Chapter 2.7, Problem 27E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Refer to the law of laminar flow given in Example 7. Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure difference 3000 dynes/cm^{2}, and viscosity

(a) Find the velocity of the blood along the centreline *r* = 0, at radius r = 0.005 cm, and at the wall *r = R* = 0.01 cm.

(b) Find the velocity gradient at r = 0, *r =* 0.005, and *r =* 0.01.

(c) Where is the velocity the greatest? Where is the velocity changing most?

To determine

**Part (a)**

**To find: ** velocity of the blood along central line at the wall

Explanation

**1) Formula: **

by law of laminar flow

**2) Given:**

**3) Calculation:**

By using law of laminar flow

Substitute all given values in

Now substitute values of

If

To determine

**Part (b)**

**To find: ** velocity gradient

To determine

**Part (c)**

**To find: ** where is velocity greatest and where changing most

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