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 Chapter 9.4 Puzzle
This assignment is due 48 hours after the Chapter Test is
given.
- Puzzle solutions are due by 5:00 PM two days after the Chapter
Test.
- Puzzles are worth 10 points of extra credit each.
- Answers must be accompanied by valid reasoning. Just like
the tests, the answer alone isn't enough!
- Please enter your solution in the text area at the bottom
of this page. DON'T FORGET TO GIVE YOUR NAME!
"Homer's Blood
Pressure"
The volume of blood that passes through a cross-section of
an artery (of radius R, with pressure difference P)
per unit time is given by the formula
( is the length of the artery and
 is viscosity of the blood - both
are assumed constant). F is often called the flux. High
blood pressure results from constriction of the arteries. As
the radius of the arteries shrinks, the blood pressure needs
to increase to maintain a constant flux. Suppose 
and  are the initial radius and the
initial pressure. Then the flux is  .
If the pressure and radius at some other time are P and
R, then the flus is  . Using
the fact that flux must remain constant, determine an expression
for P in terms of R, ,
and . As the years go by, the diameter
of Homer's arteries is given by  ,
where t is the number of years from the present.
1. What is Homer's blood pressure in terms of his original
blood pressure 10 years from now?
2. Homer's doctor would like to perform angioplasty to enlarge
the arteries when his blood pressure has doubled. When will this
happen?
Don't forget to explain your answer
as clearly as possible.
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