Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 85P

(a)

To determine

By what percentage the blood pressure difference between the ends of artery increased.

(a)

Expert Solution
Check Mark

Answer to Problem 85P

The percentage that the blood pressure difference between the ends of artery increased is 220%.

Explanation of Solution

Write the expression to find the percentage of increase of blood pressure difference between the ends of artery.

PB=ΔPaΔPuΔPu×100% (I)

Here, PB is the percentage of increase of blood pressure difference between the ends of artery, ΔPa is the pressure difference between the ends when arteriosclerosis is present, ΔPu is the pressure difference between the ends of the artery when it is undisturbed.

Write the expression for Poiseuille’s law for viscous flow.

ΔP=8ηLπr4(ΔVΔt)

Here, ΔP is the pressure difference between the ends, ΔVΔt is the volume flow rate, r is the inner radius of the artery, L is the length of the artery, η is the viscosity of the fluid.

Re-write the equation (I) using above Law to find the percentage of increase of blood pressure difference between the ends of artery.

PB=8ηLπra4(ΔVΔt)8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra41ru41ru4×100%=((rura)21)×100%

Conclusion:

Substitute 1 for ru and 0.75 for ra to find the percentage of increase of blood pressure difference between the ends of artery.

PB=((10.75)21)×100%=220%

(b)

To determine

By what factor the blood flow rate through the artery decrease.

(b)

Expert Solution
Check Mark

Answer to Problem 85P

The factor at which the blood flow rate through the artery decrease is 0.68.

Explanation of Solution

Write the expression for Poiseuille’s law for viscous flow.

ΔVΔt=πr4ΔP8ηL (II)

Here, ΔP is the pressure difference between the ends, ΔVΔt is the volume flow rate, r is the inner radius of the artery, L is the length of the artery, η is the viscosity of the fluid.

Write the expression for the factor of blood flow decreases in artery.

|changeinflowrateoriginalflowrate|=ΔVΔtuΔVΔtaΔVΔtu=1ΔVΔtaΔVΔtu

Substitute equation (II) in expression to find the factor of blood flow decreases in artery.

|changeinflowrateoriginalflowrate|=1πra4ΔP8ηLπru4ΔP8ηL=1(raru)4

Conclusion:

Substitute 1 for ru and 0.75 for ra to find the factor of blood flow decreased in artery.

|changeinflowrateoriginalflowrate|=1(0.751)4=0.68

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Chapter 9 Solutions

Physics

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