Blood pressure and Bernoulli's equation

[bentonj002]

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I have recently gained a thorough understanding of Bernoulli's equation. At least I thought I had until I read an answer explanation from one of my AAMC practice tests. The answer explanation stated that as vasoconstriction occurs blood pressure increases. How can this be true if, according to the volume flow rate equation (Q=Av), velocity increases as area decreases? In Bernoulli's equation it states that as velocity increases the pressure exerted by the fluid decreases. What am I missing here?

 

[VlLLVGE]

I think of it in a simpler way: as the superficial vasculature constricts, there is less total space for the same constant volume of blood to take up (assuming less superficial vasculature doesn't dilate in the process), so the blood is somewhat more compressed, pushing up against the walls of blood vessels at a greater pressure, opposite to the pressure exerted on it by the vasoconstriction.

I think the continuity equation A1V1 = A2V2 poorly explains this because vasoconstriction likely has little effect on the volume flow rate the heart is pumping but rather the specific vasculature it's being pumped to - it's essentially diminishing blood supply to the skin vasculature (to reduce heat loss), meaning less total space for the same volume of blood to take up.

To increase flow rate considerably, you would have to decrease the negative pressure bringing blood back from the venules and veins, as well as what's delivered by the arteries and arterioles, which is dictated by the heart rate more than constriction. Given that, I don't think Bernoulli is a good application here given the elasticity of vasculature, and that the heart is essentially a pump that trumps the effects of vasoconstriction.

 

[Ismet]

Moving to MCAT forum

 

[bentonj002]

Ok, am correct to assume that you think the question answer is referring to blood as an ideal fluid and the vasculature as a non rigid tube? If so, as you said, Bernoulli's and the continuity equation would be ruled out right? So for future reference I need to decide if the question is an ideal situation or a realistic one. In a realistic setting would the pressure equation P=F/A be more accurate?

 

[bentonj002]

Sorry, I meant that you're assuming that blood is a non ideal fluid.

 

[Hadi7183]

Sorry, I meant that you're assuming that blood is a non ideal fluid.

Blood is a non-ideal fluid and therefore the Bernoulli equation does not explain the flow of blood in vessels (unless stated otherwise in the question/passage). This is an important exception for the MCAT.

 

[Jack Westin]

I know you think the concepts are contradicting themselves but this is not the case. It is true, for the continuity equation, as area of a pipe decreases, velocity increases. And we know from Bernoulli's equation that as velocity increases, pressure decreases. And for blood vessels: vasoconstriction, which is when area decreases, we know that velocity increases, but somehow, blood pressure increases. Whack! Right? But Bernoulli's equation cannot be used for biology, especially blood/ blood pressure! Why? Because Bernoulli's equation can only be applied for moving fluid that exhibits 1. laminar flow, 2. no viscosity (resistance), 3. no turbulence.

Since blood is viscous in nature (kind of like honey is), blood is not laminar and has considerable resistance. Thus, Bernoulli's equation does not work for blood. Only use Bernoulli's equation if the question assumes laminar flow as in with water in a pipe. (Water on the MCAT is expected to be laminar unless stated directly in the passage and you can also assume no solids or liquids can be compressed). Only use Bernoulli's equation for physics. For biology, think: vasocontriction increases blood pressure and vasodilation decreases blood pressure.

Jack