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where
δ
s
ss
/(
−
1)
A
=
s
Rl
( )
s
−
00
Now, Eqs. (2) and (3) reduce to
∂
p
1
∂
μ
MB
∂
B
−+
r
zrr
()(
τ
+
0
0
)
=
0
(8)
2
∂
∂
ρ
u
∂
z
0
∂
p
1
∂
∂
B
(9)
−+
()
r
τ
+
m
=
0
1
∂
zrr
∂
∂
z
1/ 2
∂
u
⎛
⎞
ττ
≥
τ
1/ 2
=
τ
1/ 2
+
m
−
, if
(10)
⎜
⎟
H
H
2
∂
r
⎝
⎠
∂
u
r
ττ
≤
, where
=
0
H
∂
μ
μ
ρ
MB
m
=
Where considering
and
.
m
=
(
0
0
)
2
ρ
uR
1
2
u
00
0
Now, from Eq. (10),
∂
u
⎛
⎞
(
)
2
1/ 2
1/ 2
2
τ
−
τ
=
m
−
⎜
⎟
H
2
∂
r
⎝
⎠
1
∂
u
⎛
⎞
(
)
2
τ
1/ 2
−
τ
1/ 2
=
−
=
f
()
τ
⎜
⎟
(11)
H
2
m
∂
r
⎝
⎠
2
We know the volumetric flow rate
Rz
()
∫
Q
=
2
π
rudr
0
⎧
R
⎫
2
R
2
⎛
r
⎞
du r
⎪
⎪
∫
=
2
π
u
.
−
dr
⎨
⎬
⎜
⎟
2
dr
2
⎝
⎠
⎪
⎪
⎩
⎭
0
0
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