is pumped out each minute (the cardiac output). because of this, the velocity of blood flow across each level of the circulatory system is primarily determined by the total cross-sectional area of that level. cardiac output is determined by two methods. one is to use the fick equation: c o = v o 2 / c a o 2 − c v o 2 o_-c_o_ the other thermodilution method is to sense the temperature change from a liquid injected in the proximal port of a swan-ganz to the distal port. cardiac output is mathematically expressed by the following equation: c o = s v × h r where co = cardiac output (l/sec) sv = stroke volume (ml) hr = heart rate (bpm) the normal human cardiac output is 5-6 l/min at rest. not all blood that enters the left ventricle exits the heart. what is left at the end of diastole (edv) minus the stroke volume make up the end systolic volume (esv). anatomical features circulatory system of species subjected to orthostatic blood pressure (such as arboreal snakes) has evolved with physiological and morphological features to overcome the circulatory disturbance. for instance, in arboreal snakes the heart is closer to the head, in comparison with aquatic snakes. this facilitates blood perfusion to the brain. turbulence blood flow is also affected by the smoothness of the vessels, resulting in either turbulent (chaotic) or laminar (smooth) flow. smoothness is reduced by the buildup of fatty deposits on the arterial walls. the reynolds number (denoted nr or re) is a relationship that helps determine the behavior of a fluid in a tube, in this case blood in the vessel. the equation for this dimensionless relationship is written as: n r = ρ v l μ ρ: density of the blood v: mean velocity of the blood l: characteristic dimension of the vessel, in this case diameter μ: viscosity of blood the reynolds number is directly proportional to the velocity and diameter of the tube. note that nr is directly proportional to the mean velocity as well as the diameter. a reynolds number of less than 2300 is laminar fluid flow, which is characterized by constant flow motion, whereas a value of over 4000, is represented as turbulent flow. due to its smaller radius and lowest velocity compared to other vessels, the reynolds number at the capillaries is very low, resulting in laminar instead of turbulent flow. velocity often expressed in cm/s. this value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has laminar characteristics. for this reason, the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall. in most cases, the mean velocity is used. there are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame analysis, or laser doppler anemometry. blood velocities in arteries are higher during systole than during diastole. one parameter to quantify this difference is the pulsatility index (pi), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the cardiac cycle. this value decreases with distance from the heart. p i = v s y s t o l e − v d i a s t o l e v m e a n -v_ relation between blood flow velocity and total cross-section area in human type of blood vessels total cross-section area blood velocity in cm/s aorta3–5 cm240 cm/s capillaries4500–6000 cm20.03 cm/s vena cavae inferior and superior14 cm215 cm/s blood vessels vascular resistance main article: vascular resistance resistance is also related to vessel radius, vessel length, and blood viscosity. in a first approach based on fluids, as indicated by the hagen–poiseuille equation. the equation is as follows: δ p = 8 μ l q π r 4 ∆p: pressure drop/gradient µ: viscosity l: length of tube. in the case of vessels with infinitely long lengths, l is replaced with diameter of the vessel. q: flow rate of the blood in the vessel r: radius of the vessel in a second approach, more realistic of the vascular resistance and coming from experimental observations on blood flows, according to thurston, there is a plasma release-cell layering at the walls surrounding a plugged flow. it is a fluid layer in which at a distance δ, viscosity η is a function of δ written as η(δ), and these surrounding layers do not meet at the vessel centre in real blood flow. instead, there is the plugged flow which is hyperviscous because holding high concentration of rbcs. thurston assembled this layer to the flow resistance to describe blood flow by means of a viscosity η(δ) and thickness δ from the wall layer. the blood resistance law appears as r adapted to blood flow profile : r = c l η ( δ ) ( π δ r 3 ) )}}} where r = resistance to blood flow c = constant coefficient of flow l = length of the vessel η(δ) = viscosity of blood in the wall plasma release-cell layering r = radius of the blood vessel δ = distance in the plasma release-cell layer blood resistance varies depending on blood viscosity and its plugged flow (or sheath flow since they are complementary across the vessel section) size as well, and on the size of the vessels. assuming steady, laminar flow in the vessel, the blood vessels behavior is similar to that of a pipe. for instance if p1 and p2 are pressures are at the ends of the tube, the pressure drop/gradient is: p 1 − p 2 l = δ p -p_=\delta p} the larger arteries, including all large enough to see without magnification, are conduits with low vascular resistance (assuming no advanced atherosclerotic changes) with high flow rates that generate only small drops in pressure. the smaller arteries and arterioles have higher resistance, and confer the main blood pressure drop across major arteries to capillaries in the circulatory system. illustration demonstrating how vessel narrowing, or vasoconstriction, increases blood pressure. in the arterioles blood pressure is lower than in the major arteries. this is due to bifurcations, which cause a drop in pressure. the more bifurcations, the higher the total cross-sectional area, therefore the pressure across the surface drops. this is why the arterioles have the highest pressure-drop. the pressure drop of the arterioles is the product of flow rate and resistance: ∆p=q xresistance. the high resistance observed in the arterioles, which factor largely in the ∆p is a result of a smaller radius of about 30 µm. the smaller the radius of a tube, the larger the resistance to fluid flow. immediately following the arterioles are the capillaries. following the logic observed in the arterioles, we expect the blood pressure to be lower in the capillaries compared to the arterioles. since pressure is a function of force per unit area, (p = f/a), the larger the surface area, the lesser the pressure when an external force acts on it. though the radii of the capillaries are very small, the network of capillaries has the largest surface area in the vascular network. they are known to have the largest surface area (485 mm^2) in the human vascular network. the larger the total cross-sectional area, the lower the mean velocity as well as the pressure. substances called vasoconstrictors can reduce the size of blood vessels, thereby increasing blood pressure. vasodilators (such as nitroglycerin) increase the size of blood vessels, thereby decreasing arterial pressure. if the blood viscosity increases (gets thicker), the result is an increase in arterial pressure. certain medical conditions can change the viscosity of the blood. for instance, anemia (low red blood cell concentration) reduces viscosity, whereas increased red blood cell concentration increases viscosity. it had been thought that aspirin and related "blood thinner" drugs decreased the viscosity of blood, but instead studies found that they act by reducing the tendency of the blood to clot. to determine the systemic vascular resistance (svr) the formula for calculating all resistance is used. r = ( δ p r e s s u r e ) / f l o w . this translates for svr into: s v r = ( m a p − c v p ) / c o where svr = systemic vascular resistance (mmhg/l/min) map = mean arterial pressure (mmhg) cvp = central venous pressure (mmhg) co = cardiac output (l/min) to get this in wood units the answer is multiplied by 80. normal systemic vascular resistance is between 900 and 1440 dynes/sec/cm−5. wall tension components of cylinder stress. regardless of site, blood pressure is related to the wall tension of the vessel according to the young–laplace equation (assuming that the thickness of the vessel wall is very small as compared to the diameter of the lumen): σ θ = p r t =\ } where p is the blood pressure t is the wall thickness r is the inside radius of the cylinder. σ θ \!} is the cylinder stress or "hoop stress". for the thin-walled assumption to be valid the vessel must have a wall thickness of no more than about one-tenth (often cited as one twentieth) of its radius. the cylinder stress, in turn, is the average force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in the cylinder wall, and can be described as: σ θ = f t l =\ } where: f is the force exerted circumferentially on an area of the cylinder wall that has the following two lengths as sides: t is the radial thickness of the cylinder l is the axial length of the cylinder stress when force is applied to a material it starts to deform or move. as the force needed to deform a material (e.g. to make a fluid flow) increases with the size of the surface of the material a., the magnitude of this force f is proportional to the area a of the portion of the surface. therefore, the quantity (f/a) that is the force per unit area is called the stress. the shear stress at the wall that is associated with blood flow through an artery depends on the artery size and geometry and can range between 0.5 and 4 pa. σ = f a . under normal conditions, to avoid atherogenesis, thrombosis, smooth muscle proliferation and endothelial apoptosis, shear stress maintains its magnitude and direction within an acceptable range. in some cases occurring due to blood hammer, shear stress reaches larger values. while the direction of the stress may also change by the reverse flow, depending on the hemodynamic conditions. therefore, this situation can lead to atherosclerosis disease. laminar shear of fluid between two plates. v = u , τ = σ . friction between the fluid and the moving boundaries causes the fluid to shear (flow). the force required for this action per unit area is the stress. the relation between the stress (force) and the shear rate (flow velocity) determines the viscosity. capacitance main article: capacitance of blood vessels veins are described as the "capacitance vessels" of the body because over 70% of the blood volume resides in the venous system. veins are more compliant than arteries and expand to accommodate changing volume. blood pressure the blood pressure in the circulation is principally due to the pumping action of the heart. the pumping action of the heart generates pulsatile blood flow, which is conducted into the arteries, across the micro-circulation and eventually, back via the venous system to the heart. during each heartbeat, systemic arterial blood pressure varies between a maximum (systolic) and a minimum (diastolic) pressure. in physiology, these are often simplified into one value, the mean arterial pressure (map), which is calculated as follows: m a p = d p + 1 / 3 ( p p ) where: map = mean arterial pressure dp = diastolic blood pressure pp = pulse pressure which is systolic pressure minus diastolic pressure. differences in mean blood pressure are responsible for blood flow from one location to another in the circulation. the rate of mean blood flow depends on both blood pressure and the resistance to flow presented