   Chapter 2.7, Problem 27E

Chapter
Section
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/cm2, and viscosity η = 0.027 .(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

v=P4ηl(R2-r2)

2) Given:

P=3000 dynes/cm2, l=3, R=0.01 and η=0.027

r=0cm, 0.005cm, 0.01cm

3) Calculation:

By using law of laminar flow

v(r)=P4ηl(R2-r2)

Substitute all given values in v

v(r)=300040.0273((0.01)2-r2)

v(r)=30000.324(0.0001-r2)

Now substitute values of r one by one

If r=0

v(0)=30000

To determine

Part (b)

To determine

Part (c)

To find: where is velocity greatest and where changing most

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