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Physics of blood vessels

by BramhaBull
Tags: blood, physics, vessels
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BramhaBull
#1
Jun25-07, 02:29 AM
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I am taking Physics and Anatomy simultaneously and was confused by something that was taught and seemed contradictory. In Bernoulli's equation (for fluids) I learned that as the cross sectional area of a pipe or tube decreases, the velocity of the fluid increases. And I also learned that the pressure that a fluid exerts on the walls of the tube is inversely proportional to the velocity (PV = constant).

In Anatomy, when the blood pressure of a patient was high, he/she was given drugs which dilated their blood vessels. Dilating the blood vessel (increasing cross sectional area), according to Bernoulli's equation, would decrease the velocity of the blood. And if the velocity falls, shouldn't pressure INCREASE due to them being inversely proportional??
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CompuChip
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Jun25-07, 03:09 AM
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I don't think the V in the cited equation, PV = constant is the velocity, but rather the volume (I'm thinking about the ideal gas law). Then dilating the blood vessel would increase the volume and therefore reduce the pressure.

Try turning on your garden hose. Does it make sense that the more you open the water, the less pressure is on it?
gaming_addict
#3
Jun25-07, 03:17 AM
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Quote Quote by BramhaBull View Post
Dilating the blood vessel (increasing cross sectional area), according to Bernoulli's equation, would decrease the velocity of the blood. And if the velocity falls, shouldn't pressure INCREASE due to them being inversely proportional??
Dilating the blood vessels would increase the cross sectional area and the volumetric capacity of the blood vessels. Like if you increase the volume, and keeping everything constant, the pressure will decrease. Correct me if I'm wrong that for closed or sealed systems like the circulatory system, the volume will affect wall pressures more than Bernoulli effect.

It also had the added benefit of reducing the pumping pressure for the heart due to higher volume of flow.

FredGarvin
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Jun25-07, 07:14 AM
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Physics of blood vessels

Quote Quote by gaming_addict View Post
It also had the added benefit of reducing the pumping pressure for the heart due to higher volume of flow.
That's exactly what you are aiming for. Increase the cross sectional area (bigger pipe) to require a lower pressure drop to get the same flow, i.e. it's easier on the heart to pump.
BramhaBull
#5
Jun25-07, 10:07 AM
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Quote Quote by CompuChip View Post
I don't think the V in the cited equation, PV = constant is the velocity, but rather the volume (I'm thinking about the ideal gas law). Then dilating the blood vessel would increase the volume and therefore reduce the pressure.

Try turning on your garden hose. Does it make sense that the more you open the water, the less pressure is on it?
Yes, I am mistaken. The pressure velocity relationship comes from Bernoulli's equation.
Q_Goest
#6
Jun25-07, 11:56 AM
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Hi BrahmaBull,
Bernoulli's is inadequate for many - if not all - real fluid systems in which pressure drop must be accounted for. If for example, we model the heart as a pump which displaces a given volume per unit time, and the blood vessels as a single pipe that connects the outlet of the heart to the inlet, then B's equation predicts the inlet pressure on the heart will be the same as the outlet pressure on the heart, which is incorrect. Also, if we simply add some volume to this system such as by T-ing off the pipe and adding a large tank, there still won't be any change to the pressure drop between the inlet and outlet of the heart. The blood must still go through all the same passages. If however, the passages are made larger, the frictional pressure drop along the walls (which isn't accounted for by B's equation) will decrease.

B's equation doesn't do anything to tell you how this pressure drop and flow rate equate in such a fluid system. To do that, you need equations that determine frictional pressure drop such as the Darcy-Weisbach equation. Using such an equation, you find that for a fluid system in which there is a constant flow rate, such as the flow from a pump like the heart, the pressure drop per unit length decreases as diameter increases. So the reason why blood pressure drops when the arteries are dialated is because there is less restriction to flow through the arteries. This also means the heart doesn't have to do as much work since the pressure it has to generate is less. None of this is predicted by using B's equation.
Ouabache
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Jun25-07, 05:43 PM
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We've had similar questions about blood pressure, vessel diameter and Bernouli's equation before. PF is not just a forum but also a library of information. To save yourself time, just google some key words

In your case, if you choose key words: "blood pressure" Bernoulli and physicsforums; you'll find these past threads.

ref01
ref02

Notice I use quotations to search on a "string" of more than one word.


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