Consider whether the non-linear relationship between flow and degree of reductio

Question

Consider whether the non-linear relationship between flow and degree of reduction of cross-sectional area can explain why a 50% blockage typically does not produce symptoms whereas a 70% blockage does: A. What is the predicted new flow rate given a 50% reduction in cross-sectional area? Show your work. What is the predicted new flow rate given a 70% reduction in cross-sectional area? Show your work. Given these results, does it seem plausible to you that no symptoms would be felt until 70% occlusion? Explain. B. In reality, the analysis above overestimates the effect of a given reduction in effective artery cross section on blood flow through an artery. The artery itself provides resistance to flow, as considered above, but other blood vessels with which the artery in question is in series contribute resistance to flow as well. Not until occlusion of the coronary arteries exceeds around 75% does the increased resistance in the coronary arteries themselves become the dominant factor limiting blood delivery to the heart muscle. Suppose the artery in question is just one of ten blood vessels contributing equally to the total resistance to flow. If resistance doubles in one of these blood vessels, by what percentage does total resistance increase?

Explanation / Answer

Thanks for the question.

The formula for calculation of volumetric flow rate is Q=av

where Q is volumetric flow rate,A is cross sectional area and v is the speed of fluid in that section.

A. Let us assume that the cross sectional area was 100% to start with.

thus, Q=100v

Now if there is 75% blockage Q=75v

If 50 % blockage Q=50v

We cannot conclude whether the symptoms will occur after 70% blockage in one artery, as the heart is supplied by more than 3 arteries, and even if there is block in one, others can make up for the loss provided there is no major occlusion in them as well.

Regards

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