Two options: 1) no pressure gradient; 2) pressure gradient

2

210zu

xp

Two options:

1) no pressure gradient;

2) pressure gradient

upgDtuD

2

Uzzu

Constant Shear

COUETTE FLOW

1) no pressure gradient

zH

Same for horizontally sheared flow

2) pressure gradient

zHzxpu

2

21

0xp

2

210yu

xp

21

2

21 cycyxpu

Also applies to the horizontal plane:

00@ uy 02 c

0@ uBy BcBxp

1

2

210

21

1B

xpc

yByxpu

2

21

yByxpu

2

21 0

xp

2

210zu

xp

21

2

21 czczxpu

00@ uz 02 c

0@

zuHz

110 cHxp

Other form for Poiseuille Flow

11 czxp

zu

HzzxpzH

xpz

xpu

211

21 2

Hzzxpu

21

0xp

COUETTE & POISEUILLE FLOW

zHzxpzu

2

21

0xp

COUETTE & POISEUILLE FLOW

zHzxpzu

21 2

0xp

COUETTE & POISEUILLE FLOW

zHzxpzu

2

21

0xp

Flow down a plane

2

2

sin0zug

00@ uz 02 c

0@

zuHz Hgc

sin1

z

x

H 212sin

2czczgu

Hzgzgu

sinsin2

2 zHzg 2sin

2