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Unformatted text preview: of the blood as it travels through a vessel is R = K Â· L r 4 where r and L are the radius and length of the vessel respectively, and K is a constant that reï¬‚ects the viscosity of the blood. Suppose K = 1 . Show that the total resistance of the blood traveling from A to B to C is R ( Î¸ ) = 16 9 [ 2cot( Î¸ ) ] + 9 csc( Î¸ ) in the case of the vessels shown below. Use a calculator to ï¬nd the value of the resistence when Î¸ has the values 1 , 1 . 2 , 1 . 3 , 1 . 4 , 1 . 5 radians. Î¸ = 1 Î¸ = 1 . 2 Î¸ = 1 . 3 Î¸ = 1 . 4 Î¸ = 1 . 5 Resistance R ( Î¸ ) Which of those angles produce the lowest resistence? What is its degree measure? Where would point B lie in that case? Later in the semester, we will be able to calculate the exact angle that minimizes the resistence in this case and a law for two vessels in general....
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 Spring '08
 ALL
 Calculus, Continuous function, Blood vessel

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