?
Lys0some
#6
Jun27-14, 02:34 PM
P: 3
Well that's a new perspective to me. Yes, I am not really a physics student, I'm a pure physiology student, so that's why I am quite unfamiliar with this. Thanks a lot to both of you :)
256bits
#7
Jun28-14, 09:46 AM
P: 1,411
You are welcome.


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