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

Question

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Answer 1

Question

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

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Answer 2

Question

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

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Answer 3

Question

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

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Answer 4

Question

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

Answer 6

Chapter 9, Problem 85P

(a)

To determine

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

(a)

Expert Solution

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.

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

Answer 7

Chapter 9, Problem 85P

(a)

To determine

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

Answer 8

(a)

Expert Solution

Answer to Problem 85P

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

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

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

$PB=ΔPa−ΔPuΔPu×100%$ (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.

$PB=8ηLπra4(ΔVΔt)−8ηLπru4(ΔVΔt)8ηLπru4(ΔVΔt)×100%=1ra4−1ru41ru4×100%=((rura)2−1)×100%$

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.

$PB=((10.75)2−1)×100%=220%$

Answer 13

(b)

To determine

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

(b)

Expert Solution

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.

$|change in flow rateoriginal flow rate|=ΔVΔtu−ΔVΔtaΔVΔtu=1−ΔVΔtaΔVΔtu$

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

$|change in flow rateoriginal flow rate|=1−πra4ΔP8ηLπru4ΔP8ηL=1−(raru)4$

Conclusion:

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

$|change in flow rateoriginal flow rate|=1−(0.751)4=0.68$

Answer 14

(b)

To determine

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

Answer 15

(b)

Expert Solution

Answer to Problem 85P

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

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

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.