Propaganda
```Generaliza&ccedil;&atilde;o da lei de Newton
Taxa de deforma&ccedil;&atilde;o
Cisalhamento simples
Lei de Newton
μ
τ yx
tens&atilde;o de cisalhamen to

dv x
taxa de deforma&ccedil;&atilde;o
dy
δ t  Δt  δ t
dδ

 lim Δx, Δy,Δt 0
dt
Δt

dδ
 lim Δx, Δy,Δt 0
dt


π/2

arctan

(v x



Δt 
 v x y )   π/2 
y  Δy
Δy 

Δt

dv x
dy
Escoamento multidimensional
v
π ij  pδ ij  τ ij
Taxa de deforma&ccedil;&atilde;o
Cisalhamento multidirecional no plano xy
δ t  Δt  δ t
dδ

 lim Δx, Δy,Δt 0
dt
Δt

dδ xy
dt
 lim Δx, Δy,Δt 0

π/2  arctan


Δt 
(v x yΔy  v x y ) Δy   arctan


Δt
v y
v x



dt
x
y
dδ xy

Δt 

(v y x Δx  v y x ) Δx   π/2

Analogamente para as outras dire&ccedil;&otilde;es
v y
v x



 xy
dt
x
y
dδ xy

dδ xz v z v x


 xz
dt
x
z
v y
v z



  yz
dt
z
y
dδ yz
τ ij  τ ji  μ ij
μ
tens&atilde;o de cisalhamen to
taxa de deforma&ccedil;&atilde;o
Stokes:
τ xy  τ yx  μ xy
τ xz  τ zx  μ xz
τ zy  τ yz  μ zy
v i v j

 γ ij
x j x i
Tens&otilde;es viscosas normais
τ xx
v x  2
 v x
 2μ
 μ  κ
x  3
 x
v y
2
 v y
τ yy  2μ
  μ  κ
y  3
 y
v z  2
 v z
τ zz  2μ
 μ  κ
z  3
 z