Fluid Dynamics Question: Volumetric flow rate, velocity, pressure, and FL question.

[themurph9252]

Hello All,

Kinda of confused right now. I was reviewing a MCAT FL of mine and was wondering if you all could explain something to me. Let me first post the question that I am concerned with:

In an attempt to understand the properties of arterial blood flow, scientists measure the volume of fluid displaced along the artery in figure 1 as a function of time. **** Figure one shows an artery that is not occluded at all at one end and is narrowed by an atherosclerotic plaque at the other (increasing resistance of the vessel and the effective radius)*****. How do the volume displacements per second at points A and B (A being at the point of no occlusion and at the point of occlusion by the sclerotic plaque) compare to each other.

Company's answer and rationale: they are the same at A and B; The continuity equation dictates that while the velocity of fluid at point B is greater that at point A due the the smaller cross-sectional area at point B, the volume displaced per second must be the same.

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Now, I understand that by the principles of the continuity equation that the volume per unit (flow rate) time has to be the same according A*V=constant, hence their rationale. I also understand that pressure is a function of ideal fluid velocity, that is that Bernouli states that where there is faster fluid velocity pressure is lower and where lower fluid velocity, pressure is higher. However, I guess where I am confused is that I also know that vasoconstriction also increased blood pressure due to increased resistance and decreased laminar flow and effectively changes flow rate. Shouldn't the sclerotic plaque also increase resistance, decrease laminar flow, and decrease flow rate? I guess I am just confused because of the conflicting ideas between the increased resistance and decreased flow rate (hence increased pressure) and the continuity equation.


Thanks in advanced for your help and replies!

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[theonlytycrane]

Can you post a screenshot of the q?

 

[themurph9252]

Sure. It's attached.

 

[wizzed101]

Continuity equation is just mass balance.
Bernoulli's is an energy balance along a streamline, not mass balance.
Resistance has to do with Poiseuille's, which takes into account energy lost and fluid viscosity, either of which is incompatible with Bernoulli's. There is no one size fit all model. For blood, Poiseuille is superior.

 

[themurph9252]

Ok, so if in respect to blood, Poiseuille's law wins out, and incorporates vessel diameter, shouldn't the flow of blood change due to the sclerotic plaque. The company stated that the flow is the same at both points suggesting continuity? When I answered the question, I was reasoning the problem along the line of Poiseuille's law as well considering the changing radius at the downstream point to affect the flow (reasoning the sclerotic plaque would have the same effects say as vasoconstriction at that point).

 

[wizzed101]

Your reasoning is correct.

 

[themurph9252]

Thanks for the help!