   Chapter 12, Problem 49PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider a coronary artery constricted by arteriosclerosis. Construct a problem in which you calculate the amount by which the diameter of the artery is decreased, based on an assessment of the decrease in flow rate.

To determine

Construct a problem in which you calculate the amount by which diameter of the artery is decreased, based on an assessment of the decrease in flow rate.

Explanation

Given:

Let us assume the following values

velocity before blockage  = 0.6 m/svelocity after blockage  = 0.8 m/sFlow before blockage = 0.1 m3/sFlow after blockage = 0.085 m3/s

Formula used:

A1=(Q1)/v1π4d12= (Q1)/v1A2=(Q2)/v2π4d22= (Q2)/v2

d1 = diameter of the artery before blockage

A1= Area of the artery before blockage

d2 = diameter of the artery after blockage

A2= Area of the artery after blockage Q1= flow before the blockage

Q2= flow after the blockage

Calculation:

As we know that the area of the artery is directly proportional to the flow through it considering that arteries are nothing but cylindrical tube. Thus substituting the values in above equation, we get-

A1=(Q1)/v1π4d12=(Q1)/v1=(0

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