In this problem we model the human circulatory system as an electronic circuit.

Question

In this problem we model the human circulatory system as an electronic circuit. Assuming that the heart is a 100-V battery:

a) Determine the electric current (representing blood flow) through the circulatory system shown below.

b) Now assume that the aorta has considerable plaque buildup and its diameter is reduced so that its resistance increases by a factor of 5. (You may recall from your study of fluid flow that the resistance is proportional to 1/r^4, so a fivefold increase in resistance is not rare). What battery emf is needed to get the same current as in (a)?

c) Suppose instead that the diameters of the arterioles are reduced so that their resistance increases by a factor of 2 -a condition called essential hypertension. In this case, what battery emf is needed to get the same current (blood flow) as in (a)?

Explanation / Answer

a)

equivalent resistance

Req=2+10+(6/4)+(32/7)+(50/4)

Req=30.57 ohms

Electric current flowing is

I=E/Req=100/30.57

I=3.27 A

b)

Given

Raorta=5*10=50 ohms

equivalent resistance

Req=2+50+(6/4)+(32/7)+(50/4)

Req=70.57 ohms

Emf of the battery is

E=I*Req=3.27*70.57

E=230.8 Volts =231 Volts (approx)

c)

Rarterioles=2*50=100 ohms

equivalent resistance

Req=2+10+(6/4)+(32/7)+(100/4)

Req=43.07 ohms

Emf of the battery

E=43.07*3.27

E=140.84 Volts =141 Volts

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