Flow between two points within a tube is proportional to the pressure difference between the points. The flows in these two identical tubes are the same (10 ml/min was selected arbitrarily), because the pressure differences are the same.
Knowing only the pressure difference between two points will not tell you the flow rate, however. For this, you also need to know the resistance (R) to flow—that is, how difficult it is for blood to flow between two points at any given pressure difference. Resistance is the measure of the friction that impedes flow. The basic equation relating these variables is:
In words, flow rate is directly proportional to the pressure difference between two points and inversely proportional to the resistance. This equation applies not only to the cardiovascular system but to any system in which liquid or air moves by bulk flow (for example, in the urinary and respiratory systems, respectively).
Resistance cannot be measured directly, but it can be calculated from the directly measured F and AP. For example, in Figure 14-10 the resistances in both tubes can be calculated to be 90 mmHg 10 ml/min = 9 mmHg/ml per minute.
This example illustrates how resistance can be calculated, but what is it that actually determines the resistance? (The distinction between how a thing is calculated or measured and its determinants may seem confusing, but consider the following: By standing on a scale you measure your weight, but your weight is not determined by the scale but rather by how much you eat and exercise, and so on.) One determinant of resistance is the fluid property known as viscosity, which is a function of the friction between adjacent layers of a flowing fluid; the greater the friction, the greater the viscosity. The other determinants of resistance are the length and radius of the tube through which the fluid is flowing, since these characteristics determine the amount of friction between the fluid and the wall of the tube. The following equation defines the contributions of these three determinants:
where ^ = fluid viscosity
L = length of the tube r = inside radius of the tube 8/^ = a constant
In other words, resistance is directly proportional to both the fluid viscosity and the structure's length, and inversely proportional to the fourth power of the structure's radius (that is, the radius multiplied by itself four times).
Blood viscosity is not fixed but increases as hemat-ocrit increases, and changes in hematocrit, therefore, can have significant effects on the resistance to flow in certain situations. Under most physiological conditions, however, the hematocrit and, hence, viscosity of blood is relatively constant and does not play a role in the control of resistance.
Similarly, since the lengths of the blood vessels remain constant in the body, length is also not a factor in the control of resistance along these vessels. In contrast, as we shall see, the radii of the blood vessels do not remain constant, and so vessel radius—the 1/r4 term in our equation—is the most important determinant of changes in resistance along the blood vessels. Just how important changes in radius can be is illustrated in Figure 14-11: Decreasing the radius of a tube twofold increases its resistance sixteenfold. If AP is held constant in this example, flow through the tube decreases sixteenfold since F = AP/R.
Because resistance in the cardiovascular system is so often discussed in the context of blood vessels—the "tubes"—it is easy to forget that the equation relating pressure, flow, and resistance applies not only to flow through blood vessels but to the flows into and out of the various chambers of the heart. As we shall see, these flows occur through valves, and the resistance offered by a valvular opening determines the flow through the valve at any given pressure difference across it.
This completes our introductory survey of the cardiovascular system. We now turn to a description of its components and their control. In so doing, we might very easily lose sight of the forest for the trees if we do not persistently ask of each section: How does this component of the circulation contribute to adequate blood flow through the capillaries of the various organs or to an adequate exchange of materials between blood and cells? Refer to the summary in Table 14-5 as you read the description of each component to keep focused on this question.
Vander et al.: Human I III. Coordinated Body I 14. Circulation I I © The McGraw-Hill
Physiology: The Functions Companies, 2001 Mechanism of Body Function, Eighth Edition
PART THREE Coordinated Body Functions
TABLE 14-5 The Cardiovascular System
Atria Chambers through which blood flows from veins to ventricles. Atrial contraction adds to ventricular filling but is not essential for it.
Ventricles Chambers whose contractions produce the pressures that drive blood through the pulmonary and systemic vascular systems and back to the heart.
Low-resistance tubes conducting blood to the various organs with little loss in pressure. They also act as pressure reservoirs for maintaining blood flow during ventricular relaxation.
Major sites of resistance to flow; responsible for the pattern of blood-flow distribution to the various organs; participate in the regulation of arterial blood pressure.
Sites of nutrient, metabolic end product, and fluid exchange between blood and tissues. Sites of nutrient, metabolic end product, and fluid exchange between blood and tissues. Low-resistance conduits for blood flow back to the heart. Their capacity for blood is adjusted to facilitate this flow.
Therefore flow in B = 16 th of flow in A
Effect of tube radius (r) on resistance (R) and flow.
Vander et al.: Human Physiology: The Mechanism of Body Function, Eighth Edition
Circulation CHAPTER FOURTEEN
Circulation CHAPTER FOURTEEN
I. The cardiovascular system consists of two circuits: the pulmonary circulation, from the right ventricle to the lungs and then to the left atrium, and the systemic circulation, from the left ventricle to all peripheral organs and tissues and then to the right atrium.
II. Arteries carry blood away from the heart, and veins carry blood toward the heart.
a. In the systemic circuit, the large artery leaving the left heart is the aorta, and the large veins emptying into the right heart are the superior vena cava and inferior vena cava. The analogous vessels in the pulmonary circulation are the pulmonary trunk and the four pulmonary veins.
b. The microcirculation consists of the vessels between arteries and veins: the arterioles, capillaries, and venules.
III. Flow between two points in the cardiovascular system is directly proportional to the pressure difference between the points and inversely proportional to the resistance: F = AP/R.
IV. Resistance is directly proportional to the viscosity of a fluid and to the length of the tube. It is inversely proportional to the fourth power of the tube's radius, which is the major variable controlling changes in resistance.
bulk flow atrium ventricle pulmonary circulation systemic circulation artery vein aorta arteriole capillary venule microcirculation inferior vena cava superior vena cava pulmonary trunk pulmonary arteries pulmonary veins hydrostatic pressure resistance (R) viscosity
SECTION B REVIEW QUESTIONS
1. State the formula relating flow, pressure difference, and resistance.
2. What are the three determinants of resistance?
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