   Chapter 8.4, Problem 20E

Chapter
Section
Textbook Problem

High blood pressure results from constriction of the arteries. To maintain a normal flow rate (flux), the heart has to pump harder, thus increasing the blood pressure. Use Poiseuille’s Law to show that if R0 and P0 and are normal values of the radius and pressure in an artery and the constricted values are R and P, then for the flux to remain constant. P and R are related by the equation P P 0 = ( R 0 R ) 4 Deduce that if the radius of an artery is reduced to three-fourths of its former value, then the pressure is more than tripled.

To determine

To prove: The pressure is more than tripled when the radius of an artery is reduced to three-fourths of its former value by using Poiseuille’s law

Explanation

Given information:

P0 and R0 are normal values of the radius and pressure in an artery.

Pressure and radius are related by the equation PP0=(R0R)4 .

Calculation:

Show the pressure and radius are related by the equation as follows:

PP0=(R0R)4 (1)

Radius of an artery is reduced to three-fourths of its former value.

R=34R0

Substitute 34R0 for R in Equation (1)

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