   Chapter 14.3, Problem 92E

Chapter
Section
Textbook Problem

One of Poiseuille’s laws states that the resistance of blood flowing through an artery is R = C L r 4 where L and r are the length and radius of the artery and C is a positive constant determined by the viscosity of the blood. Calculate ∂R/∂L and ∂R/∂r and interpret them.

To determine

To calculate: The value of RL and Rr if R=CLr4 and interpret these values.

Explanation

Given:

The resistance of blood flowing through an artery is given by Poiseuille’s law, R=CLr4 where L is length, C is a positive constant and r is radius of the artery.

Calculation:

Find the partial derivative of R with respect to L and obtain RL .

RL=L(CLr4)=Cr4L(L)=Cr4(1)=Cr4

Thus, the value of RL=Cr4

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