Finite Element Techniques for Fluid Flow

164 BASIC PRINCIPLES AND GOVERNING EQUATIONS

For two-dimensional flow

(X

l

,X

2

plane), only ω

3

is finite, and

in the absence of body forces (4.81) reduces to

vV

2

co = 5^ (4.82)

We note that the frictional stress contribution vanishes when the

flow is frictional.

4.7 THE PRINCIPLE OF VIRTUAL POWER

We derive the Principle of Virtual Power by operating in the stress

equilibrium equations and stress boundary relations [equations

(4.45)]:

d Ov

k

ä^ + ^ = 'DTi inK (4.83)

Pk = <*nf}k on S

Let us multiply (4.83) by a piecewise continuous function Sv

k

, and

integrate over the domain

ί JÏ {έ>

+pbk

~

p

m\

öVk

d

v+

j

I

{h

~ *

(4.84)

This expression must be satisfie ...