I know, I know this is probably a question too simple to be asked on a forum like biology stack exchange. Problem is, I looked many places and can't seem to find a more mathematical approach to explain why the contraction of a BV leads to increased blood pressure (BP). The main formula i'm looking at is Flow = Pressure/Resistance. In addition, Flow = Area x velocity so Area x velocity = Pressure/Resistance. As the BV constricts, the radius, ie. area, decreases, and so the pressure decreases. But clearly, that is not the case.

What am I missing here?

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    $\begingroup$ Basic physiology questions are my personal favourite +1...anyways have you tried it this way (I'm supposing):area decreases, so flow decreases (possibly because resistance (R) increases in the blood vessel)...now to keep the flow constant the pressure (P) needs to be increased...what I 'm trying to say is that P increases to counter reduced flow as R increases. $\endgroup$
    – user 33690
    Apr 17, 2018 at 7:50

1 Answer 1


There is an important missing assumption in your statement, I've added it in italics:

Contraction of blood vessels leads to increased blood pressure if total flow stays constant.

All you need is your first equation:

Flow = Pressure/Resistance

Decreasing the radius increases the resistance. If flow is constant, then pressure has to increase to get the same flow through the smaller vessel.


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