Calculating Pressure Increase in Arteries with Fatty Tissue Build-Up

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The discussion focuses on calculating the pressure increase required to maintain constant blood flow in arteries with a 10% reduction in radius due to fatty tissue build-up. The user initially estimates a 52% increase in pressure but is confused about the calculations leading to a 23% increase based on Poiseuille's equation and the area ratio derived from continuity. Clarification is sought on how to arrive at the 52% figure, indicating a need for deeper analysis of the equations involved. The conversation highlights the complexities of fluid dynamics in biological systems. Accurate calculations are essential for understanding the implications of arterial blockages on cardiovascular health.
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Homework Statement


Suppose that the build-up of fatty tissue on the wall of an artery decreased the radius by 10%. By how much would the pressure provided by the heart have to be increased to maintain a constant blood flow?


Homework Equations


Poiseuille's equation


The Attempt at a Solution


52%?
 
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This was a while ago, but I hope someone can help me. I'm using continuity and get A1/A2 = 1.23, and using P = F/A, it looks like P1 = 1.23P2, which is a 23 percent increase. How do you get 52%? A little help? Thanks.
 

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