Human Physiology, 14th edition (2016)

464 Chapter 14

of the blood (the “thickness,” or ability of molecules to “slip

over” each other; for example, honey is quite viscous). Of par-

ticular physiological importance, the resistance is inversely

proportional to the fourth power of the radius of the vessel:

Resistance ~

Lh

r^4

where

L 5  length of vessel

h 5  viscosity of blood

r 5  radius of vessel

For example, if one vessel has half the radius of another

and if all other factors are the same, the smaller vessel will

have 16 times (2^4 ) the resistance of the larger vessel. Blood

flow through the larger vessel, as a result, will be 16 times

greater than in the smaller vessel ( fig. 14.15 ).

When physical constants are added to this relationship, the

rate of blood flow can be calculated according to Poiseuille’s

( pw ˇ a-zuh’yez ) law:

Blood flow ~

DPr^4 (p)

hL(8)

Vessel length ( L ) and blood viscosity (the Greek letter

eta, written h ) do not vary significantly in normal physiology,

although blood viscosity is increased in severe dehydration and

in the polycythemia (high red blood cell count) that occurs as

an adaptation to life at high altitudes. The major physiological

regulators of blood flow through an organ are the mean arte-

rial pressure ( P, driving the flow) and the vascular resistance to

flow. At a given mean arterial pressure, blood can be diverted

from one organ to another by variations in the degree of vaso-

constriction and vasodilation of small arteries and arterioles

(that is, by variations in vessel radius, r ). Vasoconstriction in

Physical Laws Describing Blood Flow

The flow of blood through the vascular system, like the flow
of any fluid through a tube, depends in part on the difference
in pressure at the two ends of the tube. If the pressure at both
ends of the tube is the same, there will be no flow. If the pres-
sure at one end is greater than at the other, blood will flow
from the region of higher to the region of lower pressure.
The rate of blood flow is proportional to the pressure differ-
ence ( P 1 2 P 2 ) between the two ends of the tube. The term
pressure difference is abbreviated Δ P, in which the Greek let-
ter Δ ( delta ) means “change in.”
If the systemic circulation is pictured as a single tube lead-
ing from and back to the heart ( fig. 14.14 ), blood flow through
this system would occur as a result of the pressure difference
between the beginning of the tube (the aorta) and the end of
the tube (the junction of the venae cavae with the right atrium).
The average pressure, or mean arterial pressure (MAP), is
about 100 mmHg; the pressure at the right atrium is 0 mmHg.
The “pressure head,” or driving force (Δ  P ), is therefore about
100  2  0  5  100 mmHg.
Blood flow is directly proportional to the pressure differ-
ence between the two ends of the tube (Δ P ) but is inversely
proportional to the frictional resistance to blood flow through
the vessels. Inverse proportionality is expressed by showing
one of the factors in the denominator of a fraction, since a frac-
tion decreases when the denominator increases:

Blood flow ~

DP

resistance
The resistance to blood flow through a vessel is directly
proportional to the length of the vessel and to the viscosity

Table 14.3 | Estimated Distribution of the
Cardiac Output at Rest

Organs Blood Flow

Milliliters

per Minute

Percent

Total

Gastrointestinal tract and

liver

1,400 24

Kidneys 1,100 19

Brain 750 13

Heart 250 4

Skeletal muscles 1,200 21

Skin 500 9

Other organs 600 10

Total organs 5,800 100

Source: From O. L. Wade and J. M. Bishop, Cardiac Output and Regional
Blood Flow. Copyright © 1962 Blackwell Science, Ltd. Used with permission.

Figure 14.14 Blood flow is produced by a pressure

difference. The flow of blood in the systemic circulation is

ultimately dependent on the pressure difference (Δ  P ) between

the mean pressure of about 100 mmHg at the origin of flow in the

aorta and the pressure at the end of the circuit—0 mmHg in the

vena cava, where it joins the right atrium (RA). (LA  5  left atrium;

RV  5  right ventricle; LV  5  left ventricle.)

ΔP = 100 – 0

= 100 mmHg

Pressure = 0 mmHg

Pressure = 120/80

(mean ≅ 100 mmHg)

RA

RV

LA

LV