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?


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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