Chapter 6 Drainage Design
Chapter 6 Drainage Design
Chapter 6 Drainage Design
Rigid linings include concrete, stone masonry, soil cement, grouted riprap, and precast interlocking
blocks.
Channels with rigid lining are preferred for in a variety of cases, such as to
(1) transport water at high velocities to reduce construction and excavation costs,
(2) decrease seepage losses,
(3) decrease operation and maintenance costs, and
(4) ensure the stability of the channel section.
All channels carrying supercritical flow should be lined with concrete and continuously reinforced
both longitudinally and laterally. Since channels with rigid linings are capable of high conveyance
and high-velocity flow, flood-control channels with rigid linings are often used to reduce the
amount of land required for a surface-drainage system.
When land is costly or unavailable because of restrictions, use of rigid-channel linings is preferred.
A concrete-lined channel under construction using prefabricated concrete panels is shown in
Figure 6.5.
Channels with rigid linings are highly susceptible to failure from structural instability caused by
freeze-thaw, swelling, and excessive soil pore-water pressures, and rigid linings tend to fail when
a portion of the lining is damaged.
Figure 6.6 Hydrostatic pressure from ground water cracking a concrete canal lining.
Figure 6.7 A crack in the canal allowed water to erode the soil beneath the liner.
Construction of rigid linings requires specialized equipment using relatively costly material. As a
result, the cost of rigid linings is high. Prefabricated linings can be a less expensive alternative if
shipping distances are not excessive.
Flexible linings are called “flexible” because they are able to conform to changes in channel shape
while maintaining the overall integrity of the channel lining. Channels with flexible linings are
sometimes called flexible-boundary channels.
However, channels with flexible linings have the disadvantage of being limited in the magnitude
of the erosive force that they can sustain without damage to either the channel or the lining.
Flexible linings are widely used as temporary channel linings for erosion control during
construction or reclamation of disturbed areas.
EXERCISES
Together we identify the type of lining material the images are displaying:
2. What are the differences between rigid-lined channel and flexible-lined channel?
3. Why do you think you have to choose a specific type of lining material in constructing a
channel?
4. What will be the consequences in choosing the wrong type of lining material in building a
channel?
RESOURCES:
Chin, D. (2012). Water-Resources Engineering (3rd ed.) [E-book]. Pearson.
Mays, L. (2010, Aug.). Water Resource Engineering 2nd Edition.
INTRODUCTION
Roads have an impact on the natural surface and subsurface drainage patterns of a
watershed or a single hillslope. The primary goal of Drainage Structures is to reduce and/or
eliminate the energy generated by flowing water. Flowing has an exponentially increasing
destructive power as its velocity increases. As a result, water should not be allowed to build up to
such a volume or velocity that it causes excessive wear along ditches, beneath culverts, or along
LEARNING OUTCOMES
A road drainage structure must satisfy two main criteria if it is to be effective throughout
its design life: It must allow for a minimum of disturbance of the natural drainage pattern and It
must drain surface and subsurface water away from the roadway and dissipate it in a way that
prevents excessive collection of water in unstable areas and subsequent downstream erosion. The
• Students will be able to collect and organize appropriate clinical data of different drainage
structures.
• Students will be able to identify the appropriate drainage structure to be used considering
• Students will be able to articulate basic designs and materials used in constructing drainage
structures.
DISCUSSIONS
The design of drainage structures is based on the sciences of hydrology and hydraulics-the
former deals with the occurrence and form of water in the natural environment (precipitation,
streamflow, soil moisture, etc.) while the latter deals with the engineering properties of fluids in
motion.
1. Channel Crossings
a. Fords
b. Culverts
d. Bridges
a. Surface Sloping
3. Subsurface Drainage
a. Pipe Underdrains
b. Drilled Drains
c. French Drains
1. Channel Crossings
Channel crossings require careful design and construction. Functionally, they must (1)
allow for passage of the maximum amount of water which can reasonably be expected to occur
within the lifetime of the structure and (2) not degrade water quality or endanger the structure
Fords are a convenient way to provide waterway crossing in areas subject to flash
floods, seasonal high storm runoff peaks, or frequent heavy passage of debris or
avalanches. Debris will simply wash over the road structure. After the incident, some
Rawney Ford on the Bothrigg Burn, a tributary of the White Lyne in Cumbria, England.
Figure 1 shows a very simple ford construction where rock-filled gabions are used
Figure 1. Ford construction stabilized by gabions placed on the downstream end. (Megahan, 1977).
b. Culverts
Culverts are by far the most commonly used channel crossing structure used on
forest roads. Culvert types normally used, and the conditions under which they are
(RCP)
3. CM pipe-arch
6. Reinforced concrete box
Alignment should be such that water enters and exits the culvert directly.
Any abrupt change in direction at either end will retard flow and cause ponding,
culvert.)
Figure 2. Possible culvert alignments to minimize channel scouring. (USDA, Forest Service, 1971).
Figure 3. Proper culvert grades. (Highway Task Force, 1971).
capacity is its allowance for handling or passing debris. Past experience has shown
that channel crossings have failed not because of inadequate design to handle
unanticipated water flows, but because of inadequate allowances for floatable debris
which eventually blocked water passage through the culvert. Therefore, each channel
Figure 5. Debris control structure--trash rack made of steel rail (I-beam) placed over inlet
d. Bridges
Bridges often represent the preferred channel crossing alternative in areas where
footings, foundations, or abutments can cause channel scour and contribute to debris
blockage.
Reducing the erosive power of water can achieved by reducing its velocity. If, for
practical reasons, water velocity cannot be reduced, surfaces must be hardened or protected as
much as possible to minimize erosion from high velocity flows. Road surface drainage attempts
to remove the surface water before it accelerates to erosive velocities and/or infiltrates into the
road prism destroying soil strength by increasing pore water pressures. This is especially true for
a. Surface Sloping
toward the downhill side of the road. Outsloped roads are simple to build and
permanent roads, roads with high anticipated traffic volumes and/or loads, or
in areas with sensitive soils or severe climatic conditions. Insloping is
achieved by grading the road surface towards the uphill side of the road at a 3
to 5 percent grade.
• Crowned surfaces provide the fastest water removal since the distance water
has to travel is cut in half. The crowned surface slopes at 3 to 10 percent from
either side of the road centerline. Crowned surfaces and any associated cross
Water moves across the road surface laterally or longitudinally. Lateral drainage is
Figure 6. Road cross section grading patterns used to control surface drainage.
b. Surface Cross Drains
Surface cross drains are often needed to intercept the longitudinal, or down-road,
There are three types of cross drains used for intercepting road surface water:
• Open top culverts are most effective on steeper road grades. Open top culverts
• Cross ditches or water bars, are typically used on temporary roads. They are
the easiest and most inexpensive method for cross drain installation (Figure
10).
Figure 10. Cross ditch construction for forest roads with limited or no traffic
c. Ditches and Berms
Ditches and berms serve two primary functions on upland roads: (1) they intercept
surface run-off before it reaches erodible areas, such as fill slopes, and (2) they carry
run-off and sediment to properly designed settling basins during peak flow events
Ditch interception near stream to divert ditch water onto stable areas instead of into the stream. (U. S.
Environmental Protection Agency,1975).
Water collected in the cutslope ditch line has to be drained across the road prism
for discharge at regular intervals. Ditch relief culverts do not impact or impede traffic
as dips and open-top culverts do. Intercepting dips may become a safety hazard on
steep slopes as well as being difficult to construct. It is also undesirable to have large
amounts of water running across the road surface because of sediment generation and
Ditch relief culvert installation showing the use of headwall, downspout and a splash barrier/energy
dissipator at the outlet.
3. Subsurface Drainage
subsurface drainage techniques are required. If water is not removed from subgrade or pavement
structures it may create instability, reduce load bearing capacity, increase the danger of frost
a. Pipe Underdrains
This system consists of perforated pipe placed at the bottom of a narrow trench
and backfilled with a filter material such as coarse sand. It is generally used along the
This system consists of perforated metal pipes placed in holes drilled into cut or
c. French Drains
This system consists of trenches backfilled with porous material, such as very
coarse sand or gravel. This type of drain is apt to become clogged with fines and is not
recommended.
EXERCISES:
Make a diagram involving the different drainage structures including its sub components.
ASSIGNMENT:
Provide five pictures of any discussed drainage structures near to your community.
LITERATURE CITED:
Darrach, A. G., W. J. Sauerwein, and C. E. Halley. 1981. Building water pollution control into small private
forest and ranchland roads. U. S. Department of Agriculture, Forest Service and Soil Conservation Service.
Forest Soils Committee of the Douglas Fir Region. 1957. An introduction to the forest soils of the Douglasfir
Region of the Pacific Northwest. University of Washington.
Highway Task Force. 1971. Handbook of steel drainage and highway construction products (2nd Ed).
American Iron and Steel Institute, 150 E 2nd Street; New York. 368 p.
Megahan, W.F. 1977. Reducing erosional impacts of roads. In: Guidelines for Watershed Management.
Food and Agriculture Organization, United Nations, Rome. p 237-261.
Reid, L.M. 1981. Sediment production from gravel-surfaced forest roads, Clearwater basin, Washington.
Publ. FRI-UW--8108, Univ. of Washington, Seattle. 247 p.
Searcy, J. K. 1967. Use of riprap for bank protection. Federal Highway Administration, Washington D. C.
43 p.
USDA, Forest Service. 1971. Transportation engineering handbook. Handbook No. 7709.11.
Yee, C. S. and T. D. Roelofs. 1980. Planning forest roads to protect salmonid habitat. U. S. Department of
Agriculture, Forest Service. General Technical Report PNW-109. 26 p.
U.S. Dept. of Commerce, Bureau of Public Roads. 1963. Hydraulic Charts for the Selection of Highway
Culverts, Hydraulic Engineering Circular No. 5.
U.S. Dept. of the Interior, Bureau of Reclamation. 1974. Earth Manual, a water resources technical
publication. Second edition. Government Printing Office, Washington D.C.
NEGROS ORIENTAL STATE UNIVERSITY
MAIN CAMPUS II, BAJUMPANDAN, DUMAGUETE CITY
COLLEGE OF ENGINEERING AND ARCHITECTURE
CHAPTER VI
BEST HYDRAULIC SECTIONS
I. Introduction
The flow of water in a conduit may be either open channel or pipe flow. The two kinds are similar
in many ways but differ in one important respect. Open channel flow must have a free surface, while pipe
flow has none, since the water must fill the whole conduit. A free surface is subjected to atmospheric
pressure. Pipe flow, being confined in a closed conduit, exerts no direct atmospheric pressure but
hydraulic pressure only (Chow,1970).
There are various types of open channels encountered in transportation facilities: stream channel,
roadside channel or ditch, irrigation channel, and drainage ditch. Hydraulic design associated with natural
channels and roadway ditches is a process which selects and evaluates alternatives according to
established criteria. These criteria are the standards established to ensure that a highway facility meets its
intended purpose with without endangering the structural integrity of the facility itself and without undue
adverse effects on the environment or the public welfare.
Learning Outcomes:
The purpose of this chapter is to acknowledge the relevance of hydraulic cross-sections in the
hydraulic design and analysis. At the end of this chapter, the student will be able to:
• recall the importance and mechanism of open-channel flows;
• understand the relevance of most efficient cross-sections of conduits ; and
• perform calculations relating to the movement of water in open channels focusing on uniform flows.
II. Discussion
In most problems of steady flow, the discharge is constant throughout the reach of the channel of the
channel under consideration; in other words, the flow is continuous. When the discharge of a steady
flow is nonuniform along the channel, that is where water runs in or out the course of flow. This type
of flow, also known as spatially varied or discontinuous flow, is found in roadside gutters, side-
channel spillways, the washwater troughs in filters, the effluent channels around sewage-treatment
tanks, and the main drainage channels and feeding channels in irrigation systems.
• Uniform Flow and Varied Flow: Space as the criterion. Open-channel flow is said to be uniform flow
(UF) if the depth of flow does not vary along the channel. Conversely, it is nonuniform flow or varied
flow if the depth varies with distance. Nonuniform flows are further classified as rapidly varying flow
(RVF) if the flow depth changes considerably over a relatively short distance. Gradually varying
flows (GVF) are those in which the flow depth changes slowly with distance along the channel.
Examples of these types of flow are illustrated in Fig. 6.1.
The steady uniform flow case and the steady nonuniform flow case are the most fundamental types of
flow treated in highway engineering hydraulics.
In Fig.6.1, due to existence of a weir, a hydraulic jump occurred. A hydraulic jump occurs when
there is a significant change in depth and velocity and an abrupt transition from supercritical to subcritical
flow in the flow direction. The hydraulic jump is often employed to dissipate energy and control erosion
at highway drainage structures.
In Fig.6.2, two piezometer tubes are installed in the pipe at sections 1 and 2. The water levels in the tubes
are maintained by the pressure in the pipe at elevations represented by the so-called hydraulic grade line.
The pressure exerted by the water in each section of the pipe is indicated by the height d and the velocity
head, V2/2g, where V is the mean velocity of flow. The energy is represented in the figure by what is
called the energy grade line or simply the energy line. The loss of energy that results when water flows
from section 1 to section 2 by hf. It is assumed that the flow is parallel and has a uniform velocity
distribution and that the slope of the channel is small (Chow, 1970).
Equations
The following equations are those commonly used to analyze open channel flow.
• Continuity Equation
The continuity equation is the statement of conservation of mass in fluid mechanics.
Q=A1V1=A2V2
Where Q=discharge
A= cross-sectional area of flow (m2) or (ft2)
V= mean cross-sectional velocity (ft/s) or (m/s)
• Manning’s Equation
For a given depth of flow in an open channel with steady, uniform flow, the mean velocity can be
computed with Manning’s equation:
V= (R2/3S1/2)/n For S.I. unit
V=1.486(R2/3S1/2)/n For English unit
Where V= mean velocity (ft/s) or (m/s)
n= Manning’s roughness coefficient (see Table 6.1)
R= hydraulic radius (ft) or (m) or R= A/P (area/ wetted perimeter)
A= cross-sectional area of flow (m2) or (ft2)
P= = wetted perimeter
S= slope of the energy grade line (dimensionless)
For steady uniform flow, S= channel slope
The continuity equation can be combined with Manning’s equation to obtain the steady, uniform
flow discharge as:
Q=AV=(A)(R2/3S1/2)/n For S.I. unit
Q=AV=(A)1.486(R2/3S1/2)/n For English unit
For a given channel geometry, slope and roughness, and a specified value of discharge Q, a unique
value of depth occurs in steady, uniform flow. It is called normal depth. If the normal depth is greater than
critical depth, the slope is classified as mild slope, while on a steep slope, the normal depth is less than
critical depth. Thus, uniform flow is subcritical on a mild slope and supercritical on a steep slope.
• Energy Equation
The energy equation expresses conservation of energy in open channel flow expressed as energy per
unit fluid which has dimensions of length and is therefore called energy head. The energy head is
composed of potential energy head (elevation head), pressure head, and kinetic energy head (velocity
head).
h1+ (V12)/2g = h2+ (V22)/2g +hL
Where h1 = upstream (m or ft)
h2 = downstream (m or ft)
V= velocity (m/s or ft/s)
hL= head loss due to local cross-sectional changes (minor losses) as well as boundary
resistance (m or ft)
The energy equation states that the total energy head at the upstream cross-section is equal to the energy
head at the downstream section plus the intervening energy loss. The stage, h, is the sum of the elevation,
z at the bottom and the pressure head or the depth of flow, d, (h=z+d) as illustrated in Fig 6.2.
• Shear Stress
The shear stress is the hydrodynamic force of water flowing in a channel. The average boundary shear
stress, τ acting over the wetted surface of the channel is:
τ = γRS
Where γ= unit weight of the liquid
R= hydraulic radius = (Area/ Wetted Perimeter)
S= slope of the energy grade line
Table 6.1
Values of Manning Coefficient , n
The range of n values for various types of channels is given in Table 6.1.
Many channels are designed to carry fluid at a uniform depth along their length. Irrigation canals
are frequently of uniform depth and cross section for considerable lengths. Natural channels such as rivers
and creeks are seldom of uniform shape, although a reasonable approximation to the flowrate in such
channels can be obtained by assuming uniform flow.
In this section, we will be focusing on the most efficient hydraulic cross-sections of shapes that
are commonly used to allow the open channel to flow in uniform depth namely the rectangular, circular,
triangular, trapezoidal, and semi-circle.
According to El-Hazek (2012), The best hydraulic section of an open channel is characterized by
provision of maximum discharge with a given cross sectional area. For instance, for a given discharge rate
the use of best hydraulic section could guarantee the least cross-sectional area of the channels. Substantial
savings could be made from the reduction in the amount of excavation and from the use of less channel
linings. For a given flow, the best hydraulic channel section can be obtained by minimizing the wetted
perimeter (or the cross-sectional area).
Here are some keywords to be remembered in connection to the best hydraulic cross-section:
• maximum/optimum discharge;
A, n, and S are constant. Q (discharge) is at its maximum when R (hydraulic radius) is at maximum,
having a direct relationship. The hydraulic radius, being R= A/P (area/ wetted perimeter), is maximum
when the wetted perimeter is at minimum (inverse relationship). Thus,
Q max=(A) (R max2/3S1/2)/n
Q max=(A) (A/P min)2/3 (S1/2)/n
A cross-section with the least perimeter requires the least cost of grading and lining, making it known as
the most economical.
Figure 6.3. Precast reinforced oncrete rectangular channel(right) and its cross-section (left).
For a rectangular channel, as seen in Fig.6.3, with d as the height and b as the base width, the most
economical cross-section is:
Perimeter, P=b +2d
Area, A=bd
b= A/d
P=(A/d)+2d
(dP/dd) = -[(A)(1)]/d2+2=0
A/d2=2
A= 2d2
bd= 2d2
Therefore, b=2d
In getting the hydraulic radius of the most efficient section,
R=(A/P) = d2/(b+2d)
R= d2/(2d+2d)
R=d/2
Figure 6.4. Triangular cross-section (left) and triangular water irrigation (right).
Next, we have a triangular cross-section in Fig. 6.4. In order to obtain its most efficient cross-
section,
Perimeter, P=2d sec ( )
Area, A= 2d tan ( )] (d)
tan ( )=
sec ( )=
Then, P= 2d sec ( )
P=2d( )
P=2( )
=2
2 =
A=
tan ( )=
tan ( )= =1
( )= 45°
θ=90°
Figure 6.5. Cross drainage work in a trapezoidal shape(right) and its best cross-section (left)
For the trapezoidal cross-section (Fig. 6.5), the most economic cross-section can be obtained by solving,
The most efficient trapezoidal section (including the rectangle) has its top width (x) equal to the sum of
the sides (2y), which is a proportion for a half-hexagon. This shows that the best of all efficient
trapezoidal section is half- regular hexagon with all sides being equal.
Figure 6.6. Drainage circular channel with central slot. (left) and Concrete Drainage Pipe (right)
In Fig. 6.6, artificial drainage channels may have the most economic cross- section when.,
III. Summary
Open-channel flows are essential to the world as we know it. The natural drainage of water
through the numerous creek and river systems is a complex example of open-channel flow. Other
examples of open-channel flows include the flow of rainwater in the gutters of our houses; the flow in
canals, drainage ditches, sewers, and gutters along roads; the flow of small rivulets and sheets of water
across fields or parking lots; and the flow in the chutes of water rides in amusement parks.
With the application of the most- efficient sections of the common shapes used, these artificial
channels will be able to carry the maximum discharge and flow at minimum perimeter, thus lesser amount
of materials to be used, less labor and considered most economical.
IV. Exercise
V. Assignment
Examine whether or not the following statement is True or False. If found untrue, what word/s
made the statements false.
1. Uniform flow is subcritical on a steep slope and supercritical on a mild slope.
2. Gravity is the is the hydrodynamic force of water flowing in an open channel.
3. The Manning’s equation is the statement of conservation of mass in fluid mechanics.
4. The hydraulic head is composed of potential energy head (elevation head), pressure head, and
kinetic energy head (velocity head).
5. . Spatially varied or continuous flow, is found in roadside gutters, side-channel spillways, the
wash water troughs in filters, the effluent channels around sewage-treatment tanks, and the main
drainage channels and feeding channels in irrigation systems.
VI. References
American Association of State Highway and Transportation Officials (AASHTO),1992.
Highway drainage guidelines,volume vi, hydraulic analysis and design of open channels. Task
Force on Hydrology and Hydraulics, AASHTO Highway Subcommittee on Design, Washington
D.C.
Davidian, J., 1984. Computation of water surface profiles in open channels. Techniques of
Water resources Investigation, Book 3, Chapter A15, U.S. Geological Survey.
Federal Highway Administration (FHWA),1991. Users Manual for WSPRO. FHWA- SA-98-
080.
Munson, B.R., Young, D.F., Okiishi, T.H., & Huebsch, W.W. (2009). Fundamentals of fluid
mechanics (6th ed.). United States of America. John Wiley & Sons, Inc: Ingrao
Associates/Suzanne Ingrao
Walker, C. (2021).Drainage structures & their role in modern roadway infrastructure. Retrieved from
https://www.infrasteel.com/drainage-structures-their-role-in-modern-roadway-infrastructure/
Chapter III
DESIGN OF DRAINAGE CHANNELS
Introduction:
Water flowing in an open channel is restricted by resistance from the bed
and side slopes of the channel. This force of resistance conveys the boundary shear
force. Boundary shear stress is the tangential component of the hydrodynamic
forces acting along the channel bed. Flow attributes of an open channel flow are
directly dependent on the boundary shear force distribution along the wetted
perimeter of the channel. Computation of bed form resistance, channel migration,
side wall correction, sediment transport, dispersion, cavitations and conveyance
estimation, etc. can be studied and analyzed by the boundary shear stress
distribution. The shear force, for steady uniform flow is related to bed slope,
hydraulic radius and unit weight of fluid. However in a practical point of view,
these forces are not uniform even for straight prismatic channels. The
nonuniformity of shear stress is mainly due to secondary currents formed by the
anisotropy between vertical and transverse turbulent intensities, given by Gessner
(1973). Tominaga et al. (1989) and Knight and Demetriou (1983) demonstrated
that boundary shear stress increases when the secondary currents flow towards the
wall and shear stress decreases when it flows away from the wall. Other factors
affecting the shear stress distribution are the shape of channel cross-section, depth
of flow, later-longitudinal distribution of wall roughness and sediment
concentration. For the case of meandering channels, the factors increase even
more due to the nature of flow of water in such channels. Sinuosity in the case of
meandering channel is regarded to be a critical parameter in the shear stress
distribution along the channel bed and walls.
Boundary Shear Stress
Objectives: In designing a channel especially for drainage purposes, one of the few
things that a designer must take into account is the boundary shear stress. In this
chapter, we will learn
What is the boundary shear stress in a more simplified definitions
The basics and principles behind resistance offered by the walls of a channel
How to quantify these factors and relate them in the designing channels for
drainage
Discussions:
Shear force is the force that is always tangential to a given area. It gives kind
of slicing failure to whichever surface it is present on. Since force is always applied
to a finite area no matter how small it is, shear force can be analyzed as stress. Water
flowing in a channel, also experiences this stress and that’s where boundary shear
stress becomes a great factor when you are designing.
There are several devices that can be used to quantify shear force and its
relation to flowing fluid’s properties (velocity, pressure, viscosity, etc.). Pitot tube
is one of them. This device helps measure how fast a fluid is flowing in a channel.
Why knowing velocity is important? It is important because faster flowing fluid
might cause large shear stress on the wall boundaries of a channel and so it can be
used as a guide in design. How is velocity computed from a pitot tube? Consider
figure 1 below.
Left side tube is what they call piezometric tube. Inserting this piece of tube
to a pipe that has a flowing water in it will tell us the static pressure of the moving
fluid. The L – shaped tube shown on the right side is a pitot tube. This will not
only tell us the static pressure (if we compare it to peizometric tube) but also it will
tell us the dynamic pressure as the water in it rises. As soon as the water inside the
pitot tube rises it reaches a point where there will be no longer water that could
enter the tube due to water counter-acting against the flow. The moment the
velocity of the flowing water becomes zero, it now becomes the so-called
Stagnation point. By applying Bernoulli’s equation from the flowing water and the
stagnation point, will give us the equation to find the velocity of the moving water.
(See figure 2)
Where d is the outer diameter of the Preston tube, ρ is the density of the flow, υ is
the kinematic viscosity of the fluid, and F is an empirical function. Patel (1965)
further extended the research and his calibration is given in terms of two non
dimensional parameters x* and y*which are used to convert pressure readings to
boundary shear stress, where
The pressure readings are taken using pitot tubes along the predefined points
across all the sections of the channel along the bed and side slopes. The manometers
attached to the pitot tubes provide the head difference between the dynamic and
static pressures. The differential pressure is then calculated from the readings on the
vertical manometer by, ΔP = ρgΔh. Where Δh is the difference between the two
readings from the dynamic and static, g is the acceleration due to gravity and ρ is the
density of water. Here the tube coefficient is taken as unit and the error due to
turbulence is considered negligible while measuring velocity. Accordingly out of the
above given equations, the appropriate one is chosen for computing the wall shear
stress based on the range of x* values. After that the shear stress value is integrated
over the entire perimeter to calculate the total shear force per unit length normal to
flow cross-section carried by the meandering section. The total shear thus computed
is then compared with the resolved component of weight force of the liquid along
the stream-wise direction to check the accuracy of the measurements.
The experimental data of Flood Channel Facility (FCF) observed at
Wallingford UK was considered for calculation of boundary shear. This channel has
smooth surfaces and having flood plains at both sides of the meandering main
channel. The FCF is a 50 m long and 10 m wide flume. The main channel is
sinusoidal and has four meanders contained within a total length of 48 m giving rise
to a meander wavelength of 12 m each. The main channel is 150 mm deep and
trapezoidal in section with a top width of 1200 mm and a 45° bank slope. The main
channel is 60° meander giving sinuosity =1.374 and the flood plain has a slope of
0.000996. Each floodplain has a maximum width of 6.855 m and a minimum width
of 1.945 m.
The experimental data of Khatua that was observed in the lab at National
Institute of Technology, Rourkela is taken into consideration for boundary shear
calculation and analysis with other researchers. This is a rectangular channel where
a straight compound section has the main channel dimension of 120mm×120 mm,
and flood plain width B = 440 mm. The channel is cast inside a tilting flume of 12m
long, 450 mm wide, and 400 mm deep. The bed slope of the channel is kept at
0.0019.
The experimental data of Mohanty which was observed in the laboratory at
National Institute of Technology, Rourkela is used to calculate boundary shear and
analyse with various researchers. The type of channel considered here is a
meandering compound channel with trapezoidal main channel. The main channel
bottom width is 33cm and top width of compound section is 395cm.The side slope
of main channel is 1V:1H and the bed slope is 0.0011.The sinuosity is taken as 1.11
and crossover angle is 40 .The roughness criteria is rigid and smooth main channel
and smooth floodplains. (see Table 1 below)
The shear stress values are integrated over the entire perimeter of the two-stage
channel sections at the bend apex region for each of the data sets as given in Table
1. The shear force for each section is divided into different components, such as it is
individually calculated for the outer flood plain, outer main channel, inner main
channel and the inner flood plain. The percentage of shear force with respect to total
shear is analysed for each individual region to investigate the sharing of shear force
along the channel cross-section. In figure 3, the shear force, calculated as the
percentage of total shear is divided simply as Outer and Inner shear force
respectively. The regions are considered from the centre of the channel section.
Figure 4 depicts the percentage sharing of shear force among the Outer and Inner
Floodplain regions and the Main Channel section individually. Figures 5 and 6 is the
analysis of the the percentage sharing of shear force among the outer flood plain,
outer main channel, inner main channel and the inner flood plain regions separately
and as a whole respectively.
Figure 3: Boundary Shear Distribution at Outer and Inner Regions (in %age)
Figure 4: Boundary Shear Distribution at Outer Floodplain, Main Channel and Inner Floodplain
Regions (in %age)
Figure 5: Boundary Shear Distribution at Individual Regions throughout the Channel Section (in
%age) - Separately
Figure 6: Boundary Shear Distribution at Individual Regions throughout the Channel Section (in
%age) – In one Column
Exercises:
To cap it all and also as a sort of exercise to link the relationships between
flowing fluid’s properties to shear stress, below is a sample problem.
Sample Problem:
The velocity distribution for laminar flow between parallel plates is given by (see
eqn 1 below). Determine the shear stress on the upper plate and give its direction.
Equation 1
Illustration
Solution:
Assignment:
Consider steady fully developed flow between two infinite parallel fixed plates,
separated by distance 2h. It can be shown that the velocity distribution is parabolic
and is given by:
Find the magnitude of the shear stress at the top, center, and bottom boundaries.
References:
Johnson, W. (1942). “The importance of side-wall friction in bed-load
Investigation.” Civ. Eng. (N.Y.), 12, 329–331.
Keulegan, G. H. (1938). “Laws of turbulent flow in open-channels.” Natl.Bur.
Stand. Circ. (U. S.), 21, 709–741. Khatua, K. K. (2008), “Interaction of flow and
estimation of discharge in two stage meandering compound channels”.
Thesis presented to the National Institute of Technology, Rourkela, in partial
fulfilment of the requirements for the Degree of Doctor of philosophy .
Khatua, K.K., and Patra, K.C. (2010). “Evaluation of boundary shear distribution
in a meandering channel.” Proc. ninth Int. Conf. Hydro-Science and
Engineering, IIT Madras, Chennai, India, ICHE, 74.
Knight, D.W. (1981). “Boundary shear in smooth and rough channels.” J.
Hydrocarbon Div (ASCE), 107(HY7), 839– 851.
CHAPTER3:Desi
gnofDr
ainageChannel
s
Topi
cTi
tl
e:ChannelSl
ope
I
ntr
oduct
ion
Hydrologicstudi
esincl
udeacar efulapprai
saloff act
orsaffect
ingst ormrunoffto
i
nsurethedev el
opmentofadr ai
nagesy stem orcontrolworkscapableofpr ovi
dingthe
requi
reddegr eeofpr otect
ion(Guyer,2012).Dur i
ngheav yrai
nfal
l,drainagesy st
em
redi
rect
ssur facewaterrun-
offsf
rom pav ementandr oadstotheappropriatel
ydesigned
channels,eventual
lydi
schar
gingint
ot henaturalwatersyst
ems.
Drai
nagechannelsareusuall
ydr ywhenther
ei snosurfacerunoffandar edesi
gned
toaccommodat ethepeakrun-offr
atefrom adesignstor
m( Chi
n,2013).Itiscommonly
foundalongr oadsi
des.Indesigningadr ai
nagecanalt herearemanyf actor
st obe
consider
edtoensurethemostef fi
cient,
economic,anddurablehydrauli
cst r
uctur
e.One
ofthesefact
orsisthechannelsl
ope.
Lear
ningObj
ect
ives
Att
heendoft
hist
opi
c,wewi
l
llear
n;
t
odef
ineanddi
sti
ngui
shchannel
slopenadr
ainagesy
stem
whatar
elongi
tudi
nal
slopeandsi
desl
opes
t
ousechannel
slopei
nsol
vi
nghy
draul
i
cpr
obl
emst
heor
eti
cal
l
y
howt
odesi
gnspeci
fi
cchannel
slopesf
oradr
ainagechannel
s
Di
scussi
on
Inhy
drauli
cs,channelslopesareclassif
iedbasedonther
elat
ivemagni
tudeofthe
nor
maldepth,yna ndthecr it
icaldepth,yc.Theslopeofachannelisonef act
orin
det
ermi
ningthewater-
surfaceprofi
le.
Fi
gur
e1:
Par
tsofaTr
apezoi
dal
Channel
Def
ini
ti
on
Slopesar
eoneoft hebasisinclassif
yingwater-
sur
faceprof
il
es.Theimpor
tant
sl
opesconsi
deredi
nthechannel
desi
gnar elongi
tudi
nalsl
opesandsi
deslopes.
Longit
udi
nalsl
opesar
etheSo v
aluei nhy dr
aul
icproblemsinvol
vi
ngflowofwater
.
2/3 1/
2
I
nManningsequati
on,Q=(1/n)
AR So ,So i sthelongit
udinalsl
opeusual
lygi
venin
deci
malform,
rat
io,
andsomet
imespercent age.
Tabl
e1:
Hydr
aul
i
cCl
assi
fi
cat
ionofSl
opes
Name Ty
pe Condi
ti
on
Mi
l
d M y
n>y
c
St
eep S y
n<y
c
Cr
it
ical C y
n=y
c
Hor
izont
al H y
n=i
nfi
nit
y
Adv
erse A So=0
Sour
ce:
Chi
n,Dav
id.2013.Wat
erResour
cesEngi
neer
ing,3r
dEd.PEARSON,
Singapor
e.
p.134
Si
desl
opesar
etheH:
Vval
uef
oundi
ntr
apezoi
dal
andt
ri
angul
archannel
s.
Channel
Slopesi
nHy
draul
i
cPr
obl
ems
ExampleProbl
em 1:Thetar
getwat
er-
surf
aceelevat
ionofar
eserv
oiri
s50.
05m,
andthereser
voi
rdischar
gesi
ntoatr
apezoi
dalcanalt
hathasabott
om widt
hof2m,
si
deslopesof3:1(H:V),alongit
udinalsl
opeof1%,andanesti
matedManning’
snof
0.
020.Theelevat
ionoft hebott
om oft hecanalatther
eser
voi
rdi
schar
gelocat
ioni
s
47.
01m.Determinethedischar
gef r
om thereser
voi
r.
ExampleProbl
em 2:Wat erflowsat12m3/sinat r
apezoi
dalconcr
etechannel(n=
0.
015)ofbottom width4m,si deslopes2:1(
H:V),andlongi
tudi
nalslope0.0009.I
f
dept
hofflowatagagi ngstati
oni smeasur
edas0.80m, usethedir
ect
-stepmethodto
fi
ndthel
ocati
onwher ethedepthis1.00m.
Desi
gnf
orChannel
Slopes
Longit
udi
nalslopesareconstrai
nedbybot ht hegroundslopeandt hemaxi
mum
all
owableshearstr
essi nthechannell
ini
ng.Excavationisusuall
yminimizedbyl
ayi
ng
thechannelonaslopeequaltotheslopeofthegr oundsurface.Thechanneli
ssi
zeso
thatthepermi
ssi
blestressofl
ini
ngisnotexceeded.
Theall
owablesideslopesar
einfl
uencedbyt
hemat er
iali
nwhichthechannelis
excavat
ed.Indeepercut
s,sidesl
opesareoft
enst
eeperabovethewatersur
facethan
belowthewatersur
face.
Tabl
e2:
TypeofMat
eri
alandi
tsRecommendedSi
deSl
ope
Mat
eri
al Si
deSl
opes(
H:V)
Fi
rmr
ock 0:
1—0.
25:
1
Fi
ssur
edr
ock 0.
5:1
Ear
thwi
thconcr
etel
i
ning 0.
5:1—1:
1
St
if
fcl
ay 0.
75:
1
Ear
thwi
thst
onel
i
ning 1:
1
Fi
rm cl
ay,
sof
tcl
ay,
grav
ell
yloam 1.
5:1
Loosesandysoi
l
s 2:
1—2.
5:1
Ver
ysandysoi
l
,sandyl
oam,
por
ouscl
ay 3:
1
Sour
ce:
Chi
n,Dav
id.2013.Wat
erResour
cesEngi
neer
ing,3r
dEd.PEARSON,
Singapor
e.
p178
Theconstructi
onofsi
deslopesforchannel
sli
nedwit
hconcret
eshoul
dbegreat
er
than1:1.Sideslopesgr
eatert
han0.75:1(H:V)r
equir
ed l
i
ningsdesi
gnedt
owit
hstand
eart
hpr essur
es.
TheU.S.BureauofRecl
amati
onrecommendsa1.
5:1(
H:V)sl
opef
ort
heusual
sizes
ofconcret
e-l
inedcanal
s(USBR,1978)
.
TheU.S.Feder
alHi
ghwayAdmini
str
ationrecommendst
hatsi
deslopesi
nroadsi
de
andmedianchannelsnotexceed3:
1( USFHWA,2005) .I
fchannelsi
desaretobe
mowed,sl
opesof3:1orl
essshoul
dgenerall
ybeused.
TheDepartmentofPubli
cWor ksandHi
ghways(DPWH)publi
shedt heDesi
gn
Guidel
ines,Cr
it
eri
aandStandar
ds:Vol
ume3–Wat erEngi
neer
ingPr
oject
scommonly
knownast heDGCS,2015.
Inspeci
fyi
ngasi desl
ope,consi
der
ationshoul
dal
sobemadeformai
ntenanceand
saf
ety.Forchannel
sadjacentt
ohighways,thef
oll
owi
ngshoul
dappl
y:
Gener
all
ynotmor
ethan1V:
5H,
fort
raf
fi
csaf
ety
Wheretheabovecannotbeachi
eved,ort
hedept
hisgr
eat
ert
han3m,t
hena
saf
etybar
ri
eri
srequi
red
Tabl
e3:
TypeofMat
eri
alandi
tsRecommendedSi
deSl
ope
St
ream BankMat
eri
als Si
deSl
ope(
V:H)
Ri
gidLi
nedChannel
s near
lyv
ert
ical
Gr
assLi
nedChannel
s Notsteeperthan1:
4,general
l
yaimingf
or
1:
6toassistinmaintenanceandfor
publ
icsafety
Rock(
DryBoul
derRi
pRapLi
nedChannel
s) 1:
3
Gabi
onMat
tress Ref
ert
omanuf
act
urerspeci
fi
cat
ions.
Rei
nfor
cedGr
ass/
TRM Refertomanufacturerspeci
fi
cations.
Considerati
onshoul
dbegi v
enf or
maintenanceaccessaspergr asslined
channels,andt
herefore1:6would
general
lybeprefer
able.
Har
dCl
ay 1:
2to1:
1
Cl
ayLoam andSi
l
tyLoam 1:
2
SandyLoam 1:
2
Sand 1:
3
ce:DPWH.2015.DGCS:
Sour Vol
.3-Wat
erEngi
neer
ingPr
oject
s.p6-
11
Excer
sise
Exampl
e
1.Amedianchanneladjacenttoamajorhighwayistobeexcavat
edinasof
tcl
ayand
l
inedwit
hgrass.Ift
helongitudi
nalsl
opeofthehighwayi
s1%, whatwoul
dyousel
ectas
thel
ongi
tudinal
slopeandsideslopesofthemedianchannel?(
usetheUSBRand
USFHWAr ecommendations)
Sol
uti
on:
Thef
ir
stt
hingweneedt
odoi
stounder
standt
hesi
tuat
ion,
andt
ryt
oremembert
he
i
mport
antt
erms.
Thelongit
udinal
slopeofthemedianchannelshoul
dbe1%tomi
nimizeexcav
ati
on,
and
thesi
deslopesshouldbe3:1tofacil
i
tat
emowi ngandcompl
ywi
ththerecommendati
on
oftheU.S.Feder
alHighwayAdminist
rat
ion.
Longi
tudi
nalSl
ope-1%
Si
deSl
ope-3H:
1V(
asr
ecommendedbyt
heUSFHA)
2.Ari
gidli
nedchanneli
stobeexcavat
edi
nagroundsl
opeof0.2%.Usi
ngt
heDGCS:
Vol
.3,2015,desi
gnthelongi
tudi
nal
andsi
desl
opesoft
hechannel.
Sol
uti
on:
I
ndesigni
ngthel
ongit
udi
nalsl
ope,
iti
salway
srecommendedtof
oll
owthegroundsl
ope.
Baseonthegui
del
inesbyt
heDPWH, showni
ntable3t
herecommendedsi
deslopef
or
t
hischannel
isnear
lyv
ert
ical
.
Longi
tudi
nalSl
ope-0.
2%
Si
deSl
ope-near
lyv
ert
ical(
recommendedbyt
heDGCS:Vol
.3,
2015)
Assi
gnment
1.I
ll
ust
rat
ethedi
ff
erencebet
weenal
ongi
tudi
nal
slopeandchannel
slope.
2.Inyourownunder
standi
ng,
whati
sthei
mpor
tanceofchannel
slopesi
ndesi
gni
ng
drai
nagechannel
s?
3.Achannelisexcavat
edadjacentt
oahi ghwayonagr oundsur
facewithasl
opeof
0.0015.Thechannel
isli
nedwithgrass.Whatlongi
tudi
nalandsi
deslopesoft
he
channelwouldyouuse?(UsetheDPWHr ecommendati
on.)
4.Ausualsi
zeconcr
ete-l
inedcanali
sexcavatedata0.
0009gr
oundsl
ope.Usi
ngt
he
USBR'
srecommendations,desi
gnthelongi
tudinal
andsi
desl
opeoft
hecanal.
Ref
erences
Guy
erJ.P.2012.I
, ntr
oduct
iont
oAr
eaDr
ainageSy
stems.CEDengi
neer
ing.
com.
Retr
ievedat
htt
ps:/
/ www.cedengi
neer
ing.
com/
user
fi
les/
Int
ro%20t
o%20Ar
ea%20Dr
ainange%20S
yst
ems. pdf
Chi
n,Dav
id.2013.Wat
erResour
cesEngi
neer
ing,3r
dEd.PEARSON,
Singapor
e.
Ret
ri
ev edathtt
ps:
//pdf
cof
fee.
com/
wat
er-
resour
ces-
engi
neer
ing-
3rd-
edi
ti
on-
dav
id-
chi
n-pdf-
fr
ee.ht
ml
DPWH.2015.Desi
gnGui
del
i
nes,
Cri
ter
iaandSt
andar
ds:Vol
ume3–Wat
erEngi
neer
ing
Pr
oject
s.
Ret
ri
evedatht
tps:
//www.
scr
ibd.
com/
document
/356407005/
DGCS-
Vol
ume-
3-pdf
Fi
gur
esandi
magesr
etr
iev
edat
:
ht
tp:
//ecour
sesonl
i
ne.
iasr
i.
res.
in/
plugi
nfi
l
e.php/
2232/
mod_
page/
cont
ent
/1/
111.
pn
g
https:
//encry
pted-
tbn0.gstat
ic.
com/i
mages?q=t
bn:
ANd9GcROGY10Hy
Uz36Unt
d85mWFv
X-
dgXKkhVf 8FUg&usqp=CAU
CHAPTER 6
DESIGN OF DRAINAGE CHANNELS
Introduction
Drainage channels are designed either to be lined or unlined. Unlined channels are simply
excavated channels in the ground while lined channels, just like unlined, are excavated channels but with
various lining materials to provide stability and prevent erosion. Lining materials are classified as either
rigid or flexible (Chin, 2013). Rigid linings include channel pavements of concrete or asphaltic concrete
and a variety of precast interlocking blocks and articulated mats. Flexible linings include such materials
as loose stone (riprap), vegetation, manufactured mats of lightweight materials fabrics, or combinations
of these materials. Rigid linings are capable of high conveyance and high-velocity flow (Mays, 2010).
Rigid linings are called “rigid” because they tend to crack when deflected, and flexible lining are called
“flexible” because they are able to adapt to the changes in channel shapes while maintain the overall
Rigid Lining are usually used in a variety of cases, such as to (1) transport water at high velocities,
(2) decrease leakage and water losses, (3) decrease maintenance cost and (4) ensure stability. In contrast
to rigid linings, channels with flexible linings are generally less expensive, ensure infiltration and
exfiltration, provide better habitat opportunity for flora plants, and natural appearance. However, flexible
linings are more corrosive and suffer more damage, add to long term maintenance cost. Flexible linings
are usually temporary channel linings for erosion control during construction or reclamation of distributed
areas (Chin,2013). With different lining and different uses, comes with different designs and ways to
solve.
Design of Drainage Channels with Rigid and Flexible Linings
Learning Outcomes:
1. To determine the channel dimensions required to safely convey the design flow rate in
a channel, depending on the given shape, lining material, and longitudinal slop.
2. To know and understand the different linings and materials used.
Discussion
According to Mays (2011), Rigid-lined channels are nonerodable channel sides typically lined with
concrete, grouted riprap, stone masonry, or asphalt (See figure 1) (p.640).
Step 1: Estimate the roughness coefficient, n (which is dimensionless), for the specified linings and design
flow rate, Q [m3/s]. Guidance for estimating Manning’s n for rigid-boundary channels are listed in Table
5.4 (ASCE, 1992). It is also recommended that open channel designs must not use a roughness coefficient
lower than 0.013.
Step 2: Compute the normal depth of flow, y [meters], using Manning equation.
1 2 1
𝑄= 𝐴𝑅 3 𝑆 2
𝑛
Step 3: Estimate the required freeboard and increase the freeboard in channel bends as
appropriate to account for superelevation.
Note: As an additional constraint in designing concrete-lined channels, the ASCE (1992) recommends:
For nonreinforced linings:
1. 𝑉 ≤ 2.1 𝑚/𝑠 (7 𝑓𝑡/𝑠) Velocity must not exceed 2.1 m/s
2. 𝐹𝑛 > 0.8 Froude number must be greater than 0.8
For reinforced linings:
1. 𝑉 ≤ 5.5 𝑚/𝑠 (18𝑓𝑡/𝑠) Velocity must not exceed 2.1 m/s
Example:
Design a lined trapezoidal channel to carry 20m3/s on a longitudinal slope of 0.0015. The lining
Solution
(a) According to Table 5.4, n=0.015. Using the best trapezoidal hydraulic section, the bottom
width, b, and side slope, m, are given by Equations 5.9 and 5.10 as
Substituting the equations of the channel into the Manning equation yields,
Since the velocity is greater than 2.1 m/s, the lining should be reinforced. Since 𝑦 ≥ 0.30m and
V > 1.72 m/s, the freeboard, F, estimated by Equation 5.34 is given by,
Equation (5.34)
The minimum depth of the channel to be excavated and lined is equal to the normal depth plus
the freeboard, 2.09 m + 0.49 m = 2.58 m. The channel is to have a bottom width of 2.40 m and
side slopes of 0.58:1 (H:V)
(b) If the channel side slope is 1.5:1, then 𝑚 = 1.5 and Equation 5.11 gives the bottom width, b,
of the best hydraulic section (given that 𝑚 = 1.5) as,
The top width, T, flow area, A, and hydraulic radius, R, are given by
Since the velocity is greater than 2.1 m/s, the lining should be reinforced. Since 𝑦 ≥ 0.30m and
V > 1.72 m/s, the freeboard, F, estimated by Equation 5.34 is given by,
The minimum depth of the channel to be excavated and lined is equal to the normal depth plus
the freeboard, 1.94 m + 0.48 m = 2.58 m. The channel is to have a bottom width of 1.16 m and
side slopes of 1.5:1 (H:V)
There are a lot of type of flexible-lining materials that are used in practice, such as RECPs,
Vegetative lining. Vegetative lining consists of seeded or sodded grass placed in and along the channel.
There is usually a transition period between seeding and vegetation establishment, and temporary
typically used when rock riprap is either not available Figure 2.5: Gabions
Parameters that influence the design of channels with flexible linings are:
o The effective shear stress exerted by the flowing fluid on the lining material, τe
[FL−2].
Though, the approaches used to estimate n, τe, and τp can vary significantly between
linings and flow conditions; however, the design procedure for all flexible linings is similar
(Chin,2013). The following design procedure is recommended for determining the channel
Step 2: Calculate the normal flow depth, y in meters, using the Manning equation, taking into account any
relationship between the Manning’s n and y that might be a property of the selected lining. Typical
values of Manning’s n for unlined and RECP-lined channels are given in Table 5.5. In the case of
gravel-mulch, cobble, and riprap linings, n is usually dependent on the flow depth and roughness
consists of cohesive materials, the design is governed by the maximum shear stress on the bottom
Equation (5.37)
Where lining consist of non-cohesive materials, it is governed by the maximum shear stress on the
Equation (5.38)
Where Ks is the side-shear-stress factor. In trapezoidal channels, Ks depends on the side slopes and
Equation (5.18)
In some cases, a safety factor (SF) might be applied to 𝜏𝑏 𝑎𝑛𝑑 𝜏𝑠 in order to account for
uncertainties in design.
1 ≤ 𝑆𝐹 ≤ 1.5 , with SF = 1 being most common
Step 4: Estimate the permissible shear stress on the perimeter of the channel. In cases where the lining
consists of cohesive materials, the permissible shear stress, τp, is the same for both the bottom and
sides of the channel. Linings of cohesive materials include bare-soil linings with PI
(plasticity index) Ú 10. Typical permissible shear stresses for such materials are shown in Table
5.7. For non-cohesive lining materials, which includes bare soil with PI < 10, gravel mulch, and
riprap, the permissible shear stress on the sides of the channel, 𝜏𝑝𝑠 , is reduced relative to the
permissible shear stress on the bottom of the channel, 𝜏𝑝 , according to Equation 5.29 which gives
𝜏𝑜𝑠 = 𝐾𝜏𝑝 Equation (5.39)
where K is the tractive force ratio [dimensionless] that can be estimated using Equation 5.29.
Step 5: Verify the adequacy of the lining. An adequate lining requires that 𝜏𝑏 ≤ 𝜏𝑝 and 𝜏𝑠 ≤ 𝜏𝑝𝑠 . If the
lining is inadequate, repeat Steps 1 to 5 for different linings until an adequate lining is found.
Several adequate linings might be identified. The preferred lining is selected by considering
0.5%. Local regulations require that the side slope of the channel be no greater than 3:1 (H:V). A field
investigation has indicated that the native soil is non-cohesive and has a 75-percentile grain size of 10mm.
Solution
From the given data: Q = 0.5 m3/s, S0 = 0.005, m = 3, and d75 = 10mm. Use the most efficient
trapezoidal section with m = 3, in which case Equation 5.11 gives the bottom width, b, as
Step 1: Consider the case where no lining is used. In this case, the perimeter of the channel
consists of bare soil.
Step 2: A typical Manning’s n for channels in bare soil is given in Table 5.5 as n = 0.020. The
Manning equation gives
Step 3: The maximum shear stress on the bottom of the channel, τb, is given by (assuming γ =
9790 N/m3)
(interpolated) from Table 5.7 for 𝑑75 = 10 𝑚𝑚 as 7.4 Pa. Since the soil is non-cohesive, the
permissible shear stress on the side of the channel, 𝜏𝑝𝑠 (= 𝐾𝜏𝑝 ), will be less than 7.4 Pa.
Step 5: The maximum shear stress on bottom of the channel (17.8 Pa) is greater than the permissible shear
15 10
=
11 𝜏𝑝
𝜏𝑝 = 7.33𝑃𝑎
𝜏𝑏 = 17.8 𝑃𝑎 > 𝜏𝑝 = 7.33 𝑃𝑎
So, the bare-soil lining is inadequate. Try another lining.
Step 2: For typical gravel-mulch linings, the Manning’s n depends on the flow depth as shown in Table
5.6. This functional relationship can be expressed as n(y) and the Manning equation gives,
Which simplifies to
Solving Equation 5.40 simultaneously with the n-versus-y relationship in Table 5.6 (with
linear interpolation) yields 𝑦 = 0.445𝑚 and 𝑏 = 0.325𝑦 = 0.145𝑚.
Step 3: The maximum shear stress on the bottom of the channel, 𝜏𝑏 , is given by,
and the maximum shear stress exerted on the side of the channel,𝜏𝑠 , is given by
Step 4: The permissible shear stress, 𝜏𝑝 , on the gravel-mulch lining can be estimated from Table 5.7 for
𝑑50 = 50 mm = 5 cm as 38 Pa. The angle of repose, α, of the gravel mulch can be estimated
Step 5: Since the maximum shear stress on bottom of the channel is less than the permissible shear
stress on the bottom of the channel, and the maximum shear stress is less permissible shear on
Depth of flow ,𝑦 = 0.484𝑚, bottom width, 𝑏 = 0.157, flow area is, 𝐴 = 0.779𝑚2and the flow
𝐴 0.779
velocity is V = 𝑄 = = 0.642 m/s.
0.5
The height of the lining above the bottom of the channel should be at least,
0.484 + 0.30 = 0.784m (dimension can be rounded to the nearest centimeter for final
specification)
• lining should be extended at least 0.78m above the bottom of the channel.
Exercises
1. Design a trapezoidal channel to carry a discharge of 10 m3/s. The channel will be lined with
cement rubble masonry, plastered. The topography in the area is such that the longitudinal
𝐴
𝐴 = 1.73𝑦 2 , 𝑃 = 3.46𝑦, 𝑇 = 2.31𝑦, 𝑅 = = 0.5𝑦
𝑃
Substituting the equations of the channel into the Manning equation yields,
2 1
1
10 = (1.73𝑦 2 )(0.5𝑦)3 (0.0015)2
0.0015
𝑦 8/3 = 3.55
𝑦 = 1.608
b = 1.15(1.608) = 1.85 m
A = 1.73(1.608)2 = 4.473 m2
V
= Q/A = 10/4.473 = 2.236 m/s
2.2362
𝐹 = 0.15 + = 0.405 𝑚
2(9.81)
The minimum depth of the channel to be excavated and lined is equal to the normal depth plus the
freeboard, 1.608 m + 0.405 m = 2.013 m. The channel is to have a bottom width of 1.85 m and side
slopes of 0.58:1 (H:V).
Assignment
1. A trapezoidal channel has been designed with a bottom width of 10 m, side slopes of 2:1 (H:V),
and a longitudinal slope of 0.053%. The channel is to have a rigid lining of grouted riprap.
The design flow rate is 28 m3/s and the radius of curvature of the channel is 100 m.
Determine the design depth of flow in the channel and the minimum required freeboard.
2. Using the reference book, Water-resources Engineering by David Chin, Study more on flexible
National Highway Institute. (2005). Hydraulic Engineering Circular No. 15, Third Edition
https://www.fhwa.dot.gov/engineering/hydraulics/pubs/05114/05114.pdf
Mays, L. W. (2011). Water Resources Engineering 2nd Edition. John Wiley & Sons, Inc.