\"Homer\'s Blood Pressure\" The volume of blood that passes through a cross-sect
ID: 2882567 • Letter: #
Question
"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?
"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 andR, 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?
Explanation / Answer
As the flux remains constant PR4/8l = P0R04/8l
=> P = P0R04/R4
after 10 years from now radius of the aretery will be R = R0(1 - 10/100)
R = R0(0.9)
=> Homers blood pressure after 10yrs is given by P(10) = P0R04/ (R0(0.9))4
=> P(10) = 1.524P0
So Homers blood pressure increases by 1.524 times of initial blood pressure
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