Page 392 - Civil Engineering Formulas

320 CHAPTER TWELVE

2
2
where A area of flow, ft (m )
R hydraulic radius, ft (m)
3
3
Q amount of flow or discharge, ft /s (m /s)
n Manning’s roughness coefficient
S slope of energy grade line or loss of head, ft (m), due to friction per
linear ft (m), of channel
AR 2/3 is referred to as a section factor.
Critical Depth of Open-Channel Flow

For a given value of specific energy, the critical depth gives the greatest dis-
charge, or conversely, for a given discharge, the specific energy is a minimum
for the critical depth.
For rectangular channels, the critical depth, d ft (m), is given by
c
3 Q 2
d c (12.81)
2
Bb g
where d critical depth, ft (m)
c
3
3
Q quantity of flow or discharge, ft /s (m /s)
b width of channel, ft (m)
MANNING’S EQUATION FOR
OPEN CHANNELS

One of the more popular of the numerous equations developed for determina-
tion of flow in an open channel is Manning’s variation of the Chezy formula:

V C RS (12.82)
where R hydraulic radius, ft (m)
V mean velocity of flow, ft/s (m/s)
S slope of energy grade line or loss of head due to friction, ft/linear
ft (m/m), of channel
C Chezy roughness coefficient

Manning proposed:
1.486 1/6
C (12.83)
n
where n is the coefficient of roughness in the Ganguillet–Kutter formula.
When Manning’s C is used in the Chezy formula, the Manning equation for
flow velocity in an open channel results: