Blood Pressure and Bernoulli's equation

[OrthoRehab33]

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So, I'm somewhat confused. Say a person has plaque within their blood vessels which would narrow the blood vessels based on the contunity equation v1A1=v2A2 the velocity of the fluid would increase which decreases the static pressure based on Bernoulli's equation. So, how does the plaque increase someone's blood pressure? I know I'm misunderstanding something..

 

[mik30102]

I believe you are right the the velocity of blood increasing due to a constant flow rate, but I'm pretty sure Bernoullis equation cannot be used as blood does have considerable viscosity, tubular flow occurs, and overall is a poor example of a ideal fluid. A better equation to talk about what is going on here is the Hagen-Poiseuille equation which is change in pressure is inversely proportional to the radius to the 4th power if everything else is constant. As the radius decreases due to the atherosclerosis the heart must create a larger pressure difference to maintain this same amount of flow causing your blood pressure to raise. Hope this helps 🙂

 

[HesitantManatee]

So, I'm somewhat confused. Say a person has plaque within their blood vessels which would narrow the blood vessels based on the contunity equation v1A1=v2A2 the velocity of the fluid would increase which decreases the static pressure based on Bernoulli's equation. So, how does the plaque increase someone's blood pressure? I know I'm misunderstanding something..

Blood pressure doesn't refer to pressure on the walls of the vessel, it refers to the pressure the heart exerts. You should use poiseuille equation to better under stand this question. Since the radius(r^4) of the vessel decrease the blood pressure (Delta P) must increase to maintain the flow rate (Q).