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I get that bernoulli's doesn't take frictional losses into account, but at a short section of an artery, I assume it would still hold.

With bernoulli's equation, I can understand it in terms of energy that if kinetic energy (velocity) goes up, potential (pressure) energy must go down. And with the continuity equation, if radius decreases then velocity increases and so pressure must decrease.

Intuitively I still have a hard time wrapping my head around this - if a fixed volume of fluid was traveling through a pipe, and that pipe's radius got larger, the continuity equation would say that its velocity would decrease, and if velocity decreases, then bernoulli's equation will say that its pressure will increase.

This doesn't really make sense to me though when I think of pressure as the force that the fluid molecules are exerting on the vessel wall. If the same amount of fluid is exerting its force over a dilated vessel with greater surface area, then wouldn't the pressure on the walls decrease compared to a constricted vessel? Or is there a difference in the "fluid pressure" that bernoulli's equation is talking about and the actual pressure on the vessel wall?

Wouldn't something like Boyle's law apply to vessels? I know that blood is incompressible, but if the same amount of blood is contained in a larger volume, then I would think that pressure would decrease, and vice versa for blood contained in a smaller volume. But as soon as fluid starts to flow, then nothing makes sense to me anymore because if the volume gets bigger, velocity goes down and pressure goes up...

On a related note, how can the continuity equation and poiseuille's equation be related? My understanding is that velocity and flow rate aren't quite the same, but they are proportional to each other. With poiseuille's, if radius goes down then flow rate goes way down due to the 4th power relationship, but continuity equation would say that velocity would increase?

Is it ever possible that velocity of the blood would increase but the overall flow rate would decrease?

I hope this makes sense. Blood pressure is much easier to "get" when I think of it purely in terms of how much blood a vessel is holding in relation to its size - a small (constricted) vessel holding a large amount of blood will generate a high pressure on the walls, and a large (dilated) vessel with a small amount of blood will generate a low pressure on the walls. But then bernoulli's equation always jumbles it all up for me and it makes no sense.