Calculating blood pressure increase with Poiseuille's equation

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SUMMARY

The discussion revolves around calculating the pressure drop in carotid arteries using Poiseuille's equation. The patient has two carotid arteries, each 11.2 cm long with a diameter of 5.1 mm, while the left artery has a 2.0 cm stenosis with a diameter of 3.2 mm. The blood flow rate is given as Q=8.3x10^-5 m^3/s. The user initially calculated a pressure drop ratio of approximately 1.5 but did not arrive at the correct answer, indicating a need for a more precise application of the equation.

PREREQUISITES
  • Understanding of Poiseuille's equation: Q=pi(r^4)Δp/(8ηL)
  • Knowledge of fluid dynamics, particularly in biological systems
  • Familiarity with units of measurement for blood flow and pressure
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Review the application of Poiseuille's equation in different scenarios
  • Study the effects of stenosis on blood flow and pressure in arteries
  • Learn about the significance of diameter and length in fluid resistance
  • Explore case studies involving carotid artery conditions and their implications
USEFUL FOR

Students studying physics or biology, particularly those focusing on cardiovascular dynamics, as well as healthcare professionals interested in understanding blood flow mechanics.

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Homework Statement


Hello! I don't usually ask for help on homework, but I am really stuck and my physics teacher has no clue what she is doing. She doesn't really understand the material. Here is the question: There are two carotid arteries that feed blood to the brain, one on each side of the neck and head. One patient's carotid arteries are each 11.2 cm long and have an inside diameter of 5.1mm . Near the middle of the left artery, however, is a 2.0-cm-long stenosis, a section of the artery with a smaller diameter of 3.2mm. For the same blood flow rate, what is the ratio of the pressure drop along the patient's left carotid artery to the drop along his right artery?


Homework Equations


Poiseuille's equation: Q=pi(r^4)Δp/(8ηL)

Given Value of blood flow rate, Q=8.3x10^-5 m^3/s (by same they mean the one stated earlier in the text)

The Attempt at a Solution


I tried to simply plug and chug the values but did not get the answer right. I got about 1.5 for the ratio. I know this because the homework must be submitted online. Any help would really be appreciated!
 
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Can you show what you've tried? How did you set up the calculations?
 

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