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What is the reason why blood pressure and a larger cross sectional area of blood vessel cause a lower blood pressure and vice versa?

This question is related to another question I found here.

The answer given to that question says that the reason why a narrower blood vessel have higher blood pressure (which I believe refers to static pressure instead of dynamic pressure according to this website) is beacuse

the resistance is high and thus the heart needs to pump blood at higher pressure to maintain the same average flow rate as in a normal blood vessel.

However, I've found a different argument from a website that contradicts the above reason.

According to this website,

Opening and closing different arteries affects your blood pressure. The more narrow your arteries are, the less space there is for your blood to flow in and the harder it pushes against the arteries’ walls.

The argument presented in the second block quote uses the common misconception of how fluid works which Bernouli's principle shows to be not true by energy conservation i.e. faster fluid leads to higher pressure.

So which argument of the two arguments presented is right?

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    $\begingroup$ This question is probably more subtle than supposed. Blood is a non-newtonian fluid. In addition, arteries pulse, so it is likely that there is a small change in diameter as the "chunk" of blood passes down an artery. Also, the stiffness of the artery wall may not be constant, depending on what hormones are circulating in the blood (e.g., adrenaline). $\endgroup$
    – David White
    Commented Nov 24, 2018 at 7:08

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The Bernoulli equation is a poor approximation for flow of viscous fluids like blood, particularly in flow through capillaries. The dominant factor in viscous flows is that of overcoming viscous friction. In flow of a purely viscous fluid, for a speciified volumetric flow rate, the pressure gradient along the tube varies inversely as 4th power of the tube diameter. (This is described by the Hagen-Poiseulle equation). So blockage of blood vessels even a little has a strong effect on the pressure the heart must provide to pump blood through the system. In the case of shear-thinning (non-Newtonian) fluids, the effect of diameter is a little less, but the required pressure gradient still increases with decreasing diameter.

So, in short, the first explanation seems to be the correct one.

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I may be mistaken, but I believe the reason they seem to contradict each other, and the one Bernoulli, is that you are assuming the same flow rate in the second article. Bernoulli says the same flow rate through a smaller pipe leads to lower pressure. If you close an artery, the flow rate through the remaining arteries has to increase to compensate, thereby increasing the pressure.

Blood is also a Non-Newtonian fluid. It is shear thinning, so the viscosity will change with velocity, you can find more info on that here, http://www.rheosense.com/applications/viscosity/newtonian-non-newtonian

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  • $\begingroup$ Thanks for your input. But there is one part of your argument I don't quite understand. You mentioned "If you close an artery, the flow rate through the remaining arteries has to increase to compensate, thereby increasing the pressure." But if flow rate through the remaining arteries increase, then wouldn't (static) pressure decrease by Bernouli's principle as flow rate increased? $\endgroup$
    – Bøbby Leung
    Commented Nov 24, 2018 at 9:36
  • $\begingroup$ First I am sorry I didnt explain my point very well, and second this is not my area of expertise, so bear with me. There are numerous factors to take into consideration. First is the fact that blood pressure is not the pressure in the vessels, but the pressure needed to stop blood flow, which is kinda arguing semantics, but I thought it relevant. Second, blood vessels are pliable, so to a point they can dilate or constrict to moderate blood flow. This is why your face will turn red when embarrassed. Last, Bernoulli's applies to constant flow better than it does to the pulsating flow of blood. $\endgroup$
    – Bubba Hotep
    Commented Nov 24, 2018 at 15:43
  • $\begingroup$ Bernoulli is also generally applied to pumping a liquid through a pipe to another destination, constant flow rate with a discharge point. The constant flow rate is dependent upon the input and out put of fluid. The heart also acts as its own check valve, so as it pumps, the blood only has only one place to go, back to the heart. If you remove part of the plumbing, you increase the flow rate and velocity, which should decrease pressure, but you now have 2 gallons of blood in a system that is minus part of its plumbing. You are pumping against a closed valve so to speak. $\endgroup$
    – Bubba Hotep
    Commented Nov 24, 2018 at 16:12

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