1 Nov 2021
Problem 60c
Page 310
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
1 Nov 2021
Given information
Note that given,
The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended by the heart in pumping the blood. In particular, this energy is reduced when the resistance of the blood is lowered. One of Poiseuille’s Laws gives the resistance of the blood as
where is the length of the blood vessel, is the radius, and is a positive constant determined by the viscosity of the blood.
Step-by-step explanation
Step 1.
Draw the required diagram,
Divide the into two paths, one from to and one from to
Therefore,
The total resistance of as the sum of the resistance along and
Now, Use Poiseuille’s Law