2010 BME 259 Problem Set 6 Solutions

The power of pumping blood equals the rate of work

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Unformatted text preview: of pumping blood equals the rate of work done to overcome viscous resistance. This power is equal to the product of the average velocity times the viscous force acting on the vessel wall (r = R). (a) Using this relation, show that for a Newtonian fluid, the pumping power equals The definition of power is: Solution Using the definition of the power provided, The units on the right side are that of power (J/sec(W) or dyne-cm/sec). The wall shear stress for laminar flow in a cylindrical tube is obtained from Equation 2.7.36, which when combined with the definition of the average velocity, is , the power The pressure drop and flow rate are related by Poiseuille's Law, Equation 2.7.45 Solving for Replacing this equation for into the equation for above, (b) The metabolic power is assumed to be equal to the product of the metabolic energy per unit volume of blood times the blood volume. Simply treating the...
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This homework help was uploaded on 02/17/2014 for the course BIM 106 taught by Professor Leach during the Spring '12 term at UC Davis.

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