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 67P

(a)

To determine

The pressure difference of the blood flows through an artery.

(a)

Expert Solution
Check Mark

Answer to Problem 67P

The pressure difference of the blood flows through an artery is 50Pa.

Explanation of Solution

Write the equation for volume flow rate.

ΔVΔt=Av (I)

Here, ΔV/Δt is the volume flow rate of the blood, A is the area of cross section of an artery, and v is the speed of the blood flows in the artery.

Write the equation from poiseuille’s law for viscous flow.

ΔVΔt=πΔPr48ηL (II)

Here, ΔP is the change in pressure, r is the radius of the artery, η is the coefficient of viscosity of blood, and L is the length of the artery.

Compare the equation (I) and (II).

πΔPr48ηL=Av

Solve the above equation for ΔP.

ΔP=(8ηLπr4)Av

Replace πr2 for A in the above equation.

ΔP=(8ηLπr4)πr2v=8ηLvr2 (III)

Conclusion:

Substitute 2.1×103Pas for η, 0.20m for L, 6.0cm/s for v, and 2.0mm for r in equation (III).

ΔP=8(2.1×103Pas)(0.20m)(6.0cm/s)(0.01m1cm)[(2.0mm)(0.001m1mm)]2=8(2.1×103Pas)(0.20m)(0.060m/s)(0.0020m)2=50400×103Pa50Pa

Therefore, the pressure difference of the blood flows through an artery is 50Pa.

(b)

To determine

Find the pressure difference of the blood flows through a capillary.

(b)

Expert Solution
Check Mark

Answer to Problem 67P

The pressure difference of the blood flows through a capillary is 1100Pa.

Explanation of Solution

Write the relation between pressure difference from the equation (III).

ΔP=8ηLvr2

Here, ΔP is the change in pressure, r is the radius of the capillary, η is the coefficient of viscosity of blood, L is the length of the capillary, and v is the speed of the blood flows in the capillary.

Conclusion:

Substitute 2.1×103Pas for η, 1.0mm for L, 0.60mm/s for v, and 3.0μm for r.

ΔP=8(2.1×103Pas)(1.0mm)(0.001m1mm)(0.60mm/s)(0.001m1mm)[(3.0μm)(106m1μm)]2=8(2.1×103Pas)(0.0010m)(0.00060m/s)(3.0×106m)2=1120Pa1100Pa

Therefore, the pressure difference of the blood flows through an capillary is 1100Pa.

(c)

To determine

Compare the average blood pressure in 100torr.

(c)

Expert Solution
Check Mark

Answer to Problem 67P

The average blood pressure in 100torr is 13kPa.

Explanation of Solution

The average blood pressure of the human being is about 100torr.

Compare the answers in part (a) and (b) to average blood pressure.

(100torr)(101.3kPa760.0torr)=13kPa

Thus, the 100torr is approximately 13kPa which is much larger than both pressures found in part (a) and (b).

Hence the pressure change in part (b) is more than 20 times greater than the pressure change in (a). The great arteries and wide veins present little resistance to blood flow compared to capillaries.

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