CIVIL ENGINEERING FORMULAS

320 CHAPTER TWELVE

whereAarea of flow, ft^2 (m^2 )
Rhydraulic radius, ft (m)
Qamount of flow or discharge, ft^3 /s (m^3 /s)
nManning’s roughness coefficient
Sslope of energy grade line or loss of head, ft (m), due to friction per
linear ft (m), of channel

AR2/3is 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, dcft (m), is given by

(12.81)

wheredccritical depth, ft (m)
Qquantity of flow or discharge, ft^3 /s (m^3 /s)
bwidth 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:

(12.82)

whereRhydraulic radius, ft (m)
Vmean velocity of flow, ft/s (m/s)
Sslope of energy grade line or loss of head due to friction, ft/linear
ft (m/m), of channel
CChezy roughness coefficient

Manning proposed:

(12.83)

wherenis the coefficient of roughness in the Ganguillet–Kutter formula.
When Manning’s Cis used in the Chezy formula, the Manning equation for
flow velocity in an open channel results:

C

1.4861/6

n

VCRS

dc

B

(^3) Q 2
b^2 g