Essay Application Of Calculus : Blood Flow And Cardiac Output

1033 Words May 17th, 2015 5 Pages
Application of Calculus: Blood Flow & Cardiac Output We all know that our blood is continually flowing through our body, or else we would be dead! However many lack the in-depth knowledge of the processes by which the body maintains its continuous blood flow through its veins and arteries. There are both numerous biological and mathematical applications, however this paper will focus primarily on the mathematical application in the movement of blood in the human body. The first mathematical application in this field is the use of calculus to determine the blood flow in an artery or a vein at a given point in time. First, the shape of the blood vessel (either a vein or artery) is assumed to be the shape of a cylindrical tube. Due to the friction caused by the walls, the velocity (v) of the blood is greatest along the central axis. The velocity decreases as the radius increases and eventually becomes zero when it reaches the wall of the blood vessel. This relationship between velocity and radius is given by the law of laminar flow which is: where ɳ is the viscosity of the blood, P is the pressure difference between the ends of the cylindrical tube, and l is the length. If P and l are constant, then v is a function of r with domain [0, R]. This equation gives us the velocity of blood that flows along the blood vessel with radius R and length l at a distance r from the central axis. To find the rate of the blood flow, or flux, one must use smaller, equally spaced radii so…

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