Blood flow - Citizendia

Blood flow is the flow of blood in the cardiovascular system. Blood is a specialized Bodily fluid that delivers necessary substances to the body's cells ��such as nutrients and oxygen—and transports Waste products This is an article about the rock music band "Circulatory System" The discovery that blood flows is attributed to William Harvey. William Harvey ( April 1, 1578 – June 3, 1657) was an English Physician who is credited with being the first in

Mathematically, blood flow is described by Darcy's law (which can be viewed as the fluid equivalent of Ohm's law) and approximately by Hagen-Poiseuille's law. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Fluid dynamics, Darcy's law is a phenomologically derived Constitutive equation that describes the flow of a Fluid through a Porous medium Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the The Hagen-Poiseuille equation is a Physical law that describes slow Viscous Incompressible flow through a constant circular cross-section Blood is a heterogeneous medium consisting mainly of plasma and a suspension of red blood cells. White cells, or leukocytes, and platelets while present in smaller concentrations, play an important role in biochemical processes, such as immune response, inflammation, and coagulation. Red cells tend to coagulate when the flow shear rates are low, while increasing shear rates break these formations apart, thus reducing blood viscosity. This results in two non-Newtonian blood properties, shear thinning and yield stress. In healthy large arteries blood can be successfully approximated as a homogeneous, Newtonian fluid since the vessel size is much greater than the size of particles and shear rates are sufficiently high that particle interactions may have a negligible effect on the flow. In smaller vessels, however, non-Newtonian blood behavior should be taken into account. The flow in healthy vessels is generally laminar, however in diseased (e. g. atherosclerotic) arteries the flow may be transitional or turbulent. Atherosclerosis is a Disease affecting arterial Blood vessels It is a chronic inflammatory response in the walls of arteries in large part due to the accumulation The first equation below is Darcy's law, the second is the Hagen-Poiseuille law:

$F = \frac{\Delta P}{R}$

$R = (\frac{\nu L}{r^4})(\frac{8}{\pi})$

where:

F = blood flow

P = pressure

R = resistance

ν = fluid viscosity

L = length of tube

r = radius of tube

In the last equation it is important to note that resistance to flow changes dramatically with respect to the radius of the tube. This is important in angioplasty, as it enables the increase of blood flow with balloon catheter to the deprived organ significantly with only a small increase in radius of a vessel. Angioplasty is the technique of mechanically widening a narrowed or totally obstructed Blood vessel; typically as a result of Atherosclerosis. A balloon catheter is a type of "soft" Catheter with an Inflatable "balloon" at its tip which is used during a catheterization procedure to enlarge

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