CONTENTS Section Page SCOPE ...4 REFERENCES...4 OBJECTIVE...5 DESIGN CONSIDERATIONS ...5
WASTE STREAM IDENTIFICATION ...5
HYDROLOGIC DESIGN ...6
BASIC RUNOFF HYDROLOGY ...6
Design Storms and Return Period Storms, Storm Durations, and Hourly Intensities...6
Runoff Flow Rate, Based on the Rational Formula...9
Calculation of “Time of Concentration" ...10
Runoff Volume Calculation Using Simple Methods ...11
Storm Runoff Hydrograph...12
Sewer System Flow Routing; Computerized Models ...13
HYDRAULIC DESIGN ...14
BASIC HYDRAULIC DESIGN CONSIDERATIONS ...14
HYDRAULIC DESIGN OF BURIED SEWER PIPES ...16
HYDRAULIC DESIGN OF OPEN CHANNELS...17
CULVERT CROSSINGS OVER OPEN CHANNELS...18
HYDROLOGY / HYDRAULICS ENGINEERING SOFTWARE ...19
STRUCTURAL DESIGN ...20
DETERMINATION OF LOADS IMPOSED ON A BURIED PIPE ...20
Marston Formula for Earth Portion of the Total Load on Buried Conduits ...21
Effects of Surface Live Loads or Other Surface Loads ...22
STRUCTURAL DESIGN METHODS FOR SELECTING PIPE WALL THICKNESS...25
Rigid Pipe Design ...25
Flexible Pipe Design ...27
Use of HDPE Pipe for Sewers in Plant Areas Where there are Hot Process Streams ...30
Thermal Effects ...37
Corrugated Metal Pipe...37
Open Channels...37
STRUCTURAL ANALYSIS / DESIGN SOFTWARE ...38
CONTENTS (Cont)
Section Page
APPENDIX A - EXAMPLE PROBLEMS ... 67
HYDROLOGIC DESIGN ... 67
Example Problem No. 1, Synthesizing a Local Intensity-Duration-Frequency (IDF) Curve from 30-Minute Storm Data ... 67
Example Problem No. 2, Calculating Time of Concentration for Use in the Rational Formula ... 69
Example Problem No. 3, Use of the Rational Formula for Runoff Flow Rate ... 70
Example Problem No.4, Runoff Volume via Simple Runoff Coefficient, and via SCS Curve Number Method ... 70
Hydraulic Design ... 70
Example Problem No. 5, Pipe Flowing Partly Full (Gravity Flow) ... 70
Example Problem No. 6, Flow in Small Pipe Network using Rational Method ... 71
Example Problem No. 7, Open Channel Flow... 74
Example Problem No. 8, Culvert Sizing ... 74
Structural Design... 75
Example Problem No. 9, Calculating Earth Load via Marston Formula, Conventional Cut-and-Cover Pipe in Trench ... 75
Example Problem No. 10, Load Imposed by Nearby Uniform Distributed Surface Load... 75
Example Problem No. 11, Loads Imposed by Surface Traffic ... 76
Example Problem No. 12, Selecting Wall Thickness, Reinforcing Requirements for Reinforced Concrete Pipe ... 76
Example Problem No. 13, Selecting Wall Thickness Requirements for Plain (non-reinforced) Concrete Pipe ... 77
Example Problem No. 14, Selecting Wall Thickness, Reinforcing Requirements for Vitrified Clay Pipe (VCP) ... 77
Example Problem No. 15, Selecting Wall Thickness Requirements for Ductile Iron Pipe ... 77
Example Problem No. 16, Selecting Wall Thickness for HDPE Pipe, Smooth Wall Type ... 78
Example Problem No. 17, Selecting Wall Thickness for HDPE Pipe, Profile (Ribbed) Wall Type ... 81
APPENDIX B - Formulas for Calculating Hydraulic Radius (R) and Flow Area (A) for Circular Pipes Flowing Partly Full ... 83
TABLES Table 1 Typical Runoff Coefficients For Use In The Rational Formula... 10
Table 2 Estimates Of Manning's “N" For Overland Flow ... 11
Table 3 Overview Of Stormwater Modeling Computer Programs ... 14
Table 4 Manning's Coefficient “N" For Commonly Used Drainage Pipe Materials ... 16
Table 5 Manning's Coefficient “N" For Commonly Used For Open Channels ... 17
Table 6 Description Of Parameters Implicit In Marston Coefficient ... 22
Table 7 Critical Loading Configurations, Highway Truck Loadings ... 24
Table 8 Impact Factors As A Function Of Depth Of Cover, Concrete Pipes ... 24
Table 9 Allowances For Casting Tolerances, Ductile Iron (DI) Pipe... 29
Table 10 Kb Values For Various Bedding Angles For Use With Modified Iowa Formula ...33
Table 11 Treatment Of Design Considerations By Commercial HDPE Pipe Manufacturers ... 34
Table 12 Stiffness Requirements For Plastic Sewer Pipe Parallel Plate Loadings ... 36
Table 13 Long Term (50 Year) Elastic Modulus E For HDPE Pipe ... 37
Table 14 Maximum Permissible Velocities For Various Channel Lining Types... 38
Table A-1 Factors For Converting From 30-Minute Duration Storm Depths To Depths For Other Storm Durations, Continental U.S. ... 67 Table A-2 Factors For Estimating Total Rainfall Depth For Various Recurrence Intervals,
CONTENTS (Cont)
Section Page
FIGURES
Figure 1 Example Of Rainfall Depth Map, Continental U.S., From U.S. Weather Bureau's
TP 40 10 Year, 1 Hour Storm, Inches ...41
Figure 2 Relationship Between Design Return Period And Exceedance Probability ...42
Figure 3-A Example Of Published IDF Curve, Houston TX, From TP 25 (U.S. Weath. Bur.) ...43
Figure 3-B Example Of User Synthesized IDF Curve, Houston TX, From Example No. 1 In Appendix A...44
Figure 4 Example Of Hourly Rainfall Distribution Within A Storm, SCS Type II Storm, U.S. ...44
Figure 5 Nomograph For Solution Of “Time Of Concentration" For Overland Flow ...45
Figure 6 Curve Numbers (CN) For Various Land Use Classifications And Soil Types...46
Figure 7 Direct Runoff Vs. Rainfall For Various CN (Curve Numbers)...46
Figure 8 Example Of Runoff Hydrograph ...47
Figure 9 Examples Of Refinery Manhole Seal Arrangements...47
Figure 10 Ratios Of Hydraulic Elements For Circular Conduits Flowing Part Full...48
Figure 11-A Inlet Control Nomograph For Corrugated Metal Pipe (CMP) Culvert ...49
Figure 11-B Inlet Control Nomograph For Concrete Pipe Culvert...50
Figure 11-C Outlet Control Nomograph For CMP Culvert ...51
Figure 11-D Outlet Control Nomograph For Concrete Pipe Culvert...52
Figure 12 Illustration Of Earth Loads On Buried Conduit ...53
Figure 13 Marston Coefficient Cd ...54
Figure 14 Summary Of Standard Methods For Calculating Earth Loads On Buried Conduits ...55
Figure 15 Influence Diagram For Effects Of Distributed Surface Loads On Buried Pipe ...57
Figure 16 AASHTO HS-20 Truck Loads On Buried Pipe ...58
Figure 17 Illustration Of “Three Edge Bearing" Test For Use In Indirect Design Of Rigid Pipes ....59
Figure 18 Bedding Factor “Bf" For Concrete Pipe...60
Figure 19-A Bedding Factor “Bf" For Vitrified Clay Pipe ...62
Figure 19-B Bedding Factor “Bf" For Vitrified Clay Pipe ...63
Figure 20 Manufacturer Specific Design Charts/Tables For Thickness Design Of HDPE...64
Figure 21 Soil Modulus E' For Use In Modified Iowa Formula For Flexible Pipe Design...65
Figure 22 Rip-Rap Sizing Requirements For Use As Channel Lining ...66
Revision Memo
12/01 DP updated to include information Hydrology / Hydraulics and Structural Design on computer software programs available in the public domain. New guidance also provided on using HDPE pipe in plant areas where there are not process streams. General editorial revisions, including new Nomenclature.
SCOPE
This section covers the hydrologic, hydraulic, and structural design of industrial plant sewers and open channels which serve to convey storm runoff and firewater return flows away from operational areas to a point at which they can be treated and/or released in accordance with applicable law or recovered into the water supply system. The methods customarily used to estimate the quantity and discharge rates for storm runoff, hydraulic design of sewers and open channels, and methods dealing with the structural design of sewers are described in this Design Practice. Firefighting flows are established by company and/or plant practice and are described in the applicable Global Practices.
The methods described in this Design Practice are drawn from generally accepted procedures commonly used by civil engineers to design storm sewer systems. While these are expected to be applicable to most routine storm drainage problems, they should not be viewed as the only methods available. The designer is ultimately responsible for selecting the analytical and design methods appropriate to a particular problem, and it is certainly possible that methods other than those described herein may be more applicable to a given problem.
This Design Practice does not directly address process wastewaters, their treatment, nor the design of process wastewater sewers except to the extent that process wastewaters are sometimes conveyed along with storm runoff in combined sewers. It should be recognized that disposition of such combined flows can have a major impact on the design of drainage systems, the same as the large flow rates and volumes from storm runoff can impact process wastewater treatment strategy and treatment system design.
REFERENCES DESIGN PRACTICES
Section XIX-A Water Pollution Control, Guidelines for Selecting Wastewater Treatment Systems
Section XIX-A1 Water Pollution Control, Primary Oil / Water Separators
GLOBAL PRACTICES
GP 3-2-1 Sewer Systems
OTHER REFERENCES
ACPA Concrete Pipe Design Manual, American Concrete Pipe Association, 1992 ANSI / AWWA C150/A21.50 Thickness Design of Ductile Iron Pipe
ANSI / AWWA C906-90 Polyethylene (PE) Pressure PIpe and Fittings, 4 in. through 63 in., for Water Distribution ANSI / AWWA C950-88 Fiberglass Pressure Pipe
ASCE No. 77 Design and Construction of Urban Stormwater Management Systems, Manual of Practice No. 77, American Society of Civil Engineers, 1992
ASCE No. 37 Design and Construction of Sanitary and Storm Sewers, Manual of Practice No. 37, American Society of Civil Engineers, 1982
ASTM C 14 - 94 Standard Specification for Concrete Sewer, Storm Drain, and Culvert Pipe
ASTM C 76 - 94 Standard Specification for Reinforced Concrete Culvert, Storm Drain, and Sewer Pipe ASTM C 301 - 93 Standard Methods of Testing Clay Pipe
ASTM C-497 - 95a Standard Test Methods for Concrete Pipe, Manhole Sections, or Tile
ASTM C 700 - 95 Standard Specification for Vitrified Clay Pipe, Extra Strength, Standard Strength, and Perforated Chow, V. T., Handbook of Applied Hydrology, McGraw-Hill Book Company, 1964
Design of Small Dams, U.S. Dept. of the Interior, Bureau of Reclamation, 1974
Holman, J. P., Heat Transfer, 4th ed.
NCPI Clay Pipe Engineering Manual, National Clay Pipe Institute, 1974
TP 40 Rainfall Frequency Atlas of the United States, U.S. Dept. of Commerce, Weather Bureau, 1961 TP 25 Rainfall Intensity-Duration-Frequency Curves, U.S. Dept. of Commerce, Weather Bureau, 1955
OBJECTIVE
The primary objective of this Design Practice is to provide the designer with a technical guide relating to:
• Calculation of the appropriate design flow in an open channel or pipe (hydrologic design).
• Sizing of the channel or pipe to handle the design flow (hydraulic design).
• Determining the required wall thickness for pipes or lining requirements for open channels as necessary to minimize maintenance costs and assure operability over the design life of the conduit (structural design).
A secondary objective is to provide the means necessary to compute storm runoff volumes and flow rates. These may be needed in the design of treatment works for combined waste streams (storm flows and other wastewater streams), or for stormwater permitting considerations.
DESIGN CONSIDERATIONS
The following factors would be expected to have a bearing on the design, and should be considered at an early stage of the design process.
• Plant safety; Petrochemical plant sewers can contain hydrocarbon vapors which require special systems to control the risk of explosions. Plant sewers are in general isolated via water seal boxes to prevent vapor releases from drop inlets and to prevent the spread of a fire or explosion between fire risk zones. Seals in plant sewer systems are described in GP 3-2-1.
• Plant layout and the topography of the area of interest and any tributary area.
• Possible future expansion of the plant, or changes to the drainage area tributary to the plant.
• Source of flow in the line or channel; entirely storm runoff, or contaminated storm runoff, or combination of storm runoff with other waste streams (see following section describing categories of wastewater streams).
• If flow includes waste streams in addition to storm runoff, the chemical quality (e.g., pH, presence and concentrations of solvents, other hydrocarbons, or other corrosive chemicals) that may affect the line's durability or the integrity of joints.
• The consequences of moderate leakage from joints. If consequences are viewed to be significant, it may impact selection of sewer line materials. For example, HDPE can be made to be continuous and virtually leak proof, and gasketted joints that are for all practical purposes leaktight under nominal sewer line pressures can be specified for jointed pipes.
• Return period or design storm; the consequences of hydraulically undersizing the line, which could include backing up or ponding of storm water in critical or inconsequential locations. Higher consequences generally imply larger design storm (i.e., selection of a greater return period).
• Firewater return flows that may be larger than the storm induced runoff for an isolated local area.
WASTE STREAM IDENTIFICATION
Waste streams within a plant may be separated into the following categories:
• Clean water or storm water; storm or firewater runoff from areas that are not normally subject to oil or toxic chemical
contamination, including – oil free stormwater – steam turbine condensate – boiler plant condensate blowdown
– once-through cooling water and cooling water tower blowdown where possible hydrocarbon contaminants are equivalent to C5 and lighter
• Oily water or industrial wastewater; oil-contaminated wastewater that is low in sulfides, COD and BOD, including
– process plant area stormwater runoff and firewater runoff, or runoff from any areas that are normally subject to hydrocarbon or oil contamination
– normal oily and non-oily process wastewater – water drawn off from atmospheric storage tanks – ballast water
WASTE STREAM IDENTIFICATION (Cont)
• Chemical wastes; acidic, caustic, and other wastes which are not permitted to be released to either sanitary or industrial
sewers in the plant, including
– waste streams high in acids, alkalis, COD or BOD – laboratory chemical wastes
– sour water stripper effluent
– slop tank drawoff and flare seal water
• Sanitary wastewater; waste from toilet facilities, lavatories, showers and floor drains in restrooms, locker rooms,
cafeterias, wash rooms, etc.
For combined sewers, which are defined as sewers that carry more than one type of wastewater, the design requirements will be controlled by the most stringent requirements of the individual sewers included in the system. The most common type of combined sewer is a combined industrial wastewater/stormwater sewer system. It will be subject to the environmental and permitting considerations for the industrial effluent (which are the subject of Section XIX-A) as well as the wide range in flow rates and runoff volumes associated with storm runoff events, which are the subject of this Section XXIX-C.
HYDROLOGIC DESIGN
Hydrologic design involves the determination of flow rates and runoff volumes that would result from precipitation runoff. For the design of the sewer systems, the primary item of interest is the runoff flow rate. Common units of measurement are gpm (gallons per minute), cfs (cubic ft per second), m3/sec (cubic meters per second), MGD (million gallons per day), etc. Conversely, the design of storage and detention systems, which may be a factor in permitting questions for combined sewer systems, is more concerned with runoff volumes. Common units of measurement for runoff volumes are MG (million gallons), acre ft, Km3 (thousand cubic meters), etc. If storm routing studies are anticipated, which consider temporary storage during and after the passage of a runoff event, then both the flow rates and the runoff volumes are of interest. In such cases it is customary to consider both the flow rate and the runoff volume by developing the runoff hydrograph, which provides the instantaneous flow rate (e.g., cfs) as a function of time throughout a runoff event. The area under the runoff hydrograph curve is the runoff volume. Hydrologic design principles discussed in this section are the basis for calculating both runoff flow rates, runoff volumes, and runoff hydrographs.
In most industrial sites, runoff that results from rainfall will control the design of pipes and channels, wherein peak flow rate is the item of interest. Snowmelt runoff can be of interest in extreme northern latitudes, or in alpine environments, but the runoff flow rates associated with large melt events are typically small compared to flow rates resulting from rainfall events. By contrast, the runoff volumes produced by snowmelt are typically much larger than runoff volumes from individual return period rain storms. Because the design of plant drainage systems (i.e., conveyances) is tied more toward the flow rates than to volumes, the hydrologic design aspects of drainage systems included in this Design Practice are limited to runoff produced by rainfall events. Depending on the application (conveyance design or temporary detention storage), the methods used to calculate runoff will range from simple ones that produce only peak flow rates or runoff volumes to more sophisticated computerized methods that produce the entire storm runoff hydrograph.
BASIC RUNOFF HYDROLOGY
Design Storms and Return Period Storms, Storm Durations, and Hourly Intensities
The following terms are commonly used in rainfall runoff determination:
• Return period storm; a storm which has a defined statistical probability of occurring within a specified return period;
example, a “10 year storm". The concept is described in more detail below. “Return period" is often referred to as “recurrence interval".
• Storm duration; the theoretical beginning and end of the return period storm. Total rainfall depths for storms of specific
return periods and specified durations are tabulated and published, usually in a “rainfall atlas" by weather bureaus or similar government agencies.
• Rainfall intensity or hourly intensity; the instantaneous or hourly average rainfall rate within a given storm, expressed in
units of L/T. Average hourly intensities for a storms of specified durations and specified recurrence intervals for various geographic locations are often presented in “intensity-duration-frequency", or “IDF" curves. An IDF curve is specific to a given geographic location, and may be published by government bureaus. Average hourly rainfall intensities are fundamental to calculating runoff flow rates.
• Total rainfall or total rainfall depth; the total accumulated rainfall for the specified storm duration and return period,
HYDROLOGIC DESIGN (Cont)
• Time of concentration; the time, usually in minutes, that it would take water from the hydraulically most remote location in
the catchment area, to arrive at the point of interest.
• Rainfall hyetograph; the time distribution of rainfall within a storm of defined duration, usually expressed as a plot of
rainfall intensity (e.g., in./hr) vs. elapsed time into the storm.
All surface hydrologic evaluations are based on statistically defined return period storms. Typically, the design of a hydraulic facility will be specified in terms of a return period storm, such as a “10 year storm." In some cases, in particular those cases in which the volume of runoff is as important as the flow rate, both the return period and the duration have to be specified (e.g., a 10 year, 24 hour storm). The total rainfall amount for storms of various durations and various return periods are tabulated for most locations. In the U.S., the tabulation is generally in the form of rainfall atlases, which provide total rainfall amounts for storm durations from 30 minutes to 24 hours and return periods of 1 to 100 years. Figure 1 is excerpted from TP-40 published by the U.S. Weather Bureau, depicting rainfall amounts for storms of several recurrence intervals and several durations for the United States. Similar maps are maintained by local government agencies for various other locations.
A “10 year" storm is the storm which would occur or be exceeded on an average of once every 10 years. Storms are thus defined in accordance with an exceedance probability. It does not mean that a 10 year storm will occur once in every ten year period, although the probability is 65% that at least one 10 year storm will occur in any given ten year period. If the designer wants to be 90% sure that a conduit will not be undersized in any single year, he should design for the 10 year storm (see
Figure 2). 95% assurance that the flow would not be exceeded in any single year would require selection of the 20 year storm
as the design storm. Normally, the design period is greater than a single year, and is related to the expected service life of the facility in question. Thus, if a designer wanted to be 90% certain that a conveyance or conduit would not be under-sized throughout a 25 year service life, the appropriate design storm would be on the order of a 250 year event. Obviously, such a design criterion would be appropriate only if the anticipated failure consequences are severe. Normally much shorter recurrence intervals are used in sizing drainage systems, as discussed below.
Selecting the appropriate return period is a critical first step. Typically, storm sewers are designed for return periods of 2 to 25 years, depending on the consequences of their being undersized, which may involve no more than temporary and tolerable flooding in isolated areas of the plant. However, if expensive equipment would be damaged or if a health/safety risk is posed by the temporary flooding, a greater return period (i.e., larger design storm) should be considered. At one extreme, residential drainage systems are usually designed for return periods of 2 to 5 years, and drainage systems in high value commercial areas are typically designed at 5 to 10 year storms. At the other extreme, large above ground impoundments, which could cause significant damage if they were to overtop, are usually designed for at least the 100 year storm. Exxon's current practice, as reflected in GP 3-2-1 Sewer Systems, calls for storm sewers to be designed for the 10 year storm unless otherwise specified. At sites where storm response flow records have been maintained for a considerable period of time there may exist enough historical data to enable the designer to extrapolate directly to flows associated with other return periods. This is expected to be a rare situation at most industrial sites, since continuous recording flow meters on storm sewers are not likely to exist. For example, it can be shown by statistics that a period of record of about 22 years would be needed in order to be 90% certain that the 10 year flow had been experienced. To be 95% certain, a period of record of about 28 years would be required. Therefore, it is more likely that flow estimates will be prepared based on regional rainfall data than on site specific flow data.
Hourly precipitation rates during storms of a specified duration are defined according to a set of rainfall distribution curves. The most commonly used hourly distribution for the U.S. (SCS Type II distribution) places about 55% of the rainfall within the two hour period at the center of a 24 hour storm (see Figure 4). Other hourly distributions of rainfall within a storm are possible, but the hourly distribution within a given storm is of interest only if the designer is attempting to produce a runoff hydrograph. For instantaneous peak flow, all that is needed is the peak rainfall intensity for a specified time period (called “time of concentration," discussed below), an appropriate runoff coefficient, and the catchment area. If only the total runoff volume is desired, all that is needed is the total rainfall amount, an appropriate runoff coefficient, and the catchment area. If more sophisticated storm routing through a sewer system is required, then determination of the runoff hydrograph will be required, including appropriate assumptions regarding hourly rainfall intensity during the storm. For the latter cases, the runoff hydrograph will probably be calculated using one of a number of rainfall-runoff models (e.g., SCS, TR 55, HEC), many of which are included within the comprehensive storm runoff modeling programs described later.
Since storm duration does directly affect the runoff volume, it is necessary to specify storm duration as well as return period in cases where detention storage (off-line or on-line) is being considered to reduce peak flow rates.
HYDROLOGIC DESIGN (Cont)
Probably the simplest application, and certainly the most common in the design of drainage structures, is the determination of the peak flow rate. For this application, a quantity called “time of concentration" or “Tc" is defined. This is the time, usually in minutes, that it would take water from the hydraulically most remote location in the catchment area, to arrive at the point of interest (i.e., the “point of concentration"). The hydraulically most remote point is not necessarily the farthest point geographically, as it involves both the distance and the speed at which the water must travel. The latter is dependent on the slope of the terrain or the slope and diameter of the pipes conveying the water to the point of concentration. There are simple methods and formulas to determine time of concentration for any given catchment area, which take into account site topography for undeveloped land, and slow times in site sewers or surface ditches for developed land. Methods to estimate Tc are presented later in this Design Practice.
Once the time of concentration is defined by an appropriate means, the parameter of interest is the peak rainfall intensity (usually in in./hr or mm/hr) that would be sustained for a duration equal to that previously defined time of concentration. The theory is that if it would rain at this intensity for this length of time, the entire catchment area would be reporting to the point of concentration, and the runoff flow rate would thus be at its maximum for that particular storm. Since the time of concentration will vary for specific drainage components within a given site, it is generally necessary to have a curve of rainfall intensity for various durations (i.e., various Tc) for various return periods. Such curves are referred to as “Intensity-depth-frequency" curves, or “IDF" curves. They are essential to use of the simpler runoff calculation methods, including the rational formula described below and many PC-based computer programs, and they are unique to a particular location.
IDF curves take the general form id =
(
b D)
n a +where: id = Intensity of rainfall (in./hr in Customary units, mm/hr in Metric units) D = Duration of the rainfall, minutes
a, b, and n = Equation coefficients.
Some methods to compute runoff from rainfall, including some PC-based computer programs, can create IDF curves if the user has the appropriate coefficients. However, it is more common to make use of weather bureau derived IDF curves if these are available, or to synthesize an IDF curve from weather bureau derived relationships linking return periods, storm durations and intensities, as discussed below.
Similar to the total rainfall depth curves for various return period storms and durations described previously, many government agencies have also compiled atlases of IDF curves for various locations. In the U.S., these were first consolidated by the U.S. Weather Bureau (1955) into a set of rainfall IDF curves known as TP-25. An example, taken from TP-25 (U.S. Weather Bureau), is presented as Figure 3-A. Since then, many states have updated and fine tuned the IDF curves for their particular
region. Similar curves should exist at other locations in developed areas.
If the designer has neither a set of published IDF curves for his site, nor adequate historical runoff flow records, but does have the 30-minute total rainfall depth for various return period storms, or can arrive at the 30-minute storm from storms of longer durations, it is possible to generate local IDF curves for use in calculating peak runoff by the Rational Formula. The method as applied in the U.S. is described in a number of texts on hydrology and in design manuals published by some pipe manufacturers. A comparatively simple and straightforward method to produce IDF curves needed for design is described in
Example Problem No. 1 in APPENDIX A, and the resulting IDF curve is presented as Figure 3-B.
CAUTION
When referring to return period storms, durations, and intensities, confusion sometimes arises due to the units that are used. A very common mistake is to consider that the minimum duration needed in determining a peak flow rate is the storm of one hour duration, simply because the rainfall intensity in the commonly used Rational Formula is usually expressed in in. (or mm) per hour. In fact, the peak hourly intensity for a 30 minute storm is as much as twice the hourly intensity for the 60 minute duration storm of the same return period. This difference is much greater than the difference that would occur by switching from a 10 year to a 25 year return period. Thus, if rainfall intensity is incorrectly chosen as that associated with a 1 hour duration in a catchment area that really has a time of concentration of 17 minutes, the peak flow so determined will be off (short) by more than 100%. What was thought to be a 10 year design flow may in fact be no more than a 1 year flow.
When calculating runoff based on rainfall data, it is necessary to have some estimate of the direct runoff coefficient (the fraction of the incipient precipitation that becomes runoff). The formulation of the runoff coefficient will vary with the method used to compute the runoff, but in all cases the more impervious the surface, the higher the coefficient. Industrial areas that have a significant amount of paved areas and equipment surfaces, where runoff is nearly 100%, will tend to have relatively high runoff
HYDROLOGIC DESIGN (Cont)
The methods used to convert rainfall into runoff are for the most part simple and straightforward. Some are customarily carried out using a computer program while others depend only on simple calculations. When seeking to produce a complete runoff hydrograph (plot of flow vs. elapsed time), the designer should bear in mind that a reasonably accurate prediction of the hydrograph will result if the designer knows just three input parameters:
• The catchment area (acres, meters2, ft2, etc.), usually determined from a topographic map or site drawings. • The catchment area's imperviousness, estimated based on land use.
• The rainfall hyetograph for the design storm of interest (i.e., the hourly precipitation rate at various times within the storm). In view of the above, the designer should not be concerned about whether the method selected to produce a runoff hydrograph is the most precise of the several accepted theories. Virtually any generally accepted method will be suitable. What is important is a good understanding of the three parameters described above.
Similar guidance exists for those cases in which the entire runoff hydrograph is not required. If the designer seeks only the peak runoff flow rate, then only the catchment area, a runoff coefficient, and the peak rainfall intensity associated with the correct time of concentration are needed. To determine total volume of runoff, only the catchment area, a runoff coefficient, and the total rainfall depth are needed.
Runoff Flow Rate, Based on the Rational Formula
The Rational Formula, referred to as the Lloyd-Davies method in the United Kingdom, is a simple and widely used means to calculate peak runoff rates for small watersheds. It is not recommended for catchment areas much greater than 200 acres or for any area where ponding in the catchment area might affect peak discharge. Where it is applicable, the Rational Formula relates peak discharge to rainfall intensity by the simple expression
Q = C i Ac Eq. (1)
where: Q = Peak discharge ft3/s,
C = Non-dimensional runoff coefficient,
i = Rainfall intensity over a duration equal to the time of concentration, described in detail below, in./hr,
Ac = Catchment area, acres.
The formula is most convenient when expressed in U.S. units, and then only because 1 acre in./hr = 1.008 cfs. In metric units, the rational formula becomes
2 km mm/hr /sec 3 m 0.278C xi x A Q = Eq. (2)
The method requires a good definition of the limits of the catchment area. Normally this can be developed by defining watershed divides (local high points) on a topographic map. In developed sites, the limits of the various sub-catchment areas will be defined by the grading of the surface and the presence of man-made channels and/or drainage facilities.
The normal range of runoff coefficients are described in the following Table 1. For estimating purposes it may be sufficient to
use C = 0.5 for unpaved industrial areas, and C = 1.0 for paved areas and equipment surface or roof areas. Tankage areas enclosed by dikes should be excluded from the total area calculation if stormwater release from these areas is controlled by valved drains or if the water percolates into the soil.
HYDROLOGIC DESIGN (Cont) TABLE 1
TYPICAL RUNOFF COEFFICIENTS FOR USE IN THE RATIONAL FORMULA
BY SURFACE TYPE: RUNOFF COEFFICIENT “C" BY LAND USE: RUNOFF COEFFICIENT “C"
Pavement
Asphalt and Concrete Brick 0.70 to 0.95 0.70 to 0.85 Business Downtown Neighborhood 0.70 to 0.95 0.50 to 0.70
Roofs 0.75 to 0.95 Railroad Yards 0.20 to 0.35
Lawns
Flat, in sandy soil Steep, in clayey soil
0.05 to 0.10 0.25 to 0.35 Industrial Light Heavy 0.50 to 0.80 0.60 to 0.90 Residential Residential Suburban Apartments 0.25 to 0.40 0.50 to 0.70 Unimproved Land 0.10 to 0.30
Calculation of “Time of Concentration"
As described in the previous section, in order to select the rainfall intensity from the locally applicable “intensity-duration-frequency" curve (IDF) for the return period storm of interest, it is necessary to have calculated the “time of concentration" for the particular catchment area. The hourly intensity for the storm of interest can then be read directly from the IDF curve. Time of concentration can be calculated by means of the Kirpich formula, or similar empirical expressions, for undeveloped portions of the catchment area where overland flow would prevail, and by summing up travel times for flow in discreet conveyances (upstream sewer pipes and ditches) for developed land or industrial sites.
The Kirpich formula, in Customary units is as follows:
Tc = (11.9 L3 /H) 0.385 Eq. (3)
where: L = Distance in miles, measured along the watercourse to the hydraulically most remote point in the catchment area,
H = Elevation difference from that point to the point of concentration, ft.
The above described formula is for overland flow mainly over bare earth, mowed grass, and roadside ditches. For flow over paved surfaces, it is customary to multiply the Tc calculated via the above expression by 0.4. For flows primarily over grassed areas, the Tc calculated via the above expression should be multiplied by 2.0. The calculation can be made numerically or by means of nomographs such as Figure 5.
Time of concentration can also be defined by kinematic wave theory, which couples the continuity equation with bottom slope and friction slope for overland flow. The resulting expression for time of concentration in Customary units is:
3 . 0 o 4 . 0 e 6 . 0 o 6 . 0 o c S i L n 938 . 0 T = Eq. (4)
where: Tc = Time of concentration, minutes
no = Manning's roughness coefficient for overland flow, given in Table 2
Lo = Distance from the farthest point in the catchment area to the point of interest, ft So = Dimensionless slope of the surface, averaged over the catchment area ie = Excess rainfall rate, in./hr
HYDROLOGIC DESIGN (Cont)
In metric units, the expression is:
3 . 0 o 4 . 0 e 6 . 0 o 6 . 0 o c S i L n 99 . 6
T = where: L is in meters and ie is in mm/hr Eq. (5)
Note that the rainfall intensity is included in the expression for Tc. While this is technically more correct than the simpler empirical approaches such as Kirpich's formula, it complicates the calculation by forcing iteration between the above expressions and the IDF curve.
TABLE 2
ESTIMATES OF MANNING'S “n" FOR OVERLAND FLOW
SURFACE TYPE MANNING'S “no"
Concrete / asphalt 0.011
Bare sand 0.01
Bare clay / loam 0.02
Hard packed clay 0.03
Light turf 0.02
Lawns 0.025
Dense turf 0.035
Pasture 0.35
Dense shrubbery and forest litter 0.40
For developed sites where upstream areas contribute their flows primarily via pipes and channels, an estimate must be made of the actual flow time in those pipes and channels, plus a quantity referred to as the “inlet time", which is the time required for the water to flow overland from the most remote area within the catchment area to the drop inlet or catch basin. Inlet times in developed industrial areas with closely spaced storm drains are customarily taken as 5 minutes. Once inside the sewer line, flow time depends on flow velocity, which itself depends on flow rate. Initially this may appear to be an overwhelming task requiring a complex iterative procedure, but it should be remembered that the flow velocity is more dependent on conveyance dimensions (pipe diameter, ditch cross section) and gradient, both of which are fixed and known, than on the flow rate. Thus, with a reasonable estimate of the influent flow, sometimes taken as the capacity of the upstream influent pipe or ditch, the travel time can be approximated accurately enough once the conveyance dimensions, gradient, and roughness coefficient for the upstream conveyances are known. Velocities are normally calculated using Manning's Formula, described later. The time of concentration equals the sum of travel times for the various parts of the route from the hydraulically most remote point in the catchment area, including initial inlet time. Note that time of concentration is cumulative as the designer proceeds from the upstream to the downstream areas. The calculations performed to determine Tc for the uppermost reaches need not be re-done as the process moves downstream. These times only need to be accumulated as the process moves downstream. For small areas within a plant that may be flowing through a series of laterals to a main or a sub-main, it would not be unusual to calculate a time of concentration as short as 10 minutes.
An example problem illustrating the use of the Rational Formula to determine a flow rate is provided as Example Problem
No. 3 in APPENDIX A.
Runoff Volume Calculation Using Simple Methods
If the entire runoff volume is the only parameter of interest, all that is needed is the design storm (return period and duration), catchment area, and a suitable runoff coefficient. Runoff coefficients for this purpose are similar to those described for use in the Rational Formula, and can be viewed in simple terms as the fraction of the incipient rainfall that becomes runoff.
A design example is presented below for discussion purpose, and is also included as Example Problem No. 4 in
APPENDIX A. The simplest application of the above, on a small industrial catchment area 70 ft x 170 ft (21 m x 52 m), would
be to assume a runoff coefficient of 0.9, for a paved industrial area. If the design rainfall amount were specified to be the 10 year 24 hour storm, which for Houston Texas is 8.5 in. (216 mm), the volume of runoff (Vr) would be
Vr = 0.9 x (8.5 in./12) x 0.27 acres = 0.172 ac ft = 56,000 gallons
HYDROLOGIC DESIGN (Cont)
A somewhat more sophisticated approach is the use of the runoff Curve Numbers (CN) as developed by the USDA/SCS. This methodology is intended mainly for use on undeveloped acreage, but it can be applied to other small watersheds. The method takes into account the degree of surface imperviousness in a more rigorous manner than the broad based coefficients used in the Rational Formula. The method takes into account the initial interception and depression storage that occurs as a result of surface irregularities, and it takes into account the rate at which infiltration can consume a portion of the incipient precipitation. Theoretically, these factors are already included in the coefficients used with the Rational Formula, but there is no direct connection between the two methods. For nearly impervious surfaces, such as paved areas within a plant, the CN is very high, and the portion of the runoff that is consumed by the initial depression storage and infiltration during the storm are consequently both very low. Conversely, for unpaved surfaces, or areas covered with vegetation, the above two factors consume a considerable portion of the incipient precipitation. If a particular catchment area includes several types of land use and cover, the CN approach is probably preferred. It is in some ways less judgmental and easier to document, which may be of importance if third party review or approval is involved. Curve Numbers (CNs) for various land uses and various soil types are presented in numerous references (e.g., Design of Small Dams, U.S. Bureau of Reclamation, 1974). An abbreviated summary is included in this Design Practice as Figure 7.
The method is fairly easy to use. Surfaces are classified in accordance with their land use, and in accordance with the soil type. The catchment area is broken up into sections of approximately uniform land cover and soil type, and a weighted average CN is developed for the catchment area. The direct runoff (Qd, in.) is then calculated according to the following formula or read directly from a graph such as Figure 7.
(
)
S 8 . 0 P S 2 . 0 P Q 2 d = −+ Eq. (6) where: S = 10 CN 1000 − P = total precipitationCN = USDA / SCS Curve Number
For the previously described example (10 year, 24 hour storm at Houston, Texas), in an industrial area with CN = 92, the direct runoff (Q) and runoff volume (Vr) would be:
(
)
(
)
(
)
(
8.5 0.8 0.8696)
8696 . 0 2 . 0 5 . 8 Q 2 d = −+ = 7.5 in.Vr = 7.5 in./12 x 0.27 acres = 0.169 ac ft = 54,980 gallons
Had a CN of 95 been selected, the calculated direct runoff would be 7.9 in., and the corresponding runoff volume would be 57,900 gallons. These two CNs bracket the assumption of a runoff coefficient of 0.9 in the previous method. While the Curve Number method is somewhat more complex than a simple runoff coefficient, it has the advantage of being compatible with most of the methods used to produce complete runoff hydrographs, many of which are included within the more common drainage system modeling programs (e.g., XP-SWMM, TR-55).
Storm Runoff Hydrograph
There may be occasions when it is desired to produce the complete storm runoff hydrograph for one or more return period storms at a given site. For example, a complete hydrograph is generally needed if the issue is temporary detention of storm flows in on-line or off-line storage, unless it is planned to contain the entire runoff flow. The latter is generally impracticable for return period storms larger than one or two year events, and even then a substantial amount of land is required for the detention basins. Nevertheless, if retention of the entire storm runoff is required, the simpler manual calculation methods described in the previous section would be sufficient.
If it is intended to contain only a portion of the runoff, such as the first 30 minutes, synthesis of the entire hydrograph would be required. It should be noted, however, that in cases such as this, it is likely that a sophisticated sewer system routing analysis would be required anyway (discussed in following section). The computer programs that perform system routing also include routines for developing the runoff hydrograph, which is one part of the input required for the storm response modeling. While the techniques to develop a runoff hydrograph are simple enough to be programmed in a BASIC program or a spreadsheet, it is unlikely that these would be used out of context of a formal sewer system routing analysis. Therefore, only the concepts involved in constructing a runoff hydrograph will be described here. Techniques for creating a runoff hydrograph from rainfall are provided in references (SCS National Engineering Handbook, Section 4) and (Design of Small Dams).
HYDROLOGIC DESIGN (Cont)
The input parameters for synthesizing a runoff hydrograph when given only the total rainfall amount (presumably from a rainfall atlas), are similar to those described in the previous sections. Parameters include watershed imperviousness, which is analogous to the runoff coefficient in the Rational Formula. The SCS curve numbers (CNs) are in fact used directly in some hydrograph synthesis methods. Watershed topography is also needed to set lag times for individual sub-drainage areas within the watershed. This is analogous to the time of concentration concept in the Rational Formula. Mini-hydrographs from sub-drainage areas of the watershed will not, in most cases, line up peak to peak. Rather, they will be offset by their respective travel times. Finally, the rainfall distribution throughout the storm (i.e., rainfall rate at various points in the storm, also know as the rainfall hyetograph) is needed. This is analogous to the rainfall intensity in the Rational Method, although the Rational Method concerns itself only with the instantaneous peak rainfall intensity applicable to the particular component of interest (i.e., a single pipe or ditch for which the peak flow is desired).
The SCS methods used in TR-55 and other urban runoff models builds the watershed hydrograph from a series of dimensionless unit-hydrographs which are determined by the geometry of the particular catchment area. The unit hydrographs for increments within the storm are then converted to runoff hydrographs by means of the runoff coefficients, and are then added together, offset as appropriate according to their time position within the storm, to arrive at a consolidated runoff hydrograph for the entire storm. The result is a plot of flow rate (e.g., cfs) as a function of time from the start of the precipitation event to the effective end of the runoff. The end of runoff occurs some time after the rain has ceased, as would be expected. An example of a runoff hydrograph is presented as Figure 8.
The storm runoff hydrograph provides the peak flow, the total runoff volume (area under the hydrograph curve), and the time at which peak flow would occur. Fractional volumes at various points through the storm can also be obtained from the area under the curve. Development of the complete hydrograph may be viewed as an unnecessarily complicated means of obtaining something as simple as a peak flow rate. However, once the designer has obtained or written the necessary program or spreadsheet, it is as easy to obtain the complete hydrograph as to compute a single peak flow. All that is needed is the total storm depth and duration, the weighted runoff curve number (CN), the length and elevation difference (for time of concentration), and the catchment area. Note that these input parameters, or comparable ones, would have been required for the simpler hand calculations using the Rational Formula.
Sewer System Flow Routing; Computerized Models
Computer modeling of storm sewer systems has been a part of storm drainage and design since the mid-1970s. Several Federal agencies in the U.S. undertook to develop software for this purpose, including the U.S. Army Corps of Engineers with their Storm Treatment and Overflow Runoff Model (STORM) and their previous HEC-1 and HEC-2 series models. The U.S. Soil Conservation Service (SCS) developed their program TR-20 and later specifically adapted it to urban areas in a procedure which has come to be known as TR-55. SCS did not develop computer programs for TR-55, but private vendors have done so and market them as TR-55 solutions. Finally, the U.S. EPA developed the Storm Water Management Model (SWMM) specifically for the analysis of combined sewer systems (storm and sanitary flows) to enable the analysis of response to single storm events. PC based versions of all of these programs are available, either from the sponsoring agencies or from private vendors. Except for the STORM model, the models are well suited to handle the common problem of routing a specific storm though a sewer system, taking into account live storage within the system as well as off-line detention facilities. All of the models, including STORM, can evaluate the potential for drainage design problems such as temporary flooding. A few can take into account the effects of surcharging on sewers (i.e., lines flowing full with the pressure head higher than the top of the pipe). A listing of some of the major features of the most generally accepted models is provided in the following Table 3.
Although some of the models purport to be able to predict water quality as a function of time within the runoff hydrograph (referred to as “pollutographs"), the methods to predict storm water quality during passage of a runoff event are best described as being in their infancy. This is due in a large part to the lack of scientifically controlled studies on the pollutant removal efficiencies of detention facilities. While these models may not presently be appropriate for making definitive predictions of water quality in runoff, they are certainly appropriate for determining the hydraulic and hydrologic response of sewer systems to storm events, including determinations of runoff volumes at various points within a storm event.
The process of implementing a model, including collecting the necessary input data (pipeline sizes, lengths, gradients, catchment area sizes and characteristics), setting up, and de-bugging the model is a major task. Experience with a few U.S. refineries that have made use of a private vendor version of the SWMM model (XP-SWMM) indicates that it can require 1 to 3 man-months for a 500 acre (200 hectare) site. In view of the cost associated with such an effort for a major refinery or chemical plant, it is clear that use of a sophisticated system model can only be justified when there is no other way to work the problem. In general, the simplest method that provides the desired analysis should be used.
HYDROLOGIC DESIGN (Cont) TABLE 3
OVERVIEW OF STORMWATER MODELING COMPUTER PROGRAMS
ATTRIBUTE STORM SWMM TR55 HEC-1 STORMCAD
Sponsoring agency COE/HEC EPA SCS COE/HEC Haested, Inc
Number of pollutants 6 10 None None None
Rainfall/runoff analysis Y Y Y Y Y
Sewer system flow routing N Y Y Y N
Surcharge N Y N N Y
Flow regulators, overflow structures, weirs, etc. Y Y N N Y
Storage analysis Y Y Y Y N
PC versions available N Y Y Y Y
Data and personnel requirements Low High Medium Medium Low
Overall model complexity Medium High Low High Low
➧ STORMCAD is relatively easy to use and is best suited for sizing pipes in a network for the peak flow from a given return period storm, or for evaluating the peak flow capacity of an existing system during various storm events. XP-SWMM is a complex watershed model used mainly for determining flow rates and runoff volumes at any point in the network at any time during a runoff event. It's capabilities and data input requirements are considerably more involved than those associated with STORMCAD. More complete descriptions of these programs are provided in Section XXIX-N.
HYDRAULIC DESIGN
The objective of hydraulic design is determination of the conduit dimensions necessary to carry the design flows. For pipes, the critical dimension is the diameter. For open channels, the required dimensions are the channel depth, bottom width and side slopes. Slope or gradient is a factor for both pipes and channels, although the designer normally has less control over gradient as a design variable. Gradient is usually limited by existing topography, i.e., the elevation of the point of interest vs. the elevation that the pipe or ditch must tie into. Materials that a pipe is constructed of, or channel lining materials for the case of open channels, is another variable over which the designer has some control. The pipe material or channel wall determines the conduit's frictional drag properties, which affects the flow capacity for a given set of dimensions and gradient.
BASIC HYDRAULIC DESIGN CONSIDERATIONS
Storm drainage systems are normally designed to flow as open channels as opposed to pressurized conduit flow. This concept is easy to accept for open ditches, but it also applies to buried drainage pipes. When buried pipes are flowing as partly full channels, the condition is often referred to as “gravity flow" to distinguish from pressurized flow.
Buried pipes behave as open channels as long as they are large enough to not flow full when delivering the design flow. Restricting the design to open channel flow simplifies the design calculations to the extent that the energy grade line and the hydraulic grade line are essentially parallel to the channel bottom, or pipe invert. This creates a minor computational inconvenience when determining the hydraulic radius of a pipe or ditch, which varies with the flow depth, but it allows the gradient to be treated as an independent variable, essentially equal to the pipe slope. As mentioned above, since gradient is for all practical purposes fixed by the site topography, it is convenient to allow it to be treated as an independent variable. The designer then needs only to consider the respective friction coefficients and available diameters of the various pipe materials in order to size the pipe to carry the design flow.
Buried sewer lines do in fact pressurize and flow under a condition referred to as “surcharge", which occurs whenever the applied flow is greater than the capacity of the pipe flowing full under gravity flow. Normally, the maximum pressure head that is assumed is the water level ponded over the downstream manhole, or the ground surface elevation at that manhole. Since storm drains can be sized for storms as small as 2-year events, it is not uncommon for them to be surcharged whenever a larger storm is applied. However, calculating the flow capacity during a surcharge condition is a much more complicated undertaking, as it may require treatment of the sewer system as a pipe network, with variable surcharge heads at each junction (manhole). Therefore, sizing the pipes to insure that they flow as individual open channels (i.e., the less than full condition) simplifies the calculations.
HYDRAULIC DESIGN (Cont)
The presence of seals in an industrial sewer can present special problems which need to be considered in design. For example, if the outlet of a manhole into which a pipe flows is higher than the pipe invert, which might be deliberately done to insure a vapor seal, then portions of that pipe may flow as a full conduit with the hydraulic grade line dictated by the tailwater elevation in the manhole. The mere presence of an inverted elbow, which is another common means to effect a vapor seal (see Figure 9), would not cause the pipe to flow as a full conduit so long as the liquid level in the manhole is less than 2/3 the pipe thickness.
There are also physical considerations that encourage the designer to restrict sewer design to a non-pressurized condition. While joints in new sewer lines are practically leak proof under the nominal pressures applied to the sewer, sewers (other than force mains) are generally not designed to be leakproof under pressurized flows. Water escaping through joints or defects in a sewer wall during surcharge events often returns to the sewer when the storm has receded, but in the process it can carry with it soil from the outside of the line. This gradually weakens the soil-structure arch that contributes a portion of the sewer's structural strength. This is the classical case of gradual deterioration of the line due to frequent surcharging. Thus, frequent surcharging of buried sewers is generally viewed as a poor practice primarily because it tends to shorten the service life of the system.
Another practical constraint on sewer design is the flow velocity. Flow velocity must be kept above a certain minimum to ensure that grit and other debris does not build up in the line or channel. For pipes, which tend to be more difficult to clean than channels, it is customary to keep the flow velocity limits at least 2.5 fps when the pipe is delivering the design flow at its design depth (typically 0.7 times the diameter). At the other extreme, maximum velocities are usually limited by erosion and scour considerations. For pipes, it is customary to limit the maximum velocity to about 10 fps. Occasional bursts of over 10 fps are not likely to cause any damage to pipes in good condition. For channels, the maximum velocity is set by erosion considerations, which are dictated by the material used in the channel lining (if any). Another complication unique to petrochemical plants is that firewater return flows may control the design of the laterals, which might otherwise be sized to carry smaller storm flows.
While flow velocity limitations may appear to present another variable to an already complex problem, the velocity when flowing partly full is more dependent on the gradient than on the pipe dimensions. The gradient is often fixed by topographic considerations, simplifying the designer's task somewhat by removing gradient as a variable. Indeed, there are cases in which the designer would like to have the luxury of treating pipe slope as a variable, but more often the gradient will be fixed by other constraints and therefore out of the designer's control. Under these circumstances, the designer need only select the conduit dimensions and check to see that the design flow can be accommodated in the pipe flowing partly full at velocities within the generally accepted limits. If the gradient is too flat to allow the minimum velocity to be attained, use of a smaller or larger pipe will unfortunately not make a large enough difference. That conduit will simply require more frequent maintenance (flushing) than would have been required if a better velocity mix could have been achieved. As a practical matter, topography within an industrial site is usually fairly flat, so the designer will have a fairly narrow band of gradients to consider.
For flow in open channels, it is customary to provide some nominal freeboard to keep the flow from jumping out of the channel and to account for undulations in the water surface which might be present if the water is flowing relatively fast. A minimum of one ft or one velocity head (V2/2g) is a customary allowance. If the consequences of the flow jumping the channel are significant at any particular location, it would be reasonable to an increase in the freeboard requirements at that location. Similarly, ride-up on bends in an open channel is accommodated by providing additional freeboard, estimated on the basis of the centrifugal forces on the flowing stream.
Flow in buried pipes and in open channels is defined by Manning's Equation (in Customary units), as follows 2 / 1 3 / 2 S R n 49 . 1 ) fps ( V = Eq. (7)
where: n = Manning's roughness coefficient (frictional drag coefficient), which depends on the pipe or ditch material
R = Hydraulic radius, which is the flow area divided by the wetted perimeter, ft.
For pipes flowing full, it is simply half the radius, but for pipes flowing partly full it must be calculated and is a function of the flow depth. For open channels it also must be calculated for each flow depth.
S = Pipe or channel gradient (slope) in decimal form (e.g., 1.5% slope is S = 0.015). In metric units, Manning's Equation is
n S R ) m/s ( V 2 / 1 3 / 2
HYDRAULIC DESIGN (Cont)
Since the water is incompressible, continuity requires that
Q = V A Eq. (9)
where: A = The cross sectional area of flow. For pipes flowing partly full and for open channels, A also must be calculated as a function of flow depth.
HYDRAULIC DESIGN OF BURIED SEWER PIPES
Manning's Equation is used in an iterative process to size the line for given design flow. Except for the fact that R varies with flow depth, the calculation is simple and straightforward. Normally the gradient is fixed, and the design flow has been calculated. The first task is to select a pipe diameter that will deliver the design flow at a flow depth of approximately 0.7 times the diameter. Since the friction coefficient “n" varies with pipe material, it is also necessary to select a trial pipe material. Prior to the advent of PCs and programmable calculators it was customary to select a trial diameter (D), assume a trial depth of 0.7 D, and then read R and A from a table or a chart such as Figure 10 for that trial D. Given S and n, and R and A from the chart, the flow at depth = 0.7 D could be calculated using Manning's Equation. If the calculated flow was smaller than the desired design flow, a larger pipe was selected and the process repeated. Each pipe diameter required a separate trip to the chart to define R and A, which are both functions of D and depth.
It is a simple matter to program the expression for R and A into a spreadsheet or a BASIC utility program. The derivation of the algorithms is provided in APPENDIX B.
Manning's roughness coefficients have been tabulated for the common materials used in sewer pipes, and a summary is provided in Table 4 below. For the materials commonly used in industrial sewers, it can be observed that the Manning's “n" does not vary much from the from the range of 0.011 to 0.015 listed for concrete, mortar lined cast iron, vitrified clay, and plastic pipe. To account for wear and corrosion that may occur as pipes age, it is customary to select “n" values at the upper end of the range for design purposes.
TABLE 4
MANNING'S COEFFICIENT “n" FOR COMMONLY USED DRAINAGE PIPE MATERIALS
MATERIAL RANGE OF MANNING'S “n" COMMON DESIGN VALUE Asbestos-Cement pipe 0.011 - 0.015 0.013 Brick 0.013 - 0.017 0.015
Cast iron pipe, cement mortar lined and seal coated 0.011 - 0.015 0.015
Concrete pipe 0.011 - 0.015 0.015
Corrugate metal pipe (1/2 in. x 2-1/2 in. corrugations) Plain
Paved invert Spun asphalt lined
0.022 - 0.026 0.018 - 0.022 0.011 - 0.015
0.024
Plastic pipe (smooth) 0.008 - 0.015 0.011 *
Vitrified clay pipe 0.011 - 0.015 0.013
* Plastic pipe manufacturers claim that a value of 0.009 can be used for HDPE pipe and 0.010 for PVC pipe, while ASCE leans toward the higher value within a range of 0.011 to 0.015. Since plastic pipe is generally viewed to be less susceptible to corrosion, pitting, tuberculation or biological growth, it is not necessary to design for the upper limit of the friction coefficient. A value of 0.011 is considered a reasonable compromise.
An example problem illustrating the use of Manning's Formula for a buried pipe flowing partly full is provided as Example
HYDRAULIC DESIGN (Cont) HYDRAULIC DESIGN OF OPEN CHANNELS
As in the case of buried pipes, Manning's Equation is also used in an iterative process to arrive at a set of dimensions for open channels. However, in the case of open channels there is an infinite number of combinations of bottom width and side slopes which could be hydraulically satisfactory. Gradient is usually restricted by topography, but it is not uncommon for an open channel to more or less follow the lay of the land (within reason). The intent is to avoid excessive excavation depths while still providing a reasonable bottom gradient, the required flow depth, and a reasonable freeboard allowance.
Open channels, by virtue of their large cross section, are capable of conveying considerably greater flows than closed pipes. However, practical limitations on channel cross section include the obvious space limitations which may be applicable in confined areas. In open terrain, side slopes can be laid back at slopes of 1(vt) on 3 (hz), which allows a vegetative cover to be established. 1 on 3 slopes are probably near the limit of what can be practicably mowed, and slopes as flat as 1(vt) on 6(hz) are preferred if regular mowing is contemplated and if space permits. In confined areas, steeper slopes would be required. If side slopes are steeper than about 1.25 (hz): 1 (vt), vegetative linings will be precluded. Rip-rap linings, gabions, or paved lining (concrete or asphalt) may be required for these steeper slopes. Flow area that is lost as the side slopes are steepened generally has to be compensated by a wider bottom width, although channels with steeper side slopes are hydraulically more efficient than extremely broad ditch sections. In any case, both the channel side slopes and the bottom width are dimensions that the designer may choose to vary.
Open channel flow is categorized as either sub-critical or super-critical, based on the hydraulic principle that open channel flow with a given specific energy can flow at either of two conjugate depths. The sub-critical, or “tranquil", flow regime is characterized by deeper flow depth and a slower velocity, while the super-critical, or “shooting flow", regime has a shallower depth but a higher velocity. The channel should be designed to assure that the flow will remain either sub-critical or super-critical and will not shift from one to the other except under deliberately controlled conditions. Even if the design results in subcritical flow for the design storm, the conditions that would occur when passing larger events should be checked. The condition of rapid changes from one flow regime to the other is referred to “rapidly varied flow", and it involves hydraulic jumps and “holes" in the water surface. These are inherently difficult to control, which is the reason that changes from one flow regime to the other should be avoided or at least controlled. Similarly, any changes in the channel geometry from one section to the next need to be accomplished gradually to avoid triggering a hydraulic jump or a shift to super-critical flow.
Manning's coefficients for various types of open channel linings are tabulated in a number of references. Typical values for Manning's “n" for various open channel conditions that might be encountered in practice are presented in Table 5.
TABLE 5
MANNING'S COEFFICIENT “n" FOR COMMONLY USED FOR OPEN CHANNELS
CHANNEL CONDITION MANNING'S “n" DESIGN VALUE
Lined Channels Asphalt
Concrete Rubble or rip-rap Vegetative cover (grass)
0.013 - 0.017 0.011 - 0.020 0.020 - 0.035 0.030 - 0.040 0.015 0.016 0.035 0.035 Excavated or Dredged Channels Earth, straight and uniform
Earth, winding but uniform Rock Unmaintained 0.020 - 0.030 0.025 - 0.040 0.030 - 0.045 0.050 - 0.14 0.025 0.035 0.045 0.1 Natural Channels (Minor Streams) Fairly regular section
Irregular section with pools
0.03 - 0.07 0.04 - 0.10
0.06 0.07
As is the case with computations for pipe flows, the calculations for flow in open channels can be computerized or can be carried out using nomographs. The problem can easily be set up in a utility BASIC or spreadsheet format. A summary of the derivation of Manning's solution for trapezoidal channels of any dimensions is presented in APPENDIX B. A design example of the solution of Manning's Equation for an open channel problem is presented as Example Problem No. 7 in APPENDIX A.
HYDRAULIC DESIGN (Cont)
Freeboard requirements are generally based on velocity, although a minimum of 1 ft is sometimes specified. A simple relationship to velocity is:
d C Hfb = fb , ft
where: Cfb = Coefficient varying from 1.5 for channels with capacities of 20 ft3/s to 2.5 for channels with capacities of 3000 ft3/s or more
d = Depth of flow, ft. Superelevation, or “ride-up" on a curve can be calculated as:
c w 2 r g T V h=
where: h = Additional elevation, ft V = Velocity, ft/s
Tw = Top width of the channel, ft g = Gravitational constant rc = Radius of curvature, ft.
This expression is also valid for metric units provided consistent units are used.
CULVERT CROSSINGS OVER OPEN CHANNELS
A consequence of the use of open channels is the requirement to provide bridges over the channel at various locations. Most often this is accomplished by the used of pre-fabricated pipes, either CMP (corrugated metal pipes) or concrete pipes. The primary design consideration is to provide a waterway opening large enough to allow the design flow to pass through the culvert without backing up water excessively on the upstream side. The depth required to force the water through the pipe must be lower than the roadway elevation (unless overtopping can be tolerated) and low enough so as not to cause upstream backwater effects (ponding) or upstream bank overflows. In general, it is unusual to select a pipe so small that the headwater required to drive the design flow through the pipe is more than twice the diameter of the culvert (total headwater depth measured from the pipe invert). Situations such as this often require consideration of several parallel pipes or shift to a hydraulically more efficient pipe-arch culvert or a bridge.
Most culvert design is carried out using a set of nomographs developed by the Federal Highway Administration. The solution considers two possible controlling mechanisms:
• Inlet control, wherein the flow through the culvert is limited by head losses at the entry point.
• Outlet control, where the limiting factor is frictional losses incurred as the water flows through the pipe.
The condition which requires the greater headwater (upstream side) for a given flow in a given pipe (or set of parallel pipes) is the controlling condition, and the headwater is then determined according to that condition. If the required headwater depth is excessive, then a larger culvert must be considered.
Outlet control nomographs can be derived by considering Bernoulli's' equation for conservation of energy, continuity for conservation of mass, and using Manning's equation to relate frictional energy losses to flow velocity. The outlet control nomographs can therefore be adapted to simple spreadsheets or BASIC programs. However, the inlet control solution is based on experimental work on pipes of various diameters and various inlet conditions (e.g., projecting, mitered) that was sponsored by the US. Dept. of Transportation, Federal Highway Administration in the 1950s. Some programmed solutions exist, but it remains common practice to rely on the nomographs, which are reproduced here as Figure 11-A through D. Since the
nomographs are needed for the inlet control condition, it is customary to use the parallel set of outlet control nomographs as well. However, the use of the nomographs forces a trial-and-error solution. Nomographs included in Figure 11 are only for circular corrugated metal and circular concrete pipes. There are additional charts provided in other reference for special sections such as elliptical pipes and pipe-arch culverts. (e.g., Design of Small Dams).
Typically, the designer will have a design flow, determined as described earlier in this Design Practice. For a starting point, it is reasonable to assume the flow velocity through the culvert will be no more than 10 fps (3 m/s), which allows the selection of a trial pipe size. The pipe is then checked against the “Inlet Control" nomographs, for the pipe type (corrugated metal or concrete pipe) and entry conditions (headwall, mitered pipe, or projecting pipe). The headwater required to deliver the design flow is then read from the nomograph. If the headwater required is greater than what can be accommodated at the crossing (e.g., if the headwater would imply water flowing over the crossing or backing up water such that it flows out of the ditch), then a larger pipe is selected.
