   Chapter 12, Problem 37PE

Chapter
Section
Textbook Problem

(a) Suppose a blood vessel's radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?

(a)

To determine

The factor by which the pressure difference will increase.

Explanation

Given:

Initial pressure difference =ΔP1

Final pressure difference =ΔP2

r2r1=0.90

Formula Used:

Pressure difference is inversely proportional to fourth power of radius

ΔP1r4 hence , we can write ΔP1ΔP2=r24r14

(b)

To determine

The effect on flow rate, if turbulence is created by obstruction.

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