BloodBlood is a Non-Newtonian flow, fluidnon-Newtonian fluid, in part because of its complex, inhomogeneous composition [40]. The blood solution consists of plasma, red blood cells (erythrocytes; 5 million/mm; 45% of total blood volume), white blood cells (leukocytes; 0.3%), and platelets (0.15%). (The red blood cell volume fraction is called the Hematocrithematocrit.) The red blood cells are biconcave disks that are toroidal in shape with the center partially filled in, and have a diameter of m and maximum thickness of m. CapillariesTheir diameter is about the same as the inner diameter of capillaries, but they can deform and flow in even smaller tubes. White blood cells are spherical, with a diameter of m, while the platelets are much smaller. The blood plasma is 90% water and behaves like a Newtonian flow, fluidNewtonian fluid with a Viscosityviscosity of 0.0012 Pa-s. The blood rheology is greatly altered by the red blood cells, and not much by the white blood cells or platelets because they comprise very small fractions of the blood volume. (Rheology is the study of the deformation and flow of materials, particularly unusual materials.) The blood viscosity increases with the Hematocrithematocrit, as seen in Fig. 8.10.

The effectiveViscosity viscosityBlood of blood decreases as the shear rate increases (Fig. 8.11). For very slow shear rates, this viscosity is more than 100 that of water, while at the high shear rates characteristic of flow in larger vessels it is about 4 that of water, with a value of 0.004–0.005 Pa-s.

The viscosityBlood of some fluidsViscosity changes even while the strain rate is constant. Blood is a thixotropic fluid, for which the shear stress decreases while the strain rate is constant. Still, for our purposes it will be adequate to treat blood as a Newtonian flow, fluidNewtonian fluid, even though the velocity flow profile is not the ideal Parabolic flowparabolic form for a Newtonian fluid (Fig. 7.​13).

Walls of arteriesArteries contain inner layers that are 1–2 endothelial (lining) cells thick—along with elastic issue (composed of collagen and elastic proteins). This innermost region surrounding the opening—the lumen—is known as the tunica intima. Next in the wall comes a layer of circular, smooth muscle fibers interspersed with elastic tissue (the tunica media) and finally connective tissue (the tunica adventitia) (Fig. 8.12, also see Fig. 8.43 below). Walls of veinsThe walls of veins have a thickness w that is typically , where d is the lumen diameter; they are thinner than the walls in arteries of corresponding diameters, for which . AortaThe aorta and other large arteries contain much elastic tissue and stretch during Systolesystole and recoil during Diastolediastole. The walls of the arterioles contain less elastic tissue and more smooth muscles, and stretch relatively little. CapillariesThe walls of the capillaries are composed of a single layer of endothelial cells. The diameters of the capillaries are so small that red blood cells can barely pass through them.

Walls of arteries Walls of veinsApproximately 70% of the walls of arteries and veins is composed of water, which is not elastic, except in how it withstands compression. The other 30% consists of the dry mass: Elastin Collagen Smooth muscleselastin, collagen, and smooth muscle fibers, each having different materials properties. As discussed in Chap. 4, elastin is rubber-like and has a Young’s or elastic modulusYoung’s modulus of 3  Pa; it can be stretched to twice its relaxed length. Collagen is much stiffer, having a Young’s modulus of 1  Pa. Ultimate tensile stress (UTS)Elastin has an ultimate tensile stress (UTS) less than 5% of that of collagen. Smooth muscle has a Young’s modulus more like that of elastin, with  Pa when relaxed and 2  Pa when active. About half the dry mass in vessels is elastin and collagen, with more elastin than collagen in the Aortaaorta (1.5) and relatively less elastin in other arteries (0.5) and veins (0.3). Veins contain less elastin than arteries. The fraction of smooth muscle in the dry mass averages to 50%, and is 25% in the aorta, and increases to 60% more peripherally in the arteries and arterioles. The mechanical properties of these vessels (Chap. 4) also depend on the tissue to which they are attached. CapillariesThis is particularly significant for capillaries, because the vessel walls are essentially a single layer of endothelial cells.

Blood pressure BloodBlood pressure is needed to push blood flow. Figure 8.13 is a schematic of the mean arterial and venous blood pressure at different positions in the circulation cycle, for a person lying horizontally. ArteriesThe oscillations in blood pressure along the major arteries in Systemic circulation systemsystemic circulation reflect the oscillating pressure of this blood as it leaves the Aortaaorta, at pressures between 80 mmHg (, at Diastolic pressure Diastolediastole) and 120 mmHg (, Systolic pressure Systoleat systole) (Fig. 8.13). Because systole lasts for about 1/3 of the cycle and diastole for about 2/3, the mean blood pressure is a weighted sum,
or (1/3)120 mmHg + (2/3)80 mmHg 94 mmHg in this example. This difference in Blood pressurepressure of 40 mmHg between systole and diastole is the Arterial pulse arterial pulse pressure . We will see that blood Flow rate of bloodflows at a speed of 20 cm/s in these Systemic circulation systemsystemic arteries, so with a heart rate of about 1 Hz = 1 cycle/s it is reasonable that there are quasiperiodic pressure variations every 20 cm or so. Arteries CapillariesMuch of the pressure drop in the arterial system is in the arterioles (small arteries) and the capillaries. We will see that this can be attributed to viscous flow. VeinsThere is very low pressure in the veins. It is too little pressure to pump the blood back to the Heartheart—even with the large diameters of the veins and consequently low Flow, vascular resistanceresistance to flow (7.​24). There is a Peristalsisperistaltic pumping mechanism by muscles surrounding the large veins that assists the return of venous blood to the heart, with one-way valves to prevent backflow (Fig. 8.14). (Similarly, blood flow in the capillaries is usually not continuous, but is turned on and off every few seconds or minutes, due to sphincter muscles that can contract the feeding arterioles (vasomotion).) Pulmonary circulation systemThe pulmonary system mirrors this Systemic circulation systemsystemic circulation, except the Blood pressurepressures are all lower. Figures 8.13, 8.15, and 8.16 show the blood pressure and flow speed at different points in the arterial tree.

The pumping cycle sets up a pressure pulse wave in addition to the hydrostatic Blood pressurepressure variation. This pulse wave speed is independent of the speed of blood flow—and is faster than the blood flow speed—and is 4 m/s in the Aortaaorta, 8 m/s in the large arteries, and 16 m/s in the small arteries of young adults.

Blood pressureWhen you stand upright vertically (Fig. 8.17) there is an additional pressure , where h is the height relative to the Heartheart. This is approximately the height in the upper arm where blood pressure measurements are made. For  g/cm,060 kg/m,  m/s and  m, this pressure is 10,400 N/m,400 Pa  mmHg (with 1 MPa 7,600 mmHg). Arteries VeinsAt any given height, the driving pressure difference from the arteries to the veins is unchanged. Also, this pressure change is not important when considering pressure changes between the inside and outside of a vessel because is added both inside and outside the vessel.

Still, this effect of gravity can be significant. Blood pressure AortaThe blood pressure at the aorta has to be high enough to pump the blood to the top of your brain. This distance is about  cm, so the pressure drop is about 30 mmHg (Diastolic pressurecompared to the diastolic pressure of 80 mmHg). Problems 8.1 and 8.2 explore what happens to cranial Brainblood circulation in humans in rapidly climbing jets and on more massive planets with higher g, and also in giraffes. One manifestation of this effect of gravity is potential fainting when you stand. When you stand up, the volume of blood in the Legsleg Veinsveins increases and the pressure in the veins pumping blood back to the heart decreases. This can decrease the Cardiac outputcardiac output and the flow of blood to the brain. This rarely happens because there is a reflex constriction of the veins in the Legslegs (due to a contraction of the skeletal muscle surrounding the veins, Fig. 8.14) that limits the blood pool and an arteriolar constriction that increases flow Flow, vascular resistanceresistance and lessens the decrease in arterial blood pressure. The effect of gravity on humans—who normally stand upright—also explains why standing on your head for long periods is not advisable (Problem 8.3). The veins in your head are not designed to pump blood back to the heart (as are those in the lower body). Also, your feet would stop getting blood. It also explains why varicose Veinsveins are worse when you stand upright, because blood then needs to be pumped up.

Feedback and controlBody control of blood pressure is briefly described in Chap. 13.

Arteries VeinsThe mechanical properties of blood vessels can be measured under two types of conditions. (1) The length of a given vessel can be kept constant, while its diameter is measured as a function of the distending pressure. This leads to a tensile stress on the wall, directed around the circumference, which is called the circumferential or hoop stress. (2) The diameter of a vessel can be kept constant, while its length is measured as it is stretched longitudinally. Examples of both are shown in Fig. 8.18.

Arteries Flow rate of blood Walls of veinsThe flow of blood in arteries is affected by changes in the Heart rate, beatheart beat rate and Stroke volumestroke volume (which is the volume pumped per beat), and also by changes in the arteries themselves that Feedback and controlcontrol their diameters by chemical and neural mechanisms.

Figure 8.19 is a schematic describing the flow in a vessel of length L, with a volumetric Flow rate of bloodflow rate in and out. In steady state , which is averaged over a heart beat. At the beginning of the vessel the Blood pressurepressure is and at the end it is . The pressure outside the vessel is , which can be taken to be 0 when using a Gauge pressuregauge pressure. The volume of the vessel is V. The relation between these various parameters depends on the properties of the vessels.

Flow rate of bloodThere are two physical attributes of blood vessels in steady state. (a)Flow, vascular resistance They have a resistance to flow, and so they need a pressure difference along the length of the vessel to drive the blood flow. (b) They have a Compliance compliance in response to a distending pressureBlood pressure. This is much like a balloon expanding when the pressure inside increases much above that outside.

One special case is a rigid vessel with constant volume V, which is called a Resistance vessel resistance vessel (Fig. 8.20). Equation (7.​25) applies to this vessel, so
or
where the Flow, vascular resistancevascular resistance is for a tube with radius r. The former equation has the same form as Ohm’s Law , which relates the drop in voltage, , when a current of charges I traverses a structure with electrical resistance .

A second special case is an elastic vessel that has no Flow, vascular resistancenoticeable resistance, which is called a Compliance vessel compliance vessel. There is no pressure drop, so . One model (Fig. 8.21) of the properties of such a vessel isCompliance
where is the compliance and is taken to be 0. Because the vessel usually has a volume with no pressure, called the dead volume , a better relation is
Note that a property of the Resistance vesselresistance vessel, namely the Flow rate of bloodflow rate, is affected by the Blood pressurepressure drop along (and inside the vessel), while a property of the Compliance Compliance vesselcompliance vessel, its volume, is affected by the pressure difference between the inside and outside of the vessel. We can also describe compliance by changes in the area A
where is the area with no pressure difference and is the compliance per unit length, or by changes in the radius r
where is the radius with no pressure difference. Because and for a vessel of radius r and length L, these formulations can be interrelated, with and (the latter set being true for small changes in r or V).

Blood pressureReal vessels have some attributes of both types of vessels. Still, the Aortaaorta, Arteries Veinslarge arteries and large veins are much like Compliance vesselcompliance vessels. We will see that the pressure drops along them are relatively small. CapillariesArterioles, capillaries, and venules act like Resistance vesselresistance vessels. We will see that they, and in particular the arterioles, are the main sites of the pressure drop, and this is the reason why the Heartheart needs to pump blood to such high Blood pressurepressures.

Blood pressureWe will use Poiseuille’s LawPoiseuille’s Law (7.​25) to estimate the pressure drop across the Arteries Aortaaorta, large arteries, arterioles, and capillaries, and compare these results to the plot in Fig. 8.13 (and also see Fig. 8.15). First we calculate the Flow, vascular resistanceresistance for a standard radius  cm and standard length  cm and scale the results for each specific case. With the viscosity  Pa-s  (N-s/m poise for whole blood at 37 C

Flow, vascular resistance Blood pressurewhere we have used 0.1 N/mm atm.  mmHg. The units in (8.9) are mmHg-s/cm. This is the resistance when the pressure difference is 1 mmHg and the flow rate is 1 mL/s, and is also known as a PRU, a peripheral resistance unit. This unit is commonly used in physiology.

Flow, vascular resistance Blood pressureThe resistance of a vessel of an arbitrary length and radius is
and so
The total Flow rate of bloodflow rate, , from the aorta, enters the Arterieslarge arteries, and the whole flow from the large arteries enters the arterioles, and finally this whole flow enters the Capillariescapillaries. In each level of flow we will model the arteries as n parallel vessels of roughly equivalent length and radius carrying roughly the same flow (Fig. 8.22), where n increases for each successive level of flow. So in a given level of flow with n vessels, the flow rate in each vessel is .

Flow, vascular resistance Blood pressureWith  cms and , we get

This is the pressure drop across any vessel in a given level of flow and, because they are in parallel, it is the pressure drop across the entire given level of arterial flow. We now determine this for the various levels of arteries.

Aorta Flow, vascular resistance Aorta. There is one aorta () with  cm and  cm, and so across the aorta is 0.025 mmHg, which is insignificant.

Arteries Flow, vascular resistance Largest arteries. There are about 200 large arteries with  cm and  cm, and so is 1.4 mmHg, which is pretty insignificant.

Smallest arteries and arterioles. Flow, vascular resistanceThere are about arterioles with m and  cm  mm, and so is 91 mmHg, which is very significant.

Capillaries. Capillaries Flow, vascular resistanceThere are about capillaries with m and  cm  mm, and so is 8.2 mmHg, which is fairly significant.

Flow, vascular resistanceWe could have just plugged the parameters for each vessel directly into (7.​25), without calculating , but our scaling approach does provide some new insight.

Flow, vascular resistance Blood pressureThese estimates agree with what we would expect from Fig. 8.13. CapillariesAlso, arterioles and capillaries are seen to be well modeled as Resistance vesselresistance vessels. The Aortaaorta and large arteries have very small pressure drops across them, and behave more like Compliance vesselcompliance vessels. VeinsVeins have larger radii than the corresponding arteries, and consequently much lower resistances and pressure drops across them.

Flow, vascular resistanceAlong any vessel there is obviously a linear pressure drop with distance x along the vessel. Poiseuille’s LawThis is seen from Poiseuille’s Law, (7.​25), or, expressing this in the differential limit and recognizing that this change in pressure is negative,
where this has also been given in terms of the area A. This represents a “distributed” or “transmission-line” view of blood flow, in which flow is analyzed per unit length along the vessel, whereas in (8.2) and (8.11) flow was analyzed with the vessel as a “lumped” parameter (see Appendix D).

Flow, vascular resistance Blood pressureWe can study the pressure drop in Clogged arteriesclogged arteries. There could be a larger pressure drop for the same Q or a smaller Q for the same pressure drop if r decreases, as occurs with clogged arteries, or with fewer vessels. This can stimulate an increase in Blood pressureblood pressure to maintain the flow rate or lead to a reduction in flow at a given inlet pressure, which is what actually happens in coronary artery disease.

How can we “optimize” the design of resistive vessels and how such vessels bifurcate and otherwise branch into smaller vessels (and what does it really mean to optimize the design)? Bifurcated flowSee Problems 8.34–8.37.

Blood flow in vessels is not uniform. We have implicitly been assuming that the blood flow is Parabolic flowparabolic ((7.​40) and Fig. 7.​11) because we are modeling blood as a Newtonian fluid. However, the parabolic profile of blood flow speed in a resistive vessel from (7.​40) is not quite accurate. Because whole blood is not Non-Newtonian flow, fluidNewtonian, the steady-state profile is not parabolic, as is seen in Fig. 7.​13. Moreover, we have assumed that flow is always steady state (ignoring the pulsatile nature of blood flow); however, it enters the steady state regime only a certain distance after a Bifurcated flowbifurcation (7.​54)–(7.​56). This approach to steady-state flow is depicted for a specific Initial conditionsinitial condition in Fig. 7.​11.

Compliance vessel ComplianceIn Chap. 7 we showed that (8.4) and (8.5) are reasonable models of an elastic compliance vessel. We can determine the compliance of such vessels and analyze how blood pressure can increase the volume of vessels.

For large arteries, the Young’s modulus Y, radius r and wall thickness w are interrelated by , with = 2.0 MPa, = 22.53/cm, and = 86.5 kPa [57]. Using (7.​46), the compliance of a vessel per unit volume is 2r / wY, so this fit shows that the compliance per unit volume is the same for large arteries with larger radius  MPa during systole. The value of Y for such vessels is about 1 MPa (Table 4.​2) and so . The thickness of arterial walls is typically 1/5 of the radius, so . Using (7.​43), this means that the fractional increase in radius of these vessels due to this internal pressure is 8% and the fractional increase in volume (and area) is 16%—both sizeable fractions. (We did not need to explicitly determine the compliance to calculate this.) Also, this predicts that the radius changes by 3% during each Heart rate, beatheart beat during the changes between systolic (120 mmHg) and diastolic (80 mmHg) pressure. Veins are also Compliance vesselcompliance vessels.

Pulmonary arteries in the lungs are more compliant than those in the systemic system. Veins have compliances about 24 those of arteries because they have larger radii and more compliant walls. Because of this and their larger radii, they can store much blood, especially when the venous pressure is increased only a little. When the pressure in arteries and arterioles becomes very low, and below that of the fluid outside them, they can collapse and prevent flow of the blood plasma for 5–10 mmHg and for red blood cells below 20 mmHg [40].

Flow, vascular resistance ComplianceIf a vessel is resistive and compliant [40, 50], the change in Blood pressurepressure with distance is
using (8.6). Setting this equal to from (8.14) and bringing the A terms to the left and the x terms to the right, gives
where the flow rate Q is a constant. After integrating over a vessel length from to , we get
and after using (8.6)
(See Appendix C.)

Flow, vascular resistance ComplianceBoth terms on the left side can be expanded to four terms. The first terms are both , which cancel, and for relatively small compliance () only the next two of the remaining three terms in each need to be retained, giving
Poiseuille’s LawThis is Poiseuille’s Law (7.​24) with a correction for compliance. So, for a rigid wall vessel () the Flow rate of bloodflow rate Q is linear with the Blood pressurepressure drop, but when compliance is included, the variation with pressure drop is between linear and quadratic. This relation says that for a given pressure drop, the flow rate is increased due to the compliant nature of the vessel and that a smaller pressure drop is needed to achieve a given flow rate. (The smaller pressure drop in veins than in arteries is explained both by their larger radii and their larger compliances.) The next term in the expansion within the brackets is (see Problem 8.26).

Equation (8.19) can also be expressed in terms of the vessel radius
which can also be obtained directly by integrating Poiseuille’s Law expressed in terms of the radius (8.14) and using (8.7) (see Problem 8.27). The next term in this expression obtained by integrating Poiseuille’s Law expressed in terms of the area, as given above, and that by integrating the form using the radius (Problem 8.28) are different. At first this may be surprising, but there is a subtle difference. In the former approach is assumed to be constant (as is ) and in the latter is assumed to be constant. Both compliances cannot be constant because of how they are defined (8.4)–(8.7), but they are approximately equal for small vessel expansions. This demonstrates how the details of a model can be very important.

The resistive pressure drop in a vessel also affects the volume of a compliant vessel [40]. With (using (8.14)) and with (using (8.6)), leads to . Integrating from 0 to L gives
or
Using (8.18) and gives
and for small pressure drops this becomes
The second term is the effect of the average pressure in the vessel and the third term shows the effect of the pressure drop due to resistance. With no pressure drop, this relation reduces to (8.5) with P equal to the average pressure in the vessel, . (Why?)

The electrical analog of blood flow is described in Appendix D.

Walls of arteries Walls of veins Blood pressureThe pressure inside blood vessel walls P exceeds that outside , by . How large of a tension should the vessel walls be able to withstand to support this positive pressure differential? Chapter 7 showed the answer is provided by the Law of LaplaceLaw of Laplace for hollow cylinders (7.​4). Radius of curvature, in Law of LaplaceFor a cylinder of radius of curvature R, this tension T is
Table 8.5 Capillaries Blood pressureshows that the tension capillaries need to withstand is very small because of their small radius. This circumferential stress, the tension (force per tube length) divided by the vessel wall thickness w, is surprisingly similar for these very different vessels. T/w can be compared to the UTS of such vessels.

Arteries Curved arteries Centripetal force Blood pressure Radius of curvature, in flow in curved tubesIn Chap. 7 we showed that the arterial walls feel a pressure due to the difference in hydrostatic pressure inside and outside the vessel. This pressure is felt equally around the wall. Walls of arteriesWhen blood flows in an artery that curves, a force equal to the Centripetal forcecentripetal force is felt on the arterial wall on the outer surface of the curve to change the direction (but not the magnitude) of the momentum vector of blood flow. How large is this force? Is it comparable to the uniform hydrostatic pressure? Does it constitute a significant extra load on the arterial wall?

Arteries Curved arteries Centripetal force Radius of curvature, in flow in curved tubesFor an artery of internal radius R that is turning with a radius (Fig. 7.​17), with blood of density and average flow speed u, (7.​57), this peak pressure is
This is largest for the fastest blood flow, which is in the Aortaaorta. Using  g/cm,  cm,  cm, and  cm/s, we find  mmHg. This 5 mmHg is the extra pressure that must be supplied by the outer aorta wall to turn the blood around the aortic arch. This is small compared to the typical average aorta pressure of 100 mmHg, and does not likely promote pathological conditions such as Aneurysmsaneurysms.

Capillaries Systemic circulation system Blood Blood pressure Osmotic pressureThe purpose of systemic circulation is to supply blood to the capillary bed. We have seen that pressure is needed to bring the blood to the capillaries. There is Diffusiondiffusion and bulk flow between the blood in the capillaries and the interstitial fluid. Diffusion Walls of capillaries CapillariesDiffusion across the capillary wall transports oxygen, which is carried in red blood cells, and carbon dioxide, which is dissolved in the blood. (Not enough oxygen can be directly dissolved in the blood for our metabolic needs.) In the systemic capillaries there is net diffusion of oxygen out of the capillaries and carbon dioxide into them. In the Pulmonary circulation systempulmonary capillaries there is net diffusion of oxygen into the capillaries and carbon dioxide out of them. There is also bulk flow of fluid across the capillary walls due to the net pressure across the walls.

Capillaries Blood pressureThere are two forces driving this bulk transport: the force/area mechanical pressure P we have been discussing, which we will call hydrostatic pressure in this section, and a chemical driving force, called Osmotic pressure osmotic pressure, . The osmotic pressure characterizes the flow across a semipermeable membrane that occurs to equalize the concentrations of solutes on either side of the wall. This drives species that can permeate across the membrane, such as water, across it from the side of low concentration of solute to the side of high concentration. Osmotic pressureFor low concentrations, the osmotic pressure is given by the van’t Hoff equation
where is the density (or concentration) of the solute in solution in moles per unit volume. This looks deceptively similar to the Ideal gas lawideal gas law (7.​2). It is the difference in the sum of these on either side of the Walls of capillariescapillary walls, , that drives the net transport across these walls.

Capillaries Blood pressure Osmotic pressureAs seen in Fig. 8.23, the hydrostatic force in the capillary is always greater inside the vessel than outside, and it decreases from about 36 mmHg at the arteriole side to 15 mmHg at the venule end because of viscosity. If this were the only driving force, there would be a large net flow of fluid from inside the capillary to the interstitial fluid! Small molecules, such as oxygen and carbon dioxide, are able to diffuse across the capillary wall, but larger molecules, such as proteins, cannot. Because there is a much higher density of proteins in the Bloodblood than in the interstitial fluid, there is a chemical driving force of fluid into the capillary to try to equalize these densities. This leads to a net osmotic pressure of about 25 mmHg into the capillary. In Fig. 8.23, the net pressure is 36 mmHg 25 mmHg = 11 mmHg outward at the arteriole end and 15 mmHg 25 mmHg = 10 mmHg inward at the venule end. Therefore, there is net flow out of the capillary in the arteriole end and net flow into the capillary in the venule end. There is a small imbalance in this and a small net bulk flow out of the capillary.

Capillaries Blood pressureWe have assumed that the flow in all blood vessels, including the capillaries, is Laminar, streamline, steady flowlaminar. This cannot be really true for capillaries because many capillaries have an inner diameter of 5 or 6 m and the red blood cells have a diameter of about 7.5 m. The red blood cells deform to pass through the capillary and the resulting flow is called Bolus flow bolus flow. The red blood cells form plugs and the blood plasma is trapped in the regions between these plugs and moves in Streamlinesstreamlines. Nowhere else in the body is the multicomponent nature of blood more apparent.

BloodOne major function of this capillary blood flow is the transfer of oxygen to the cells, leaving oxygen-depleted blood in the veins. As in (6.​18), the rate of body consumption of O, equals the product of the Cardiac outputcardiac output (see below) and the difference in the oxygen partial pressure in the Arteries Veinsarteries and veins,
If the Lungslungs are bringing in air fast enough, then is fixed, and during aerobic Exerciseexercise increases linearly with . For a person with average fitness, the maximum Flow rate of bloodblood flow rate is 19 L/min, for a highly fit person it is 25 L/min, and for an elite athlete it can be 35 L/min.

BloodOxygen combines with Hemoglobinhemoglobin in the red blood cells in the lungs where the partial pressure of oxygen is high, about 100 mmHg. It is transported in the Arteries Veinsarteries to the tissues where it is released because the partial pressure of oxygen is low—and it is then used. The blood in the veins is then depleted in oxygen. Figure 8.24a shows the hemoglobin–oxygen dissociation curve. Clearly, hemoglobin is over 90% saturated with O for partial pressures above 60 mmHg O. Increased CO levels, increased temperature, and decreased pH all shift this curve to the right (Fig. 8.24b), which improves body performance. In Fig. 8.24a the dissociation curve for the lung is seen to be to the left of that in the tissues because the pH is higher and the CO level is lower in the lung, increasing oxygen binding in the lungs relative to that in the tissues. During Exerciseexercise, the muscle tissue pH falls and the local partial pressure of CO and the local temperature increase. All of these changes move the curve to the right and this leads to more oxygen release (Fig. 8.24b). During exercise increases from the resting value of about 50 mL of oxygen per L of blood to 150 mL/L in normal people at (and to 160–170 mL/L in very fit people), in part because blood flow is being diverted from the organs to the muscles, where oxygen extraction is higher because of the exercise (see Fig. 8.24).

Flow rate of blood Heart BloodThe heart pumps about 80 mL (= 80 cm) of blood per contraction; this quantity is called the Stroke volume stroke volume . The pump rate is the heart beat rate F of about 60/min or 1/s = 1 Hz. Cardiac outputThe cardiac output or total volumetric Flow rate of bloodflow rate is the product of these two
or about 80 cms  L/min. The total volume of blood is about 4.5–5.0 L, so all the blood is pumped throughout the body every minute. Arteries Veins CapillariesThe flow rate in the arteries, arterioles, capillaries, venules, and veins are all the same because of the Continuity equationcontinuity of flow. ( is actually a little less in the venules and veins because of the net fluid loss in the capillaries.) PregnancyDuring the full term of pregnancy, cardiac output increases by 30%, from 5.0 to 6.7 L/min due to increased stroke volume and heart rate, and the blood volume increases by 40–50% [47, 55].

Flow rate of bloodThe total flow in each of these vessel systems, , equals the total cross-sectional area A times the blood speed u, . The parameters A and u are plotted in Fig. 8.16, which shows this inverse relationship for a flow rate of 90 cms. The cross-sectional area of the Aortaaorta is 3 cm, so in the aorta  cms)/3 cm cm/s. CapillariesIn the capillaries the flow speed is much slower, (90 cms cm cm/s  mm/s. The net cross-sectional area in the capillaries is larger (4,000 cm) even though they are very small (3.5 m in radius) because there are so many of them (10). In the vena cava the flow speed is relatively fast (90 cms)/18 cm cm/s. Arteries VeinsIn the arterial and venous systems, the smaller the vessel radius, the larger the total cross-section of all vessels in that order and the slower the blood speed. These are actually average blood flows during each cycle.