Blood Flow Velocity • The velocity of blood flow varies in the circulatory system • And is slowest in the capillary beds as a result of the high resistance and large total cross-sectional area • Slower flow will allows time for exchange to occur • After passing through the capillaries blood speeds up as it enters the venules Precapillary sphincters Thoroughfare channel Venule Arteriole Artery Capillaries Tissue cells Vein (a) (b) (a) Precapillary sphincters are rings of smooth muscle that regulate the flow of blood through capillaries; they help control the location of blood flow to where it is needed. (b) Valves in the veins prevent blood from moving backward The interrelationship of blood flow velocity, cross-sectional area of blood vessels and blood pressure. 5,000 4,000 3,000 2,000 1,000 Area (cm") 50 40 30 20 10 Velocity (cm/sec) 120 100 80 60 40 20 0 Pressure (mm Hg) Systolic pressure Diastolic pressure Aorta Arteries Arterioles Capillaries Venules Veins Venae cavae
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In humans, blood flows from the heart into the aorta, from which it passes into the major arteries. These major arteries branch into the small arteries (arterioles), which in turn branch into myriad of tiny capillaries as shown schematically in the figure below. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm/s. A typical capillary has a radius of about 4x10^-4 cm and blood flows through it at a speed of about 5x10^-4 m/s. Show by using the equation of continuity what the approximate number of capillaries in the body is. (Hint: Assume the density of blood does not vary significantly from the aorta to the capillaries, and that, by the equation of continuity, the volume flow rate in the aorta must equal the volume flow rate through all the capillaries. The total area of all the capillaries can be given by the area of one capillary multiplied by the total number N of capillaries.)
Jacob F.
(a) Calculate the mass flow rate (in grams per second) of blood (ρ = 1.0 g/cm³) in an aorta with a cross-sectional area of 2.0 cm² if the flow speed is 33 cm/s. (b) Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of 3.0 × 10³ cm². What is the flow speed in the capillaries? cm/s 2. The approximate inside diameter of the aorta is 0.47 cm; that of a capillary is 12 µm. The approximate average blood flow speed is 1.0 m/s in the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.
Eduard S.
The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the outside. The speed of the blood is given by $$V=\frac{p}{4 L v}\left(R^{2}-r^{2}\right)$$ where $R$ is the radius of the blood vessel, $r$ is the distance of the blood from the center of the vessel, and $p, v,$ and $L$ are physical constants related to the pressure and viscosity of the blood and the length of the blood vessel. II $R$ is constant, we can think of $V$ as a lunction of $r:$ $$V(r)=\frac{p}{4 L v}\left(R^{2}-r^{2}\right)$$ (IMAGES CANNOT COPY) The total blood flow, $Q,$ is given by $Q=\int_{0}^{R} 2 \pi \cdot V(r) \cdot r \cdot d r$ Find $Q$
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