MODULE 3 OPEN CHANNEL DESIGN - NC State University

MODULE 3

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OPEN CHANNEL DESIGN

Introduction

An open channel is defined as any conveyance system where a liquid is moved
under the influence of gravity in the presence of an air-water interface. Open channel flow
occurs in natural water courses, channels, diversions, and culverts. In all of these cases,
the energy source causing the water to move is gravity; water flows down hill. This
chapter will discuss the principles and equations needed to properly analyze and design
open channels used to convey water.

There are two accepted methods of designing open channels; (1) to limit the
average water velocity, or (2) limit the tractive force (shear stress) on the channel lining.
Depth of water and channel slope tend to increase both of these parameters thus causing
the channel lining and the soil under the lining to erode.

The continuity equation

Q = AV (1)

where Q is the discharge in ft3/sec (cfs), A is the channel’s cross-sectional area of flow in
ft2, and V is the average flow velocity perpendicular to the cross-sectional area in ft/sec or
fps. The cross-sectional area used in equation 1, is the area through which the water is
flowing as it moves down a channel, see Figure 3-1.

Figure 3-1. Typical Channel Cross Section.

F

Wetted parameter
Cross-sectional area

The velocity of water flowing in an open channel, has been described by Manning's
equation (Chow, 1959) as:

V = 1.486 R23 S 12 (2)
n

where V is the average flow velocity in a channel in fps, n is the Manning’s roughness
coefficient with units of ft1/6, R is the hydraulic radius in ft, and S is the channel’s slope in
direction of flow in ft/ft. The Manning’s n is obtained from a descriptive statement of the
channel roughness. Typical design Manning’s n values are shown in Table 3-1 and
Figure 3-3. In both of these presentations the accepted design roughness Manning n
values are given. Other references such as Chow (1959) and Schwab et al. (1966) show
ranges of Manning roughness coefficients for most of these conditions. There is no
substitute for experience in interpreting and selecting values of n.

The parameter called the hydraulic radius, R is defined as:

R= A (3)
Wp

where the cross-sectional area, A and the wetted perimeter, Wp are defined in Figure 3-1.
In a crude way the hydraulic radius can be thought of as the depth of flow.

The basic geometric relationships of cross-sectional area, wetted perimeter,
hydraulic radius, and top width are given in Figure 3-2 for several common channel
shapes. Most channels can be approximated by one of the five geometric shapes shown
in Figure 3-2. The area, wetted perimeter, and hydraulic radius formulae are most often
used in evaluation and design computations. The top width formulae are useful when
designing a channel. Most of the parameters shown in the sketches and used in the
formulae are self explanatory; d is the water flow depth in feet, D is the total depth of the
channel in feet (D is equal to the flow depth, d plus freeboard) [D = d + F], b is the
channel’s bottom width in feet, t is the channel top width at the depth of water flow, T is
the channel top width at the channel’s total depth, D in feet, and z is the side slope
expressed as a ratio as z(H):1(V). z is shown as being equal to the ratio e/d where e is
the horizontal distance and d is the vertical distance of the sloping side of a channel.

In general, Manning's equation can be used with the continuity equation to; (1)
describe and evaluate the capacity and velocity of an existing channel, or (2) to determine
the required channel dimensions so the desired amount of water can be safely
transported.

Channel Freeboard

Freeboard is an unused portion of a structure created to hold or carry water.
Freeboard is a way of adding or creating a factor of safety that is built into a water

a. Trapezoidal Cross-Section Cross-Sectional Wetted Hydraulic Radius,
Perimeter, Wp R = A/Wp
Area, A Top Width

t bd + zd 2 b + 2d z2 +1 bd + zd 2 t = b + 2dz
T = b + 2Dz
Dd or b + 2d z2 +1
b
b + 2dz or

approximate bd + zd 2

e b + 2dz

b. Triangular Cross-Section Cross-Sectional Wetted Hydraulic Radius, Top Width
t Area, A Perimeter, Wp R = A/Wp
t = 2dz
zd 2 2d z2 + 1 zd 2
T = 2Dz
Dd d or 2d z2 +1

2dz or

approximate d

e 2

c. Parabolic Cross-Section Cross-Sectional Wetted Hydraulic Radius,
t Area, A R = A/Wp
Perimeter, Wp Top Width
Dd 2 td t2d
t + 8d 2 t = A
3 3t 1.5t 2 + 4d 2 0.6 7 d

or or T = t(D / d)0.5

t approximate 2d

3

d. Semi-Circular Cross-Sectional Wetted Hydraulic Radius, Top Width
Cross-Section Area, A Perimeter, Wp R = A/Wp
t = 2d
t πd 2 πd d
2
d 2

e. Rectangular Cross-Section Cross-Sectional Wetted Hydraulic Radius, Top Width
t Area, A Perimeter, Wp R = A/Wp
t =b
bd b + 2d bd
T =b
b + 2d

Dd
b

Figure 3-2. Channel cross-section notation and formulas for a. trapezoidal, b. triangular, c. parabolic,
d. semi-circular, and e. rectangular channels. Freeboard = D - d. (Adapted from USDA-SCS
1972c)

structure. When a channel is properly designed, most of the channel depth is expected to
fill with and carry water when the design discharge occurs.

Schwab et al. (1966) states that all channels should have a minimum freeboard of
0.30 feet. A second, often used freeboard concept is to make freeboard a function of the
flow velocity and the flow depth. PA-DER (1990) requires that channel freeboard be
greater than or equal to

F = 0.075Vd (4)

where V is the channel flow velocity in fps and d is the depth of water in feet. The best
method of determining channel freeboard is to prescribe the larger of these two criteria.

Channel Design Process

Open channels, whose flow is governed by Manning’s and the continuity equations
can be evaluated or designed based on two different concepts. Failure of an open
channel can occur as a result of either of two conditions; (1) the channel does not have
the capacity to carry the water it was designed to carry and overbank flooding occurs, and
(2) the channel lining does not have the ability to with stand the flow velocities or shear
stresses on the channel lining and, therefore, erodes. One method is to determine the
maximum permissible velocity of the channel lining and then select the channel’s
geometry so that the velocity does not exceed this value. The second method is based on
the shear stress or tractive force acting on the channel lining. Again, based on the lining’s
ability to withstand a tractive force, the channel’s geometry is selected so the tractive force
does not exceed the maximum allowable tractive force. Both of these methods will be
presented. But before these two design approaches are presented, let’s take a look at
channel linings and define the design parameters for each lining.

Channel Linings

Open channels are typically distinguished by either their shape (trapezoidal,
triangular, parabolic, circular, or rectangular) of their lining. How various shapes affect the
flow of water in the channel will be discussed at length during the design section of the
module.

Channel linings can be classified several ways: (1) by the effect the lining has on
the friction or roughness of the channel, (2) by the effect the lining has on preventing
channel erosion, (3) by how quickly the lining will biodegrade and disappear, (4) by how
hard and permanent the lining is, and (5) by how much maintenance the lining will need.

Table 3-1. Manning’s roughness coefficients.

(Summarized and adapted from Schwab et al.,

1966, USDA-SCS, 1972b, and PA-DER, 1990).

Type of Channel and Lining Design n
Rigid Lined Channels 0.015
0.017
Asphalt
Concrete
Concrete rubble 0.024
Gabions 0.027
Metal, smooth (flumes) 0.013
Metal, corrugated 0.027
Plastic lined 0.013
Reno Mattress 0.025
Shotcrete 0.016
Wood, (flumes) 0.013
Earth Lined Channels
Firm loam, fine sand, sandy loam, silt loam 0.02
Stiff clay, alluvial silts, colloidal 0.025
Shales, hardpans, coarse gravels 0.025
Graded silt or loam 0.03
Alluvial silt 0.02
Earth, straight and uniform 0.023
Earth bottom, rubble sides 0.030
Coarse Gravel 0.030
Rock cuts, shale and hardpan 0.030
Durable rock cuts, jagged and irregular 0.040
Cobbles and shingles 0.035
Stony bed, weeds on bank 0.035
Straight, uniform 0.0225
Winding, sluggish 0.025
Natural Stream Channels
Clean, straight, full stage, deep pools 0.03
Clean, straight, full stage, weeds and stones 0.035
Winding, some pools and shoals 0.039
Sluggish river reaches, weedy, w/ deep pools 0.065
Very weedy reaches 0.11
Pipes
Asbestos-Cement 0.009
Cast Iron 0.012
Clay, drainage tile 0.012
Concrete 0.015
Corrugated Plastic Drainage pipe 0.015
Metal, corrugated 0.025
Steel, riveted, spiral 0.016
Vitrified Sewer pipe 0.013

Manning’s Roughness Coefficient, n

For purposes of channel design and channel performance, channel linings are best
divided into three categories, (1) linings with Manning’s roughness coefficients that remain
constant as the flow conditions in the channel change, (2) linings with Manning’s
roughness coefficients that change as the depth of flow increases, and (3) linings with
Manning’s roughness coefficients that change with a variety of flow conditions. Each of
these three types of linings will be addressed separately.

Linings with constant Manning’s roughness coefficient. Channel linings that are
generally considered to have constant roughness coefficients, meaning that Manning’s n
remains constant as the channel’s flow depth and velocity change, are summarized in
Table 3-1. Most of the linings listed in Table 3-1 are hard linings that have minimal or no
biological components. The exceptions are the natural streams, which, in some cases are
considered to change as the vegetation in the riparian buffer develops and matures.

Linings with Manning’s roughness coefficients that vary with flow depth. Rocks are
valuable channel liners. In areas were velocities are too fast for bare soil or vegetated
linings, rock placed by itself, as riprap, or placed in wire baskets, as gabions or Reno
Mattresses, forms a channel lining that will yield very good protection against erosion.

Riprap is a permanent, erosion-resistant ground cover of large, loose, angular
stone. Riprap protects the soil surface from the erosive forces of concentrated flow.
Riprap slows the velocity of concentrated runoff while enhancing the potential for
infiltration and stabilizes slopes with seepage problems and/or non-cohesive soils.

Riprap is classified as either graded or uniform depending on the range of rock
sizes present in the rock mixture. Graded riprap should contain a mixture of stones that
vary in size from about 0.5D50 to 2D50. Uniform riprap contains stones that are all nearly
the same size, D50. Graded riprap is preferred to uniform riprap in erosion and
sedimentation control. It is cheaper to install, requiring only that the stones be dumped so
they remain a well-graded mass. Hand or mechanical placement of individual stones is
limited to achieving the proper, uniform thickness.

Stone for riprap should consist of fieldstone or rough unhewn quarry stone of
approximately rectangular shape. The stone should be hard and angular and should not
disintegrate on exposure to water or weathering. Riprap should be placed by end dumping
(from a truck) to prevent segregation by sizes. It should never be pushed downhill by a
dozer or dropped down a chute, because these operations cause segregation of particles.

0.10

0.09

Manning's n 0.08 12 in
0.07 10 in
0.06 6 in 8 in
0.05
0.04 4 in5 in
3 in
2 in
1 in

0.03

0.02

0.01

0.00 1 10
0.1 Flow Depth, d (ft)

Figure 3-3. Manning's roughness coefficients for riprap lined channels. (Taken from PA-DER, 1990).

In open channels, lined with rock, the Manning’s roughness coefficient is greatest
at shallow depths of water and decreases as the depth of water increases. Figure 3-3
shows that when the depth of water in a rock or riprap lined channel is of the same order

of magnitude as the rock lining (d/D50 ≈ 1), the friction is very high, i.e. Manning’s n = 0.06
to 0.07. As the depth of flow increases relative to the rock size (d/D50 > 10, the friction
decreases and approaches a constant that is dependent on the rock size used in the
lining, i.e. n = 0.025 for D50 = 1" rock; n = 0.028 for D50 = 2" rock and n = 0.030 for D50 = 3"
rock. The curves plotted in Figure 3-3 are the solution to the following equation (USDA-
NRCS, 1977)

n = [21.6 log10 d 16 ) + 14.0] (5)
(d
/ D50

where d is the depth of flow in the rock-lined channel in feet , D50 is the average rock
diameter in feet and n is Manning's roughness coefficient.

According the PADEP (2000), some of the newer temporary erosion blankets also
create a situation where Manning’s n varies with flow depth, see Table 3-2.

Table 3-2. Manning’s roughness coefficients (n) for commonly used temporary channel linings.

(PADEP, 2000).

Manning’s n

Water Depth Ranges

Lining Type 0 – 0.5 ft 0.5 – 2.0 ft >2.0 ft

Jute Net 0.028 0.022 0.019

Curled Wood Mat 0.066 0.035 0.028

Synthetic Mat 0.036 0.025 0.021

Linings with Manning’s roughness coefficients that vary with flow depth and

velocity. Vegetation lined channels have roughness coefficients that vary greatly
depending on the type of vegetation and the length of the vegetation.

Table 3-3. Retardance Classifications of Various Grasses. (Adapted from USDA-SCS, 1947).

Retardance Class Cover Condition

A. Very High Weeping love grass Excellent stand, tall (avg 30 in)
a = -0.5 Yellow bluestem ischaemum Excellent stand, tall (avg 36 in)
B. High Very dense growth, uncut
a=2 Kudzu Good stand, tall (avg 12 in)
Bermuda grass Good stand, unmowed
C. Moderate Native grass mixture (little blue-stem, blue
a=5 gama, and other long and short Midwest Good stand, uncut (avg 20 in)
grasses. Good stand, tall (avg 13 to 24 in)
D. Low Grass-legume mixture (Timothy, bromegrass) Good stand, not woody, tall (avg 19 in)
a=7 Weeping love grass Good stand, uncut (avg 11 in)
Lespedeza series Good stand, uncut (avg 13 in)
Alfalfa Fair stand, uncut (avg 10-48 in)
Blue Gama Good stand, Mowed (avg 6 in)
Good stand, uncut (avg 11 in)
Crab grass Good stand, uncut (6 to 8 in)
Bernuda grass
Common lespedeza Very dense cover (avg 6 in)
Grass-legume mixture-summer (orchard grass, Good stand, headed (avg 6-12 in)
redtop, Italian rye grass, common lespedeza) Good stand, cutto 2.5 in height
Centipede grass Excellent stand, uncut (avg 4.5 in)
Kentucky bluegrass Good stand, uncut (avg 3-6 in)
Good stand, uncut (avg 4-5 in)
Bermuda grass
Common lespedeza After cutting to 2-in height, very good
Buffalo grass stand before cutting
Grass-legume mixture-summer (orchard grass, Good stand, cut to 1.5-inch height
redtop, Italian rye grass, common lespedeza) Burned stubble
Lespedeza series

E. Very Low Bermuda grass
a = 11 Bermuda grass

Table 3-3 shows additional information required to select the retardance classes
for the vegetation. This table also shows the “a” coefficient needed to apply equation 6,
which computes the Manning’s roughness coefficient as a function of the flow velocity
(fps) and the hydraulic radius (ft) (Schwab et al., 1993)

n = [2.1 + 2.3a + 1 . (6)
6 ln(1.0127VR)]

In addition to the difficulties that come from having a roughness coefficient that varies with
VR, it is also necessary to account for whether the grass will be maintained at or near a
constant height or left to grow throughout the growing season. As can be seen in Table 3-
3, most grasses change retardance classes when they are left to grow. For example
Bermuda grass can be in classes B, C, D, or E depending on how high it is mowed.

Table 3-4. Maximum permissible velocities for non-vegetated channel linings.
(Adapted from USDA-SCS, 1972b and PA-DER, 1990).1

Channel Linings Maximum Permissible

Velocity

(ft/sec)

Earth Lined Channels

Fine Sand 1.50

Sandy Loam 1.75

Silt Loam (non-colloidal) 2.00

Ordinary Firm Loam, Fine gravel 2.50

Stiff Clay (very colloidal) 3.75

Graded, Loam 3.75

Alluvial Silts (colloidal) 3.75

Graded, Silt 4.0

Coarse Gravel (non-colloidal) 4.0

Cobbles and Shingles 5.0

Shales and Hardpans 6.0

Durable Bedrock 8.0

Rolled Erosion Control Products (RECP)

Am. Excelsior Co.; Curlex Net Free 3.0

Am. Excelsior Co.; Straw; 1 net 3.5

Am. Excelsior Co.; Straw; 2 nets 4.5

N. Am. Green; Straw; single net 5.0

Am. Excelsior Co.; Curlex I.73; 1 net 5.0

Geocoir/Dekowe; Straw; RS-1 6.0

N. Am. Green; Straw; double net 6.0

Am. Excelsior Co.; Curlex I.98; 1 net 6.0

Am. Excelsior Co.; Curlex II.73; 2 nets 7.0

N. Am. Green; 70% straw: 30% Coconut; double net 8.0

Geocoir/Dekowe; 400 8.0

Geocoir/Dekowe; Straw; RS-2 8.0

Am. Excelsior Co.; Curlex II.98; 2 nets 8.5

N. Am. Green; Polypropylene; double net; Bare soil 9.0

Geocoir/Dekowe; 70% Straw 30% Coconut; RSS/C-3 10.0

1 Company names are used for clarity and do not imply endorsement by NCSU or NC DOT.

N. Am. Green; Coconut; double net 10.0
Am. Excelsior Co.; Curlex III; 2 nets 10.0
Am. Excelsior Co.; Curlex Enforcer; 2 nets; Bare soil 10.0
Am. Excelsior Co.; Curlex High Velocity; 2 nets 10.0
Geocoir/Dekowe; 700 10.0
Geocoir/Dekowe; Poly/Fiber; RSP-5 12.0
Geocoir/Dekowe; Coconut, RSC-4 12.0
Geocoir/Dekowe; 900 15.0
N. Am. Green; Polypropylene; double net; Vegetated 16.0

Turf Reinforced Mats (TRM) 9.5
North American Green SC250; Bare soil 10.5
North American Green C350; Bare soil 12.0
Profile/Enkamat; 7003, seed w/ bonded fiber matrix (BFM) 12.5
North American Green P550; Bare soil 13.0
Profile/Enkamat II; seed and BFM; Bare 14.0
Profile/Enkamat; 7010, 7018, 7020, seed and hydromulch 14.0
Profile/Enkamat; 7010 – 7220, seed and BFM; Vege. 15.0
North American Green SC250; Vegetated 17.0
Am. Excelsior Co.; Recyclex 19.0
Profile/Enkamat II; seed and BFM; Vege. 19.0
Profile/Enkamat; 7920, seed and BFM; Vege. 20.0
North American Green C350; Vegetated 20.0
Profile/Enkamat; 7010 - 7220, seed and BFM; Bare 25.0
North American Green P550; Vegetated
2.50
Rock Lined Channels 4.50
Graded Rock, D50a (inches) 6.50
0.75 [Min = No. 8; Max = 1.5”] 9.00
1.50 [Min = 1”; Max = 3”] 11.50
3.00 [Min = 2”; Max = 6”] 13.00
6.00 [Min = 3”; Max = 12”] 14.50
9.00 [Min = 5”; Max = 18”] 13.50
12.00 [Min = 7”; Max = 24”] 16.00
15.00 [Min = 12”; Max = 30”] 18.00
Reno Mattress, 3 to 6-inch rock, 6 inches thick 22.00
Reno Mattress, 3 to 6-inch rock, 9 inches thick
Reno Mattress, 4 to 6-inch rock, 12 inches thick 7.00
Gabions 9.00

Rigid Lined Channels
Asphalt
Wood
aD50 refers to the median rock size in graded rock.

Maximum Permissible Velocities, Vmax

When designing a channel using the maximum permissible velocity procedure, it is
necessary to have reliable values of Vmax available for use in Manning’s equation (V =
Vmax). Maximum permissible velocities non-vegetated linings are presented in Table 3-4.

Table 3-5 contains the maximum permissible velocities for vegetative linings.
Because these linings are living plants that are rooted in the soil from which the channel
was cut, it is necessary to not only consider the type of vegetation, but also the

erosiveness of the soil in which the vegetation is growing and the slope of the channel. In
this table the channel’s soil is divided into two categories defined by the RUSLE’s K-value
found in Module 2, “erosion resistant” (K < 0.37) and “easily eroded” (K > 0.37). The
values given in Table 3-5 are for good vegetative stands. If the stand of vegetation used
provides less than full coverage, the values in Table 3-5 should be decreased accordingly.

Table 3-5. Maximum permissible velocities for vegetation lined channels. (Modified from Ree, 1949
and PA-DER, 1990).

Maximum Permissible Velocities

Erosion Resistant Soils Easily Eroded Soils

K < 0.37 K > 0.37

(percent slope) (percent slope)

0-5 5-10 Over 10 0-5 5-10 Over 10

Cover fps fps fps fps fps fps

Bermuda Grass 87 6 6 5 4

Buffalo Grass

Kentucky Bluegrass

Smooth Bromegrass 76 5 5 4 3

Blue Grama

Tall Fescue 5 4 NRa 4 3 NR
Grass Mixture

Reed Canarygrass 5 4 NR 4 3 NR

Lespedeza

Weeping Lovegrass

Red Top

Kudzu 3.5 NR NR 2.5 NR NR

Alfalfa

Red Fescue

Crabgrass

Annuals for Temporary 3.5 NR NR 2.5 NR NR
Protection

Sudangrass 3.5 NR NR 2.5 NR NR

aNot Recommeded.

Maximum Allowable Shear Stress or Tractive Force, τall

Maximum allowable tractive force is a measure of the shear stress exerted by the
flowing water on the channel lining. If the actual shear stress, in lbs/ft2, exceeds the
maximum allowable shear stress or tractive force, the flowing water will erode the
channel, usually at its deepest depth. Maximum allowable tractive forces for non-cohesive
soils smaller than 6.35 mm (sands and gravels) are given in Figure 3-4. Allowable tractive
forces for a wide variety of channel linings are shown in Table 3-6. The dimensions for the
North Carolina rock classification are given in Table 3-7. Suggested products for use in
controlling erosion on side slopes are given in Table 3-8.

Allowabe Tractive Force (lbs/ft2) Allowable Tractive Force; D75 < 6.35 mm

1.00

Clear Water
Low Content
High Content

0.10

0.01 1.0 10.0
0.1 Median Particle Size (D50) mm

Figure 3-4. Allowable tractive forces for non-cohesive soils; D75 < 6.35 mm or 0.25 inches
(Adapted from USDA-SCS, 1964).

Finally, it is important to note that the tractive force, or shear stress in a channel
does not remain constant across the entire channel. Figure 3-6 shows how the shear
stress changes across a trapezoidal channel. The important thing to keep in mind is that
shear stress is almost always maximum at the point in the channel where the depth of
flow is the greatest.

Table 3-6. Allowable Tractive Forces and Manning’s n Values for Various Channel Linings
(PADEP, 2000).1

Allowable

Tractive

Channel Lining Category Lining Type Force, τ
(lbs/ft2)

Unlined – Erodible Soils (K > 0.37) Silts, Fine – Medium Sands 0.03

Coarse Sands 0.04

Very Coarse Sands 0.05

Fine Gravel 0.10

Erosion Resistant Soils (K < 0.37) Sandy loam 0.02

Gravely, Stony, Channery loam 0.05

Stony or Channery silt loam 0.07

Loam 0.07

Sandy clay loam 0.10

Silt loam 0.12

Silty clay loam 0.18

Clay loam 0.25

Shale & Hardpan 1.00

Durable Bedrock 2.00

RECP Jute Netting 0.45

Geocoir/Dekowe; Straw; RS-1 0.83

Profile; Futerra 1.00

Am. Excelsior Co.; Curlex Net Free 1.00

Am. Excelsior Co.; Straw; 1 net 1.25

Geocoir/Dekowe; Straw; RS-2 1.25

Turf Reinforced Mats (TRM) E. Coast Ero. Blank.; Straw/Coir, 2 Jute 1.35
nets
Am. Excelsior Co.; Straw; 2 nets 1.50
1.55
N. Am. Green; Straw; single net 1.55
1.55
Am. Excelsior Co.; Curlex I.73; 1 net 1.63
1.65
E. Coast Ero. Blank.; Straw, 1 net 1.75
1.75
E. Coast Ero. Blank.; Coir, 2 Jute nets 1.80
1.85
Am. Excelsior Co.; Curlex I.98; 1 net
2.00
Am. Excelsior Co.; Curlex II.73; 2 nets
2.00
N. Am. Green; Straw; double net
E. Coast Ero. Blank.; Excelsior, 1 net 2.00
Geocoir/Dekowe; 70% Straw 30% Coconut; 2.00
2.00
RSS/C-3 2.00
N. Am. Green; 70% straw: 30% Coconut; 2.10
double net 2.10
N. Am. Green; Polypropylene; double net; 2.25
Bare soil 2.30
Am. Excelsior Co.; Curlex II.98; 2 nets 2.30
Geocoir/Dekowe; Poly/Fiber; RSP-5
Geocoir/Dekowe; Coconut, RSC-4 2.60
E. Coast Ero. Blank.; Excelsior, 2 nets 3.00
E. Coast Ero. Blank.; Straw, Jute net
E. Coast Ero. Blank.; Straw, 2 nets 3.10
N. Am. Green; Coconut; double net 3.20
Am. Excelsior Co.; Curlex III; 2 nets 3.21
Am. Excelsior Co.; Curlex Enforcer; 2 nets; 4.46
4.63
Bare soil 8.00
E. Coast Ero. Blank.; Straw/Coir, 2 nets
Am. Excelsior Co.; Curlex High Velocity; 2 2.50
3.00
nets 3.25
Geocoir/Dekowe; 400 3.50
E. Coast Ero. Blank.; Coir, 2 nets 5.00
E. Coast Ero. Blank.; Polypropylene, 2 nets
Geocoir/Dekowe; 700 6.00
Geocoir/Dekowe; 900
N. Am. Green; Polypropylene; double net; 6.0-8.0
Vegetated
North Am. Green SC250; Bare soil 6.7-11.2

North Am. Green C350; Bare soil 7.00

North Am. Green P550; Bare soil 8.00
8.00
E. Coast Ero. Blank.; Coir, 3 nets

Profile/Enkamat; 7003, seed w/ bonded
fiber matrix (BFM)

Profile/Enkamat; 7010, seed and
hydromulch

Profile/Enkamat; 7010 – 7220, seed and
BFM; Vege.

Profile/Enkamat; 7010 - 7220, seed and
BFM; Bare

Profile/Enkamat; 7018, seed and
hydromulch

North Am. Green SC250; Vegetated
Profile/Enkamat; 7020, seed and

hydromulch

Grass Liners Profile/Enkamat II; seed and BFM; Vege. 8.00
Profile/Enkamat; 7920, seed and BFM; 8.00
Aggregate & Riprap
(See Table 3-7) Vege. 10.0
North Am. Green C350; Vegetated 10.0
Reno Mattress & Gabion Profile/Enkamat II; seed and BFM; Bare 10.0+
Concrete Am. Excelsior Co.; Recyclex 12.5
North Am. Green P550; Vegetated 0.60
Class D; a = 7 1.00
Class C; a = 5 2.10
Class B; a = 2 0.25
#57 0.50
#5 1.00
Class A 2.00
Class B 3.00
Class 1 4.00
Class 2 8.35
100.

Table 3-7. Aggregate and Riprap gradation.

Graded Rock Size (in)

Class or # Maximum D50 Minimum
#57 1 ½ No. 8

#5 1 3/4 3/8

A 64 2

B 12 8 5

1 17 10 5

2 23 14 9

Figure 3-5. Channel lining selection guide.

Table 3-8. Permissible Shear Stress of Various RECP’s. (Adapted from Table 6.17a NCDENR (2006))1

Max. Permissible Slopes
Shear Stress (lbs/ft2) Up to
Category Product Type

RECP N. Am. Green; Straw; 1 net 1.55 3:1

Am. Excelsior Co.; Curlex Net Free 1.00 3:1

Am. Excelsior Co.; Straw; 1 net 1.25 3:1

Geocoir/Dekowe; Straw; RS-1 0.83 3:1

N. Am. Green; Straw; 2 nets 1.75 2:1

Am. Excelsior Co.; Curlex I.73; 1 net 1.55 2:1

Am. Excelsior Co.; Curlex I.98; 1 net 1.65 2:1

Am. Excelsior Co.; Straw; 2 nets 1.50 2:1

Geocoir/Dekowe; Straw; RS-2 1.25 2:1

Geocoir/Dekowe; 70% Straw 30% 1.85 2:1

Coconut; RSS/C-3

Geocoir/Dekowe; Poly/Fiber; RSP-5 2.00 2:1

Geocoir/Dekowe; Coconut, RSC-4 2.00 2:1

Am. Excelsior Co.; Curlex II.73; 2 nets 1.75 1.5:1

Am. Excelsior Co.; Curlex II.98; 2 nets 2.0 1.5:1

Am. Excelsior Co.; Straw/Coconut; 2 1.5:1

nets

N. Am. Green; 70% straw: 30% Coir; 2 2.00 1:1

nets

N. Am. Green; Coconut; 2 nets 2.25 1:1

Am. Excelsior Co.; Curlex III; 2 nets 2.3 1:1

N. Am. Green; Polypropylene; 2 nets; 2.0 1:1

Bare soil

N. Am. Green; Polypropylene; 2 nets; 8.0 1:1

Vegetated

Am. Excelsior Co.; Coconut; 2 nets 1:1

Am. Excelsior Co.; Curlex Enforcer; 2 0.75:1

nets

Am. Excelsior Co.; Curlex High Velocity; 3.0 0.75:1

2 nets

TRM Profile/Enka; 7003, Vege. 5.0 3.5:1

Profile/Enka; 7010, 7210, 7910, Vege. 6.0 2:1

Profile/Enka; 7220, 7020, Vege. 8.0 1.5:1

Profile/Enkamat II 8.0 1:1

Profile/Enka; 7520, Vege. 8.0 0.5:1

Am. Excelsior Co.; Recyclex 10.0+ 0.5:1

NCDENR Specs

Degradable RECP’s Nets and Mulch 0.1 – 0.2 20:1

(Unvegetated) Coir Mesh 0.4 – 3.0 3:1

Blanket – Single Net 1.55 – 2.0 2:1

Blanket – Double net 1.65 – 3.0 1:1

Nondegradable Unvegetated 2–4 1:1

Turf Reinforced Mats Partially Vegetated 4–6 >1:1

Fully Vegetated 5 - 10 >1:1

Figure 3-6. How tractive force varies in a trapezoidal channel.

Selecting Channel Linings

Applying the maximum permissible velocity, Vmax criteria to channel lining
selection is difficult, requiring that the lining be chosen before the channel is designed.
The maximum allowable tractive force, can however be applied quite easily to channel
lining selection. Tractive force, τ is a measure of the frictional resistance to flow in a
channel and is the weight of the water in the channel on the channel bottom times the
channel slope or

τ = γRS . (7)

In this equation τ is the average shear stress acting on the channel lining across the
width of the channel. In a wide channel with a rectangular cross-section, the depth can
be assumed to equal the hydraulic radius, d = R. If we substitute the depth into equation
7, we get an expression of shear stress that is a function of flow depth and slope as

τ = γdS . (8)

In a channel with a rectangular cross-section, the tractive force is nearly constant, see
Figure 3-5. In channels having cross-sections where the depth is not constant, the
maximum tractive force occurs where the depth of flow is greatest. Thus, if τ is set equal
to the maximum allowable shear stress (from one of the above tables or figures),
equation 8 can be solved for, what is the maximum allowable flow depth, dmax as

d max = τ all (9)
γS

Where S is the channel slope in feet/foot and γ is the unit weight of water (62.4 lbs/ft3).
In most cases, where channel linings are to be chosen, it is better to solve equation 9
for the maximum shear stress, which occurs at the point of maximum flow depth as

τ max = γdmax S . (10)

By comparing the maximum shear stress from equation 10 with the maximum allowable
shear stresses from the tables and figures above a channel lining can be selected. The
following example will show the procedure.

Table 3-9. North Carolina DOT guidelines for selecting channel linings.

Channel Slope (%) Recommended Channel Lining

0.0 to 1.5 Seed and mulch

>1.5 to 5.0 Temporary liners

>5.0 Turf Reinforced Mats or Hard

In North Carolina, DOT has a rule of thumb to assist in selecting road ditch linings.
These guidelines are shown in Table 3-9. The following example will show that the NC
DOT guidelines are consistent with meeting the allowable shear stress limitations.

Example 1. A proposed triangular road ditch channel has 2:1 side slopes,
a slope of 3%, and the road will be serviced by an 18-inch culvert; the
design depth of flow in the proposed road ditch is generally about the
same depth as the diameter of the culvert. Select a suitable channel lining
for this channel.

Solution: Since the road is serviced by an 18-inch culvert, it is safe to
assume that the maximum flow depth in the ditch will be about 18 inches
or 1.5 feet. From equation 10 compute the maximum shear stress in this
channel as

τ max = (62.4)(1.5)(0.02) = 1.9lbs / ft 2

Now look on the tables and figures above and select a channel lining that
has a maximum allowable shear stress that is >1.9 lbs/ft2. Table 3-8
shows that a double-sided non-degradable RECP without vegetation
maybe okay (actually this channel pushes the upper limits of when such a
liner is expected to do the job of controlling erosion. This is consistent with
the guidelines in Table 3-9. It should be noted that for slopes greater than
the 2% used in this example, temporary liners are going to be subjected to
excessive shear stresses and will be expected to fail.

If this example is re-worked using a ditch slope of 1%, the maximum shear
stress in the channel will be just less than 1.0 lbs/ft2, which is probably
okay for seed and mulch. If, with the flatter slope, we also assume a

smaller culvert, say 12-inch, then the shear stresses are more reasonable
for the seed and mulch application.

It is hard to understand how channel slope relates or controls depth of
flow.

North American Green Software

A procedure, not greatly different from the one developed above for trapezoidal
channels has been developed and published by North American Green, Inc (Lancaster
and Nelsen, 2002). This software package is available from North American Green, Inc
and you are encouraged to go to http://www.nagreen.com/software/ and download the
software package named ECMDS version 4.2 onto your own computer.

Sizing Pipes for Open Channel Flow

Though circular channels obey the continuity and Manning’s equations, the
geometry of circular channels is much more complex. Therefore, it is suggested that you
use Figure 3-7 for sizing pipes that have relatively smooth linings such as clay or
concrete pipe or corrugated plastic pipe with the smooth inner lining. For corrugated
plastic pipe, Figure 3-8 is appropriate. In both of these figures the pipe slope, in %, is
located on the x-axis and the pipe discharge, in gpm, is located on the y-axis. The solid
sloping lines (low on the left and rising toward the right) represent each pipe (diameter
shown below the line) flowing full.

ACRES DRAINED

40,000 8000 4000 2000
30,000 5000
20,000
48” V=20 5000 3000 1000 4000 2000
10,000 42” V=15 4000 2000 3000
36” V=12
3000 2000 1000
30”
2000 1000 500
V=10 400 1000 500
V=9 400
300
5,000 24” V=8 1000 500 200 300
4,000 V=7 400 500
3,000 18” 400 200
2,000 16”V=6 300
14” 500 300
1,000 12” 400 200 100

DISCHARGE (GPM) 10” 300 200 100

V=5 200 100 50
V=4 40

500 8” 100 50 30 100 50
400 40 20 40

6”V=3 30
50
300 30 10 40 20
50
5” 40 20 30

200 V=2

4” 30 20 10

100 20 10 5

4
10 5

34

50
10 5
V=1
40 3
42

5

30 3 1 4 2

.1 .2 .3 .4 .5 1.0 2.0 3.0 4.0 5.0 10 1/4 1/2 1 3/8 3/4

SLOPE IN FEET PER 100 FEET (%) DRAINAGE COEFF.

Based on Manning’s n=0.0108

Figure 3-7. Pipe sizing chart for clay, concrete and corrugated plastic pipe with a smooth
inner liner (Jarrett, 2000).

ACRES DRAINED

10,000

V=12 900 600
V=10 400
V=8
V=7 15 00 1000 500
V=6
V=5 300 400
V=4
5,000 1000 500
4,000 V=3
3,000 400 200 300
V=2
2,000 500

300 400 200

500
400 200 100 300

300 200 100

1,000 18” 200 100 50
15”
40
100 50

500 12” 30 40

DISCHARGE (GPM) 400 100 50

10” 20 30
40
300
50

200 8” 30 40 20

50
40 20 10 30

6” 30 20 10

100 V=1

5” 20 10 5
4

50 4” 10 5 3 10 5
40 4 2 4
30 3” 3
20 3
5 5
2” 4 21 42
3
10 3
21

2 1 .5

V=.5 .4
1 .5

5.1 .6 .3 .4

.2 .3 .4 .5 1.0 2.0 3.0 4.0 5.0 10 1/4 1/2 1 3/8 3/4

SLOPE IN FEET PER 100 FEET (%) DRAINAGE COEFF.

Based on Manning’s n=0.015

Figure 3-8. Pipe sizing chart for corrugated plastic pipe. (Jarrett, 2000).

Flow Regimes

Water flowing in an open channel will exist in either the subcritical or supercritical
regime. Briefly, most natural streams are subcritical meaning that the energy due to the
depth of flow (potential energy) is greater than the kinetic energy of motion (velocity).
Occasionally, in steep channel reaches the flow may become supercritical. This means
that the kinetic energy of flow is greater than the depth energy.

Why is it important that you be aware of whether the flow in your channels is sub or
super critical? Because if your channel has supercritical flow, the water MUST go through
a hydraulic jump before it can return to subcritical flow. A hydraulic jump is a big energy
dissipater, which has the potential to erode large quantities of soil into the stream.

A channel can easily be checked to determine if the design flow will be sub or super
critical by computing the Froude Number as

Fr = Q2t (11)
gA3

Where Q is the flow rate in the channel (in cfs), t is the top width of flow in the channel (in
feet), g is the acceleration of gravity (as 32.2 ft/sec2), and A is the cross-sectional area of
flow (in ft2).

When the Froude Number is less than 1.0, the flow is subcritical; just the way you
want it. When the Froude Number is greater than 1.0, the flow is supercritical, and you will
need to design an energy dissipater to protect the channel where the slope decreases
and the flow will change to subcritical. If the Froude Number equals 1.0 the flow is critical.
This is so rare we need not worry about it. Table 3-10 shows how key channel flow
parameters are affected by flow regimes.

Table 3-10. Relationship between key channel flow parameters and flow regime.

Flow Regimes

Parameters Subcritical Critical Supercritical

Velocity < Vc = Vc >Vc
Depth > dc = dc < dc
Slope < Sc = Sc > Sc

Regime Changes

As discussed earlier, when subcritical flow passes through a transition the flow
depth will decrease. Conversely, when supercritical flow passes through a transition the
flow depth will increase. In many cases, the transition is so great that the flow after the
transition has not just changed in depth, but has also been transformed into a different
flow regime. For instance, when water flowing in a diversion, having a 1% slope, passes
through a slope change (transition) into a channel of conveyance, having an 8% slope,
the flow depth will not only decrease, but may also change from subcritical to supercritical

flow. The only correct way to determine whether a regime change has (or will) occur is to
check the Froude Number before and after the transition.

Subcritical to Supercritical Flow.

The transition from subcritical (Fr < 1.0) to supercritical (Fr > 1.0) flow is a smooth,
seldom noticed transition. The flow depth simply drops from a subcritical depth to a
supercritical depth as the flow velocity increases. As long as the channel lining(s) are able
to withstand the flow velocities, there is nothing to worry about. No special lining or
channel protection is generally needed.

Supercritical to Subcritical Flow.

The transition from supercritical (Fr > 1.0) to subcritical (Fr < 1.0) flow is, however,
a very different situation. This regime change occurs by passing the water through what
is called a 'hydraulic jump' where the depth of flow suddenly changes, often with “white
water”, from the supercritical depth to what appears to be the subcritical depth. The
purpose of white-water rafting is to ride these hydraulic jumps and experience the thrill of
the sudden depth change. In addition to a sudden depth change and white water (if the
change in Froude Number is great) there is also a large amount of energy lost or
dissipated onto the channel bottom at the point of the hydraulic jump. Therefore, any
portion of a channel that experiences a hydraulic jump must be carefully protected with a
channel lining that can withstand the elevated turbulence and velocities associated with a
hydraulic jump. Channel linings such as riprap, gabions or other durable material must be
used to line these channel portions.