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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 27E

(a)

To determine

**To find:** The velocity of the blood along the center line

Expert Solution

Velocity of the blood along the center line is

Velocity of the blood at 0.005cm as radius is

Velocity of the blood at the wall is

**Given:**

The law of laminar flow is as given below.

The length of the blood vessel is given below.

The pressure difference between the ends of the vessel is given below.

The viscosity of the blood is given below.

**Calculation:**

Calculate the velocity of the blood along the center line using the equation (1).

Substitute 3cm for *r*,

Thus, the Velocity of the blood at

Calculate the velocity of the blood at

Substitute 3 cm for

Thus, the Velocity of the blood at

Calculate the velocity of the blood at the wall using the equation (1).

Substitute 3 cm for

Thus, the Velocity of the blood at

(b)

To determine

**To find:** The velocity gradient at

Expert Solution

Velocity gradient at

Velocity gradient at

Velocity gradient at

Calculate the velocity gradient at center line

Differentiate equation (1) with respect to

Substitute 3 cm for *r*,

Thus, the Velocity of the blood at radius

Calculate the velocity gradient at

Substitute 3 cm for *r*,

The velocity gradient at

Calculate the velocity gradient at the wall edge

Substitute 3 cm for *r*,

The velocity gradient at

(c)

To determine

**To find:** Where is the velocity the greatest and where it changes the most.

Expert Solution

The velocity is greatest where

The velocity is greatest where