Problem #1
:
A fluid with viscosity 18.3 cp and density 1.32 g/cm3 is flowing in a long horizontal tube
of radius 1.05 in (2.67 cm). For what pressure gradient will the flow become turbulent?
Answer:
The minimum value of
Re
4
/(
)
wD
π
µ
=
needed to produce turbulent flow in a long,
smooth tube is about 2100. Poiseuille’s law holds until this critical Re value, giving
( )
4
0
critical
Re<Re
8
L
PPR
w
L
πρ
−
=
Hence, the pressure gradient needed to initiate the laminarturbulent transition is
()
2
5
44
3
88
4
Re
2100
1.1 10 Pa/km
4
critical
dp
w
D
dz
R
R
R
µµπ
ρ
==
≈
=
Problem #2:
Water is flowing through a long, straight, level run of smooth 6.00 in inner diameter pipe,
at temperature 68
0
F. The pressure gradient along the length of the pipe is 1 psi/mile.
(a)
Determine the wall shear stress
τ
0
in Pa?
(b)
Assume the flow to be turbulent and determine the radial distance from the pipe
wall at which
, using Fig. 5.53 in the
textbook (second edition), also available in the lecture note. Pay attention at the
definition of dimensionless variables.
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 Fall '08
 Peters
 Max, Turbulent Flow

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