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Rp
z
∂
τ
=−
We know that
where
R
=
R
(
z
)
R
2
∂
And the volumetric fl ow rate
Q
is given by the Rabinowitsch
equation
τ
π
R
3
R
∫
τττ
2
f
()
d
Q
=
(12)
3
τ
R
0
where
n
is the fluid index parameter.
Now, substituting the values of
f
(
τ
) from Eq. (3) to Eq. (12),
τ
π
R
3
1
R
∫
2
n
Q=
τττ τ
(
−
)
d
(13)
H
3
τ
k
R
0
(where
n
= fluid index parameter)
R
kn
πτ
3
n
τ
⎡
2
τ
2
τ
⎤
n
+
1
2
R
(1
−
H
)
1
+
(
)
H
+
(
H
)
Q =
(14)
⎢
⎥
(
+
)
τ
n
+
2
τ
(
n
+
)(
n
+
)
τ
⎣
⎦
R
R
R
τ
τ
≤
When (
)
1, the above equation reduces to
H
R
n
3
π
R
⎧
n
+
3
⎫
⎛
⎞
τ
−
τ
Q
=
⎨
⎬
(15)
⎜
⎟
(
)
R
H
kn
+
3
n
+
2
⎝
⎠
⎩
⎭
Again, the boundary conditions (4) and (5) become
τ
u
= 0 at
R
(
z
) =
r
and
is finite at
r
= 0
(16)
Therefore, Eqs. (10) and (11) and the boundary condition (16) reduce
to the velocity of blood
⎡
n
+
1
n
+
1
⎤
1
⎧∂
⎛
p
∂
B
⎞
⎫
⎧∂
⎛
p
∂
B
⎞
⎫
u
=−
−
m
r
−
2
τ
−
−
m
R
−
2
τ
⎢
⎥
⎨
⎬
⎨
⎬
(17)
⎜
⎟
⎜
⎟
1
H
1
H
⎛
∂
p
∂
B
⎞
∂
z
∂
z
∂
z
∂
z
⎝
⎠
⎝
⎠
⎢
⎩
⎭
⎩
⎭
⎥
⎣
⎦
2
n
m
−
m
⎜
⎟
2
1
∂
z
∂
z
⎝
⎠
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