Chapter 5.5, Problem 18E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The velocity *v* of blood that flows in a blood vessel with radius *R* and length *l* at a distance *r* from the central axis is

where *P* is the pressure difference between the ends of the vessel and
*r)* over the interval

To determine

**To find:**

(i) The average velocity over the interval

(ii) Compare the average velocity with the maximum velocity.

Explanation

**1) Concept:**

Use the mean value theorem for integral to find the average velocity over the interval

**2) Mean Value Theorem for Integrals**

If

that is,

**3) Given:**

The velocity

where

**4) Calculation:**

(i)

The average velocity on

Therefore,

(ii)

Differentiate

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