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Okay it should make sense intuitively, but Bernoulli's principle says that a higher cross sectional flow area means less velocity which means higher pressure!

I also read in a related post that Bernoulli's principle is for inviscid flow. Blood has viscosity. But this alone should make the changes in pressure less extreme, not reverse the effects.

But does the fact that blood is a non-newtonian fluid change anything?

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This Wiki article on vasodilation explains it all. Vasodilation decreases the resistance to blood flow while vasoconstriction increases it. So when the resistance to flow is low (high) the heart needs to pump blood at lower (higher) pressure to maintain the same average flow rate as in a normal blood vessel.

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You said is correct if there is no work done to the fluid. However, Vasodilation is the expansion of blood vessel. Because blood can be assumed to be incompressible, an slight increase in volume will reduce significantly the pressure. If you put the wall expansion into Bernoulli equation, you would need to include an extra term: work done by the wall.

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