1. .
Components of  in Rectangular and Cylindrical Coordinates
The rate of deformation is important in characterizing flows. As described earlier,
material properties like viscosity can depend on the rate of deformation. Various forms
for simple deformation in basic orthogonal coordinate systems can be used to solve
many interesting problems. For Newtonian fluids, we have ij = 
ij .
Rectangular Coordinates(x, y, z--right hand rule with x rotating into y to give z)
xx .
= 2
vx x
vx + vy
y x
xy .
yx =
yy .
vx + vz
z x
xz .
zx =
vy y
= 2
zz .
vy + vz
z y
yz .
zy =
vz z
= 2
Extensional flow components Shear flow components

2. . . . . . . . . (1 v + vr) (1 vz + v) ( vz + vr)
Cylindrical Coordinates(r, , z)
rr .
= 2
vr r
r .
r .
 ( v ) + 1 vr)
r r r  =
= ( r
 .
= 2
(1 v vr)
r  r
z . =
(1 vz v)
r  z
z =
zz .
= 2
vz z
zr .
rz = .
( vz vr)
r z =