   Chapter 12, Problem 44PE

Chapter
Section
Textbook Problem

When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 10.0% of its normal value by a blood clot and the average pressure difference has increased by 20.0%, by what factor has the clot reduced the radius of the artery?

To determine

The factor by which the clot has reduced the radius of the artery.

Explanation

Given:

Viscosity =η

Length of artery =L

Initial volume flow rate =V1

Final volume flow rate =V2

V2V1=0.10

Initial Pressure difference =ΔP1

Final Pressure difference =ΔP2

ΔP2ΔP1=1.20

Formula Used:

Volume flow rate is given as

V= (P2P1) πr48ηL

Hence for comparison, we can write

V

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