Soil Conservation Service Runoff
Equation
( P  Ia )
Q
( P  Ia )  S
2
where
Q = runoff (in.)
P = rainfall (in.)
Ia = initial abstraction (in.)
S = potential maximum retention after runoff begins (in.)
Initial Abstraction, Ia
Ia is all losses before runoff begins. It includes water retained in
surface depressions, water intercepted by vegetation, evaporation,
and infiltration. Ia is highly variable but generally is correlated with
soil and cover parameters.
Ia  0.2S
Soil Conservation Service Runoff
Equation becomes:
( P  0.2S )
Q
( P  0.8S )
2
1000
S
 10
CN
where CN = curve number
Curve Numbers
The major factors that determine CN are the hydrologic soil
group (HSG), cover type, treatment, hydrologic condition,
and antecedent runoff condition (ARC). Another factor
considered is whether impervious areas outlet directly to the
drainage system (connected) or whether the flow spreads
over pervious areas before entering the drainage system
(unconnected).
Hydrologic Soil Groups
Group A soils have low runoff potential and high infiltration rates even when thoroughly
wetted. They consist chiefly of deep, well to excessively drained sand or gravel and have a high
rate of water transmission (greater than 0.30 in/hr). Soil Texture: Sand, loamy sand, or sandy
loam
Group B soils have moderate infiltration rates when thoroughly wetted and consist chiefly of
moderately deep to deep, moderately well to well drained soils with moderately fine to
moderately coarse textures. These soils have a moderate rate of water transmission (0.15-0.30
in/hr). Soil Texture: Silt loam or loam
Group C soils have low infiltration rates when thoroughly wetted and consist chiefly of soils
with a layer that impedes downward movement of water and soils with moderately fine to fine
texture. These soils have a low rate of water transmission (0.05-0.15 in/hr). Soil Texture:
Sandy clay loam
Group D soils have high runoff potential. They have very low infiltration rates when
thoroughly wetted and consist chiefly of clay soils with a high swelling potential, soils with a
permanent high water table, soils with a claypan or clay layer at or near the surface, and shallow
soils over nearly impervious material. These soils have a very low rate of water transmission (00.05 in/hr). Soil Texture: Clay loam, silty clay loam, sandy clay, silty clay, or clay
1000
S
 10
CN
1000
S
 10  3.33 in.
75
( P  0.2S )2 (6.0  0.2(3.33)) 2
Q

 3.28 in.
( P  0.8S )
(6.0  0.8(3.33))
V  (3.28 in.) x (175 acres ) x ( 121 ftin.. )  47.83 acre  ft.
Time of Concentration and Travel Time
• Travel Time (Tt) is the time it takes water to travel
from one location to another in a watershed. It is
typically a component of Tc.
• Time of Concentration (Tc) is the time for runoff to
travel from the hydraulically most distance point of
the watershed to a point of interest in the watershed.
Factors Affecting Tt and Tc
• Surface roughness
• Channel shape and flow patterns
• Slope
Water Movers through a Watershed as:
•
•
•
•
Sheet flow
Shallow concentrated flow
Open channel flow, or
A combination of these.
L
Tt 
3600 V
where:
Tt = travel time (hr)
L = flow length (ft)
V = average velocity (ft/s)
Tc  Tt  T1  T2  T3  T4  ...
Sheet Flow
• Shallow flow depth (< 0.1 ft) over plane surfaces
• Only for flows up to 300 feet
0.007(nL)0.8
Tt 
( P2 )0.5 s 0.4
where:
Tt = travel time (hr)
n = manning’s roughness coefficient (table 3-1)
L = flow length (ft)
P2 = 2-year, 24-hour rainfall (in)
s = slope of hydraulic grade line (land slope, ft/ft)
Shallow Concentrated Flow
• After a maximum of 300 feet, sheet flow usually
becomes shallow concentrated flow.
L
Tt 
3600 V
where:
Tt = travel time (hr)
L = flow length (ft)
V = average velocity from Figure 3-1 (ft/s)
Open Channel Flow
• Based upon Manning’s Equation
1.49 r 2 / 3 s1 / 2
V
n
where:
V = average velocity (ft/s)
r = hydraulic radius (ft) and is equal to area/wetted perimeter
s = channel slope (ft/ft)
n = Manning’s roughness coefficient for open channel flow
Then plug V and L
into this equation:
L
Tt 
3600 V
Example
Segment AB: Sheet flow; dense grass; slope (s) =
0.01 ft/ft; and length (L) = 100 ft.
Segment BC: Shallow concentrated flow; unpaved;
s = 0.01 ft/ft; and L = 1,400 ft.
Segment CD: Channel flow; Manning’s n = .05;
flow area (a) = 27 ft2; wetted perimeter (pw) =
28.2 ft; s = 0.005 ft/ft; and L = 7,300 ft.
Segment AB:
Sheet flow; dense grass; slope (s) = 0.01 ft/ft; and length
(L) = 100 ft.
Segment BC:
Shallow concentrated flow; unpaved; s = 0.01 ft/ft;
and L = 1,400 ft.
Segment CD:
Channel flow; Manning’s n = .05; flow area (a) = 27 ft2;
wetted perimeter (pw) = 28.2 ft; s = 0.005 ft/ft; and L =
7,300 ft.
Graphical Peak Discharge Method
• The peak discharge equations used is:
q p  qu AmQFp
where:
qp = peak discharge (cfs)
qu =
unit peak discharge (csm/in)
Am = drainage area (mi2)
Q = runoff (in)
Fp = pond and swamp adjustment factor
Rational Method
(used for areas of less than 50 acres)
Q = CiA
where:
Q = Peak rate of runoff in cubic feet per second
C = Runoff coefficient, an empirical coefficient
representing a relationship between rainfall
and runoff
i = Average intensity of rainfall for the time of
concentration (Tc) for a selected design storm
A = Drainage area in acres
Lets convert In-Ac/Hr to CFS:
[(1ft / 12 In) x (43,560 ft2 / Ac)] / 3600 Sec / Hr =
1.008 CFS / In-Ac / Hr
The degree of accuracy does
not warrant a units conversion
factor (constant) of
1.008!!