# Describe the relationship between velocity of blood flow and cross sectional area

### Pressure, Volume, Flow and Resistance

Which vessel has the largest total cross-sectional area? why is this What is the relationship between the velocity of blood flow and the total. Describe the relationship between cross-sectional area and blood flow velocity in the blood vessels. Use a diagram in your answer. Why is this relationship so. Start studying the relationship between cross- sectional area and velocity of blood flow. Learn vocabulary, terms, and more with flashcards, games, and other .

One pound of adipose tissue contains approximately miles of vessels, whereas skeletal muscle contains more than twice that. Overall, vessels decrease in length only during loss of mass or amputation.

An individual weighing pounds has approximately 60, miles of vessels in the body. Gaining about 10 pounds adds from to miles of vessels, depending upon the nature of the gained tissue. One of the great benefits of weight reduction is the reduced stress to the heart, which does not have to overcome the resistance of as many miles of vessels. In contrast to length, the blood vessel diameter changes throughout the body, according to the type of vessel, as we discussed earlier.

The diameter of any given vessel may also change frequently throughout the day in response to neural and chemical signals that trigger vasodilation and vasoconstriction.

The vascular tone of the vessel is the contractile state of the smooth muscle and the primary determinant of diameter, and thus of resistance and flow. The effect of vessel diameter on resistance is inverse: Given the same volume of blood, an increased diameter means there is less blood contacting the vessel wall, thus lower friction and lower resistance, subsequently increasing flow.

A decreased diameter means more of the blood contacts the vessel wall, and resistance increases, subsequently decreasing flow. The influence of lumen diameter on resistance is dramatic: A slight increase or decrease in diameter causes a huge decrease or increase in resistance. This means, for example, that if an artery or arteriole constricts to one-half of its original radius, the resistance to flow will increase 16 times.

A Mathematical Approach to Factors Affecting Blood Flow Jean Louis Marie Poiseuille was a French physician and physiologist who devised a mathematical equation describing blood flow and its relationship to known parameters. The same equation also applies to engineering studies of the flow of fluids.

Although understanding the math behind the relationships among the factors affecting blood flow is not necessary to understand blood flow, it can help solidify an understanding of their relationships. Please note that even if the equation looks intimidating, breaking it down into its components and following the relationships will make these relationships clearer, even if you are weak in math.

Focus on the three critical variables: It may commonly be represented as 3. One of several things this equation allows us to do is calculate the resistance in the vascular system. Normally this value is extremely difficult to measure, but it can be calculated from this known relationship: The important thing to remember is this: Two of these variables, viscosity and vessel length, will change slowly in the body.

Only one of these factors, the radius, can be changed rapidly by vasoconstriction and vasodilation, thus dramatically impacting resistance and flow. Further, small changes in the radius will greatly affect flow, since it is raised to the fourth power in the equation.

The Roles of Vessel Diameter and Total Area in Blood Flow and Blood Pressure Recall that we classified arterioles as resistance vessels, because given their small lumen, they dramatically slow the flow of blood from arteries. In fact, arterioles are the site of greatest resistance in the entire vascular network. This may seem surprising, given that capillaries have a smaller size.

How can this phenomenon be explained? Although the diameter of an individual capillary is significantly smaller than the diameter of an arteriole, there are vastly more capillaries in the body than there are other types of blood vessels. Part c shows that blood pressure drops unevenly as blood travels from arteries to arterioles, capillaries, venules, and veins, and encounters greater resistance. However, the site of the most precipitous drop, and the site of greatest resistance, is the arterioles.

This explains why vasodilation and vasoconstriction of arterioles play more significant roles in regulating blood pressure than do the vasodilation and vasoconstriction of other vessels. Part d shows that the velocity speed of blood flow decreases dramatically as the blood moves from arteries to arterioles to capillaries. This slow flow rate allows more time for exchange processes to occur. As blood flows through the veins, the rate of velocity increases, as blood is returned to the heart.

The relationships among blood vessels that can be compared include a vessel diameter, b total cross-sectional area, c average blood pressure, and d velocity of blood flow.

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Disorders of the…Cardiovascular System: Arteriosclerosis Compliance allows an artery to expand when blood is pumped through it from the heart, and then to recoil after the surge has passed. This helps promote blood flow.

In arteriosclerosis, compliance is reduced, and pressure and resistance within the vessel increase. This is a leading cause of hypertension and coronary heart disease, as it causes the heart to work harder to generate a pressure great enough to overcome the resistance. Arteriosclerosis begins with injury to the endothelium of an artery, which may be caused by irritation from high blood glucose, infection, tobacco use, excessive blood lipids, and other factors.

Artery walls that are constantly stressed by blood flowing at high pressure are also more likely to be injured—which means that hypertension can promote arteriosclerosis, as well as result from it. Recall that tissue injury causes inflammation. As inflammation spreads into the artery wall, it weakens and scars it, leaving it stiff sclerotic. As a result, compliance is reduced.

Moreover, circulating triglycerides and cholesterol can seep between the damaged lining cells and become trapped within the artery wall, where they are frequently joined by leukocytes, calcium, and cellular debris. Eventually, this buildup, called plaque, can narrow arteries enough to impair blood flow. When this happens, platelets rush to the site to clot the blood. This clot can further obstruct the artery and—if it occurs in a coronary or cerebral artery—cause a sudden heart attack or stroke.

Alternatively, plaque can break off and travel through the bloodstream as an embolus until it blocks a more distant, smaller artery. Ischemia in turn leads to hypoxia—decreased supply of oxygen to the tissues.

Hypoxia involving cardiac muscle or brain tissue can lead to cell death and severe impairment of brain or heart function. A major risk factor for both arteriosclerosis and atherosclerosis is advanced age, as the conditions tend to progress over time. However, obesity, poor nutrition, lack of physical activity, and tobacco use all are major risk factors. Treatment includes lifestyle changes, such as weight loss, smoking cessation, regular exercise, and adoption of a diet low in sodium and saturated fats.

Medications to reduce cholesterol and blood pressure may be prescribed.

For blocked coronary arteries, surgery is warranted. In angioplasty, a catheter is inserted into the vessel at the point of narrowing, and a second catheter with a balloon-like tip is inflated to widen the opening. To prevent subsequent collapse of the vessel, a small mesh tube called a stent is often inserted. In an endarterectomy, plaque is surgically removed from the walls of a vessel.

This operation is typically performed on the carotid arteries of the neck, which are a prime source of oxygenated blood for the brain. In a coronary bypass procedure, a non-vital superficial vessel from another part of the body often the great saphenous vein or a synthetic vessel is inserted to create a path around the blocked area of a coronary artery.

21 15 Velocity of Blood Flow

Venous System The pumping action of the heart propels the blood into the arteries, from an area of higher pressure toward an area of lower pressure. If blood is to flow from the veins back into the heart, the pressure in the veins must be greater than the pressure in the atria of the heart. Two factors help maintain this pressure gradient between the veins and the heart.

First, the pressure in the atria during diastole is very low, often approaching zero when the atria are relaxed atrial diastole. These physiological pumps are less obvious.

Skeletal Muscle Pump In many body regions, the pressure within the veins can be increased by the contraction of the surrounding skeletal muscle.

This mechanism, known as the skeletal muscle pump Figure As leg muscles contract, for example during walking or running, they exert pressure on nearby veins with their numerous one-way valves. This increased pressure causes blood to flow upward, opening valves superior to the contracting muscles so blood flows through. Simultaneously, valves inferior to the contracting muscles close; thus, blood should not seep back downward toward the feet. Military recruits are trained to flex their legs slightly while standing at attention for prolonged periods.

Failure to do so may allow blood to pool in the lower limbs rather than returning to the heart. Consequently, the brain will not receive enough oxygenated blood, and the individual may lose consciousness. The contraction of skeletal muscles surrounding a vein compresses the blood and increases the pressure in that area.

This action forces blood closer to the heart where venous pressure is lower. Note the importance of the one-way valves to assure that blood flows only in the proper direction.

Respiratory Pump The respiratory pump aids blood flow through the veins of the thorax and abdomen. During inhalation, the volume of the thorax increases, largely through the contraction of the diaphragm, which moves downward and compresses the abdominal cavity. The elevation of the chest caused by the contraction of the external intercostal muscles also contributes to the increased volume of the thorax. The volume increase causes air pressure within the thorax to decrease, allowing us to inhale.

Additionally, as air pressure within the thorax drops, blood pressure in the thoracic veins also decreases, falling below the pressure in the abdominal veins. This causes blood to flow along its pressure gradient from veins outside the thorax, where pressure is higher, into the thoracic region, where pressure is now lower.

This in turn promotes the return of blood from the thoracic veins to the atria. During exhalation, when air pressure increases within the thoracic cavity, pressure in the thoracic veins increases, speeding blood flow into the heart while valves in the veins prevent blood from flowing backward from the thoracic and abdominal veins. The individual veins are larger in diameter than the venules, but their total number is much lower, so their total cross-sectional area is also lower.

Also notice that, as blood moves from venules to veins, the average blood pressure drops see Figure This pressure gradient drives blood back toward the heart.

Again, the presence of one-way valves and the skeletal muscle and respiratory pumps contribute to this increased flow. Since approximately 64 percent of the total blood volume resides in systemic veins, any action that increases the flow of blood through the veins will increase venous return to the heart.

Maintaining vascular tone within the veins prevents the veins from merely distending, dampening the flow of blood, and as you will see, vasoconstriction actually enhances the flow.

The Role of Venoconstriction in Resistance, Blood Pressure, and Flow As previously discussed, vasoconstriction of an artery or arteriole decreases the radius, increasing resistance and pressure, but decreasing flow.

Venoconstriction, on the other hand, has a very different outcome. The walls of veins are thin but irregular; thus, when the smooth muscle in those walls constricts, the lumen becomes more rounded. The more rounded the lumen, the less surface area the blood encounters, and the less resistance the vessel offers.

Vasoconstriction increases pressure within a vein as it does in an artery, but in veins, the increased pressure increases flow. Recall that the pressure in the atria, into which the venous blood will flow, is very low, approaching zero for at least part of the relaxation phase of the cardiac cycle.

Thus, venoconstriction increases the return of blood to the heart. Another way of stating this is that venoconstriction increases the preload or stretch of the cardiac muscle and increases contraction. Chapter Review Blood flow is the movement of blood through a vessel, tissue, or organ.

The slowing or blocking of blood flow is called resistance. Blood pressure is the force that blood exerts upon the walls of the blood vessels or chambers of the heart. The components of blood pressure include systolic pressure, which results from ventricular contraction, and diastolic pressure, which results from ventricular relaxation. Pulse, the expansion and recoiling of an artery, reflects the heartbeat.

The variables affecting blood flow and blood pressure in the systemic circulation are cardiac output, compliance, blood volume, blood viscosity, and the length and diameter of the blood vessels. For the same volume to pass points 1 and 2 in a given time, the speed must be greater at point 2.

## Arterial Blood Pressure

The process is exactly reversible. If the fluid flows in the opposite direction, its speed will decrease when the tube widens.

Note that the relative volumes of the two cylinders and the corresponding velocity vector arrows are not drawn to scale. Since liquids are essentially incompressible, the equation of continuity is valid for all liquids. However, gases are compressible, and so the equation must be applied with caution to gases if they are subjected to compression or expansion.

The flow rate through hose and nozzle is 0. Calculate the speed of the water a in the hose and b in the nozzle. Strategy We can use the relationship between flow rate and speed to find both velocities. We will use the subscript 1 for the hose and 2 for the nozzle.

The nozzle produces a considerably faster stream merely by constricting the flow to a narrower tube. The solution to the last part of the example shows that speed is inversely proportional to the square of the radius of the tube, making for large effects when radius varies. We can blow out a candle at quite a distance, for example, by pursing our lips, whereas blowing on a candle with our mouth wide open is quite ineffective. In many situations, including in the cardiovascular system, branching of the flow occurs.

The blood is pumped from the heart into arteries that subdivide into smaller arteries arterioles which branch into very fine vessels called capillaries. In this situation, continuity of flow is maintained but it is the sum of the flow rates in each of the branches in any portion along the tube that is maintained. Calculating Flow Speed and Vessel Diameter: Branching in the Cardiovascular System The aorta is the principal blood vessel through which blood leaves the heart in order to circulate around the body.

The aorta has a radius of 10 mm. When the rate of blood flow in the aorta is 5. This low speed is to allow sufficient time for effective exchange to occur although it is equally important for the flow not to become stationary in order to avoid the possibility of clotting.