Hydraulic 4202
Derivation of Power Formulas
The derivation of all 6 power formulas for predicting the mean velocity
m
V
in a pipe or
channel start with Chezy’s formula:
2
1
2
1
'
4
1
2
4
S
R
f
g
V
m
=
(1)
For
Range I Laminar flow
combine equation (1) with the following definition of
'
f
:
m
RV
f
1
4
'
ν
=
(2)
to obtain:
S
R
g
V
m
2
4
2
ν
=
(3)
For
Range II Smooth Turbulent Blasius flow
combine equation (1) with the following
definition of
'
4
1
f
:
8
1
'
060
.
1
'
4
1
e
R
f
=
(4)
to obtain:
7
4
7
5
7
1
7
4
72
.
7
S
R
g
V
m
ν
=
(5)
For
Range II Smooth Turbulent Hazen & Williams flow
combine equation (1) with
the following definition of
'
4
1
f
:
12
1
'
627
.
1
'
4
1
e
R
f
=
(6)
to obtain:
11
6
11
7
11
1
11
6
25
.
11
S
R
g
V
m
ν
=
(7)

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