I need help with approaching this huge word problem!
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 flux 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?
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
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?