Question
Asked Nov 15, 2019
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A small blood vessel of radius r branches off at an angle 0 from a larger vessel of radius R to supply blood along a path from
а-b cot(0)
b csc(0)
A to B. According to Poiseuille's Law, the total resistance to blood flow is proportional to T = ( -
where a
and b are as in the figure.
В.
ь
R
Find 0 that minimizes the total resistance if r = 5, R = 13.
(Use symbolic notation and fractions where needed.)
radians
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A small blood vessel of radius r branches off at an angle 0 from a larger vessel of radius R to supply blood along a path from а-b cot(0) b csc(0) A to B. According to Poiseuille's Law, the total resistance to blood flow is proportional to T = ( - where a and b are as in the figure. В. ь R Find 0 that minimizes the total resistance if r = 5, R = 13. (Use symbolic notation and fractions where needed.) radians

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Step 1

It is given that the total blood resistance is proportional to T.

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а-bcot(0) bcsc(ө) т b cot(e)sc() b a R2 r

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Step 2

Differentiate the above equation to min...

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dT d ot R2de b b d csce de a de deR b 0 R2 b (-cscecote (-sc' e)scecot 0) 4 b cose b 1 sin2 e 4 b 1 1 - cos e sin20R 4

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Calculus

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