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I have read that in an artery, the blood pressure is greater in an opene artery than in a blocked/constricted one.

Why is this the case?

Looking at the Bernoulli equation,

Pressure + 1/2*density * velocity^2 + density * gravity * height is constant. In a constriction, area goes down, and as flow-rate = velocity * area = constant, as area decreases, velocity increases. As density and gravity and height are assumed to be constant, Pressure must decrease in this constriction.

However, I can't physically udnerstand why this is the case. If I blocked off a part of a pipe, wouldn't pressure increase at that area, as fluid couldn't pass through as easily and e.g. would be putting a force on the constriction?

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  • $\begingroup$ The answer to this question might help. $\endgroup$
    – Crimson
    Commented Jan 11, 2018 at 9:20
  • $\begingroup$ What does "opene artery" mean? $\endgroup$
    – enbin
    Commented May 20 at 2:12
  • $\begingroup$ The pressure is high, have you measured it? What part is being measured? How is it measured? $\endgroup$
    – enbin
    Commented Sep 27 at 12:22

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It is the gradient in pressure that accelerates the fluid. Mass conservation dictates that the fluid must speed up in the constriction. In order to speed up, a little cube of fluid must feel higher pressure behind it than in front of it. Thus where speed increases, pressure decreases.

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