i.e.
h
f
= k
4
d
Q
where k is a constant
(7.5)
For a laminar flow, the shear stress on the cylindrical surface is given
by
dx
dp
2
r
=
τ
For Newtonian fluid,
dr
dv
µ
=
τ
Equating the two equations,
dx
dp
2
r
dr
dv
=
µ
When integrating the above equation with respect to r with the
boundary condition v = 0 when r = R (i.e. no slip condition), the result
is
)
r
R
(
dx
dp
4
1

v
2
2
−
µ
=
(7.6)
From (7.10), we can see that the velocity distribution is in parabolic
form with maximum velocity at r = 0.
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