Explanation Given information: Poiseuille’s law of laminar flow: v = P 4 η l ( R 2 − r 2 ) A blood vessel with l = 1 cm, P = 1500 dynes/cm 2 , η = 0.027 and R = 0.01 cm contracts so that R ' ( t ) = − 0.0005 cm/min at a particular moment. Calculation: Poiseuille’s law of laminar flow states that v = P 4 η l ( R 2 − r 2 ) So that, at the center of the blood vessel, i.e. r = 0, we have v = P 4 η l R 2 In the very cold weather, R contracts with time. Therefore, we need to use the Chain Rule to calculate d v / d t : d v d t = P 4 η l

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.5, Problem 92E

To determine

To calculate: dv/dt, the rate of change of the blood flow, at the center of the blood vessel at that time.

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Chapter 3.5, Problem 91E

Chapter 3.5, Problem 93E

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d v / d t , the rate of change of the blood flow, at the center of the blood vessel at that time.

Solution Summary: The author explains Poiseuille's law of laminar flow: a blood vessel with l = 1 cm, P = 1500 dynes/cm 2, eta =

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To calculate: dv/dt, the rate of change of the blood flow, at the center of the blood vessel at that time.

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