Coeficienti Manning

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1American Concrete Pipe Association www.concrete-pipe.org [email protected]

ACPA 2007 DD 10 October 2007

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INTRODUCTION

Selection of the proper value for the coefficient ofroughness of a pipe is essential in evaluating the flowthrough culverts and sewers. An excessive value isuneconomical and results in oversizing of pipe, whileequally, a low value can result in hydraulically inadequatepipe. Proper values for the coefficient of roughness ofcommercially available pipe has been the objective ofperiodic investigations and, as a result, extensive knowl-

edge and data are available on this often controversialsubject. To the designer, the presently accepted valuesfor the coefficient of roughness are of great importance.Of equal importance is an understanding of how thesevalues were determined. Research often indicates newvalues for pipe materials significantly different from thosepreviously used.

DESIGN VALUES

The difference between laboratory test values ofMannings nand accepted design values is significant.Numerous tests by public and other agencies have es-tablished Mannings nlaboratory values. These laboratory

results, however, were obtained utilizing clean water andstraight pipe sections without bends, manholes, debris,or other obstructions. The laboratory results indicated theonly differences were between smooth wall and rough wallpipes. Rough wall, such as unlined corrugated metal pipehave relatively high nvalues which are approximately 2.5to 3 times those of smooth wall pipe.

Smooth wall pipes were found to have n valuesranging between 0.009 and 0.010 but, historically, en-gineers familiar with sewers have used 0.012 or 0.013.This design factor of 20-30 percent takes into accountthe difference between laboratory testing and actual in-stalled conditions. The use of such design factors is goodengineering practice and, to be consistent for all pipematerials, the applicable Mannings n laboratory valueshould be increased a similar amount in order to arrive atcomparative design values. Recommended design valuesare shown in Table 1.

FLOW FORMULAS

The Kutter flow formula was developed about 1870

Mannings n ValuesHistory of Research

and extensively used for many years to calculate pipeflows. Roughness coefficient values for use in the Kutterformula were derived and are known as Kutter nvalues.The Kutter formula was mathematically cumbersome,even though charts and graphs were developed as de-sign aids.

The simpler Manning formula, developed in 1890, hasgenerally replaced the Kutter formula in use. Manningsformula, in terms of flow, is expressed as follows:

Q = AR2/3S1/21.486n

where: Q = flow in pipe, cubic feet per second

A = cross-sectional area of flow, squarefeet

R = hydraulic radius, equal to the cross-sec-tional area of flow divided by the wettedperimeter of pipe, feet

S = slope of pipe, feet per foot n = coefficient of roughness appropriate to

the type of pipe

Pipe

Material

Concrete 0.009-0.0101 0.010-0.0121 storm sewer - 0.011-0.0121

sanitary sewer - 0.012-0.0131

HDPE

lined 0.009-0.0152 0.009- storm sewer - 0.012-0.0202

0.0133

PVCsolid wall 0.009-0.0114 0.0094 storm & sanitary

sewer - 0.011-0.0132

Corrugated

Pipe 0.012-0.0305 0.012-0.0266 0.021-0.0297

Lab Values Promoted ACPAValues Recommended Values

Values of Manning's n

Table 1 Recommended Values of Mannings n

1 American Concrete Pipe Associations Concrete Pipe Design Manual- 2000

2 Tullis and Barfuss Study - 19893 CPPA Specifications4 Uni-Bells Handbook of PVC Pipe - 20015 University of Minnesota test on Culvert Pipes - 19506 NCSPAS Modern Sewer Design - 19997 U.S. Department of Transportation Federal Highway Administrations

Hydraulic Design of Highway Culverts - 2001


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DD 10 October 2007

The Manning formula factors are similar to those inKutter formula and are expressed in the same units. Val-ues for the coefficient of roughness, n, were at first thoughtto be the same as those used in the Kutter formula butthis assumption has been proven to be wrong.

MANNING nVALUE RESEARCH

As the Manning formula came into more common use,the direct interchange of nvalues with Kutters was ques-tioned. A series of studies, prior to 1924, at the Universityof Iowa provided the first extensive data on this disputedpoint. These were cooperative studies sponsored by theBureau of Public Roads, U.S. Department of Agriculture,and the University of Iowa. The test program consistedof 1,480 hydraulic experiments on 12, 18, 24 and 30-inch concrete pipe, corrugated metal pipe, and clay pipe.Results of these tests were published in 1926 by theUniversity of Iowa in Bulletin No. 1, The Flow of WaterThrough Culverts, by David L. Yarnell, Floyd A. Naglerand Sherman M. Woodward. Values obtained from the test

results for Manning and Kutter roughness coefficients, aregiven in Table 2. After the Iowa test results were published,many designers re-evaluated the nvalues for Manningsformula and used 0.013 for smooth wall pipe and 0.024for corrugated pipe. These values were not universallyaccepted, however, and other designers used n= 0.015for concrete and clay pipe. Metal pipe manufacturerswere advocating n= 0.021 for corrugated metal pipe, andsome designers still erroneously use this comparativelylow value for corrugated pipe today.

HDPE PIPE

Research by Tullis and Barfuss in 1989, presentedto the American Society of Civil Engineers showed thattests on corrugated HDPE pipe with a liner has a labora-tory Mannings nvalue in the range of 0.009 to 0.015,

depending on the condition of the liners. The bonding ofthe liner to the corrugations, in many cases, made the pipeinterior wavy, explaining the broad range in nvalues. Thiswaviness causes the HDPE pipe to have hydraulic valuessimilar to CMP. Mannings nconcerns regarding HDPEpipe, however, are not widely understood because thepipe has never been tested under an external load, and

further research is required. Because of the broad rangeof nvalues, an nvalue of 0.012 for HDPE pipe will notprovide a 20 to 30 % factor of safety and is not recognizedby the FHWA and the Army Corps of Engineers.

Frequently the inner liner of a double wall (profile)wall HDPE pipe undergoes a phenomenon called cor-rugation growth. After a short period of time, sometimesprior to installation, plastic deformation occurs in the linercreating waviness that makes the interior of HDPE pipeappear similar to corrugated metal pipe. The inner liningis intended to produce a smooth-walled pipe, however, acorrugated pattern results when stresses are transferredfrom the outer corrugated wall to the inner liner. The

smooth liner is unable to resist stresses from the outerwall and corrugation growth appears. Designers of pipingsystems utilizing lined HDPE pipe should size the pipeusing a Mannings nvalue similar to that of corrugatedmetal pipe.

COMPARATIVE TESTS FOR CONCRETE AND

CORRUGATED METAL PIPE

The next significant investigation of Manning nvaluesfor pipe began in 1946 and continued over a four-yearperiod at St. Anthony Falls Hydraulic Laboratory, Univer-sity of Minnesota. A primary purpose of these large-scaletests was to obtain pipe friction coefficients which wouldbe more accurate and dependable. A total of 181 hydraulictests were run on 18, 24, and 36-inch circular concretepipe and corrugated metal pipe, and corrugated metal pipe

Table 2 University of Iowa Tests on Culvert Pipe - 1926. Average Values for the Coefficient of

Roughness in Concrete, Vitrified-clay, and Corrugated Metal, Culvert Pipe

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arches for the full flow and partly full flow conditions. Manyof the shortcomings of previous hydraulic tests were elimi-nated in the Minnesota tests. Culvert test lengths were 193feet, which were longer and more representative of actualinstallation conditions. Pipe section lengths were closer toactual commercial lengths, particularly for concrete pipe,with six-foot sections being used instead of the two-footand three-foot lengths used in the 1926 Iowa test. Thetest results were published in 1950 by the University ofMinnesota in Technical Paper No. 3, Series B, Hydrau-

lic Data Comparison of Concrete and Corrugated MetalPipes by Lorenz G. Straub and Henry M. Morris and areas shown in Table 3. These results indicate a significantlylower value of Mannings nfor concrete pipe than the 1926Iowa tests. Technical Paper No. 3also included recom-mended design values for nfor both corrugated metal andconcrete pipe as reproduced in Table 4. Comparing the

values from Tables 2, 3 and 4, it is readily apparent that nosafety factors were applied to the laboratory values whenconverting them to design values. The footnote beneathTable 4, however, qualifies the application of the recom-mended values to such an extent that they could not beused for realistic pipe installation. As previously discussed,laboratory values should not be used for design purposeswithout appropriate safety factors.

During the period 1960-1962, research was conductedin Canada to determine design values of nfor pipe used in

culvert construction. The research was under the auspicesof the Cooperative Highway Research Program in Alberta,which included the provincial Department of Highways, theResearch Council of Alberta, and the Faculty of Engineer-ing of the University of Alberta as participating bodies.Tests were made on field installations of 60-inch structuralplate corrugated metal pipe culverts 70 and 150-feet long

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Table 3 University of Minnesota Test on Culvert Pipes - 1950. Summary of Test Results

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Table 4 University of Minnesota Tests on Culvert Pipe - 1950. Recommended Design Coefficients of

Corrugated Metal and Concrete Culverts


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with various inlet shapes and slopes from 1 to 3 percent,and on a 48-inch concrete pipe culvert 78-feet long on aslope of 0.5 percent. Laboratory tests were conductedon 15-inch diameter standard corrugated metal pipe 36and 724-feet long with slopes from 0 to 8 percent. Testresults were published by the Research Council of Albertain the 1962 Alberta Highway Research Report 62-1 titled

Hydraulic Tests on Pipe Culverts by C. R. Neill. Sum-maries of the Manning n values computed for the 60-inchstructural plate pipe are quoted as follows:

The n values computed from 33 tests showed anormal type of statistical scatter, with a mean of 0.0357and a standard deviation of 0.0025. Pending further tests,the value of 0.035 was adopted for structural plate cor-rugated metal pipe.

Manning nvalues determined for the 15-inch standardcorrugated metal pipe, are quoted as follows:

Values ranged from 0.021 at very low velocitiesto 0.025 at high velocities. It appeared that 0.026 wasprobably a peak value and that 0.025 was reasonable for

design purposes.Additional quotes as to values of Mannings n for

concrete pipe are as follows:No determination was made of roughness coeffi-

cients, since the pipe was too short and smooth to showappreciable friction losses.

As one purpose of the experiments was to determinethe possible hydraulic advantages of using concrete pipeinstead of corrugated metal pipe, the following statementsfrom the test report are significant:

By comparison, it can be seen that the capacity of the48-inch concrete culvert was approximately the same asthat of the 60-inch structural plate corrugated metaI one,of approximately the same length. At the upper end ofthe test range, the concrete culvert showed rather betterperformance.

The tests on concrete pipe culvert showed that aconcrete culvert of given diameter was considerably moreefficient than a corrugated metal one in most design situa-tions especially when subjected to high headwater depths,the main reason being the much smaller friction losses inthe concrete pipe. It appeared that concrete culverts primereadily when their inlets are slightly submerged, and maythen be assumed to flow full throughout, and also that thestandard type of grooved inlet is quite efficient.

CONCRETE PIPE TESTS

In addition to those previously discussed, other testshave been performed on concrete pipe. In June 1956,experimental studies on 24 and 36-inch concrete pipewere initiated by the State Road Department of Florida todetermine the effect of interior surface finishes and jointirregularities on the pipe coefficient of friction. The testprogram was expanded in May 1957, placed under joint

sponsorship of the State Road Department of Florida andthe Bureau of Public Roads, and studies were performedat St. Anthony Falls Hydraulic Laboratory, University ofMinnesota. This series of tests is significant in that fieldlaying conditions were simulated, a condition designersfound lacking in other hydraulic studies. Laboratory testinstallations were 240-feet long for the 36-inch pipe and

192-feet for the 24-inch pipe. Tests were made on pipeinstalled in two ways: (1) pipe laid with normal construc-tion practices and closely simulating field measurementsof joint irregularities, and (2) pipe laid with extreme careto eliminate, as far as possible, all flow interference at

Groove

119o

Bead or FilletJoist may have offset in additionto groove and bead or fillet

W

eb

eb= 0 to 0.72"

eo

eo= 0 to 1.37"

Wave= 5.32" b= 1.54"

b

GrooveBead

Offset

Exterior of Pipe

Diaper Seal

Fillet

Figure 1 Cross-Section of Concrete PipeTest Joints


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the joints. The first condition was referred to as averagejoints and the second as good joints. Figure 1 illustratesthe irregularities noted in field joints and a cross sectionof the pipe showing the average circumferential lengthof grooves and beads. Joint irregularities were of threebasic types:

offsets-due to misalignment or variation in diameter

of pipe. grooves-formed by annular openings between

tongue and groove ends of pipe. beads and fillets-formed by mortar smoothed over

the interior surface of the joint.Results of this series of tests were published in De-

cember 1960, by St. Anthony Falls Hydraulic Laboratory,University of Minnesota, Technical Paper No. 22, SeriesB, titled Resistance to Flow in Two Types of ConcretePipe by Lorenz G. Straub, Charles E. Bowers and MeirPilch. A comparison of the test data for pipe with goodand average field irregularities indicates a difference inMannings non the order of 1.9 percent. Numerical values

of n for 36-inch and 24-inch pipe with average joints were0.0111 and 0.0110, respectively and, as a result, ASTMSpecification C76 was written to require, the joints shall beof such design and the ends of the concrete pipe sectionsso formed that when the sections are laid together theywill make a continuous line of pipe with a smooth interiorfree from appreciable irregularities in the flow line.

In the mid-1980s, laboratory tests of concrete andplastic pipe were conducted at the T. Blench HydraulicsLaboratory, Department of Civil Engineering, The Univer-sity of Alberta. A report by D.K. May, A.W. Peterson and N.Rajaratnam, A Study of Mannings Roughness Coefficientfor Commercial Concrete and Plastic Pipe, was publishedin January, 1986. Commercially available concrete pipein 8, 10 and 15-inch diameters and PVC plastic pipe in 8,10 and 18-inch diameters were tested with clean waterand straight alignment. The average Mannings n valueswere found to be 0.010 for concrete pipe and 0.009 forPVC pipe as presented in Table 5.

To reconfirm the results of the Alberta and previousstudies, the American Concrete Pipe Association com-missioned additional tests on 8, 12 and 18-inch diameterprecast concrete pipe at the Utah Water Research Labo-ratory, Utah State University, Logan, Utah. Results werepublished in Hydraulics Report Number 157, J. Paul Tul-

lis, October, 1986. Laboratory values of Mannings nforprecast concrete pipe were reconfirmed as 0.010. Resultsare shown in Table 6.

CORRUGATED METAL PIPE TESTS

Prior to 1950, comparatively few tests had been madeon large size corrugated metal pipe. For this reason,U.S. Army Chief of Engineers Office, in 1951, authorizedtests on 3, 5, and 7-foot diameter corrugated metal pipe

at the Bonneville Hydraulic Laboratory, Bonneville, Or-egon. Length of the test installations was 350 feet for alldiameters. All pipe had a corrugation pattern of 1/

2-inch x

22/3-inch. The experimental conditions, as far as size and

length of pipe tested, exceeded any previously used. Re-sults of these tests were published in 1959, in the Journalof the Hydraulics Division, Proceedings of the AmericanSociety of Civil Engineers, Friction Factors in Corrugated

Metal Pipe by Marvin J. Webster and Laurence R. Met-calf. Recommended Manning n values are presentedgraphically in the report. As a conclusion, the report statesthat for 3, 5 and 7-foot nominal diameter corrugated pipewith a 1/

2-inch x 22/

3-inch corrugations and flowing full, a

Mannings n= 0.024 was obtained.In 1958, a program of hydraulic tests was initiated

by the U. S. Army Corps of Engineers, and the Bureau ofPublic Roads at the U. S. Army Waterways ExperimentStation, for the purpose of determining roughness factorsfor structural plate corrugated metal pipe. The results werepresented in a paper at the 44th Annual Meeting of theHighway Research Board, January 1965, and publishedin Highway Record No. 116. The paper is titled FrictionFactors for Hydraulic Design of Corrugated Metal Pipe, byJohn L. Grace, Jr. A major highlight of this research reportwas the preparation of graphs showing the relationship ofMannings nwith pipe size for three commercially avail-able corrugation patterns. These graphs are reproducedin Design Data 2 (Friction Factors for Corrugated MetalPipe). A summary of the range of nvalues and the ap-

Table 5 University of Alberta - 1986.

Summary of Test Results

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plicable equations relating Mannings nto pipe diametersare presented in Table 7.

The corrugated metal pipe industry has formallyrecognized the higher laboratory values of Manningsn, which research has proven for available corrugationpatterns. The values of n recommended for unpavedcorrugated metal pipe in the May 1999 Modern SewerDesign, published by the National Corrugated Steel PipeAssociation and the American Iron and Steel Institute, arepresented in Table 8.

To date, limited testing has been conducted on heli-cally corrugated metal pipe. Tests were conducted onhelically corrugated metal pipe by A. R. Chamberlainand the results were published in 1955 at Colorado State

University in a report titled Effect of Boundary on FineSand Transport in Twelve Inch Pipes. Charles E. Riceconducted flow tests at the Stillwater Outdoor HydraulicLaboratory, Stillwater, Oklahoma, on 8-inch and 12-inchpipe. His report titled Friction Factors for Helical Cor-rugated Pipe, was published by the U. S. Department ofAgricultural Research Service in 1966.

In 1970, the Federal Highway Administration, Of-fices of Research and Development published a report

n = 12" - 96"0.0259

to0.0237

n

ValueRange

Pipe

SizeRangeCorrugatedPatternEquation

0.02592 2/3" x

1/2"D0.044

n = 36" - 96"0.0282

to0.0262

0.03603" x 1"

D0.075

n = 36" - 96"0.0333

to0.0298

0.03776" x 2"

D0.0775

Table 7 Friction Factors for Hydraulic Design

of Corrugated Metal Pipe

5 to 20 ft.

0.031*

3 to 8 ft.

0.027

1 to 8 ft.

0.024

Diameter

Unpaved

*BPR Circ. 10, Mar. 1965, p. 78. Based on 108-in. diam.

Corrugations(Annular)

Structural Plate6 x 2 in.2

2/3 x1/2 in.. 3 x 1 in.

Table 8 Values of Coefficient of Roughness n

for Corrugated Steel Pipe (Mannings

Formula)

Hydraulic Flow Resistance Factors for Corrugated MetalConduits by J. M. Norman and H. G. Bossy. The obser-vations by the authors were that, as the pipe diametersincreases, the helix angle also increases, and as the helixangle approaches 90 degrees the pipe must behave asa corrugated pipe with annular corrugations. For a partlyfull flow condition in a helically corrugated metal pipe in

which the spiral flow cannot be maintained, it is presumedthat even a small helix angle would cause little reductionin resistance and that the same resistance coefficient asthat for standard corrugated metal pipe should be used.There is a need to further test helically corrugated metalpipe, especially the larger sizes. At present, the use of areduced resistance coefficient is indicated only for smalldiameters, 2 feet or less, and then only under full flowconditions.... The best course for conservative design,pending further test results, is to use annular corrugatedmetal pipe resistance coefficients for helically corrugatedpipe.

An updated Hydraulic Flow Resistance Factors for

Corrugated Metal Conduits was published by the FederalHighway Administration in January, 1980. In 2001, theFederal Highway Administration published Hydraulic De-sign of Highway Culverts, Hydraulic Design Series No. 5by J.M. Norman, R.J. Houghtalen and W.J. Johnston. Bothpublications recommend annular flow resistance factorsbe used for helically corrugated metal pipe installationsunless all the following conditions are met:

The conduit flows full. The conduit is circular in shape. There is no erosion resistant sediment build-up in

the conduit. The conduit is greater than 20 diameters long. The conduit is unpaved. There are no manholes, wyes and tees. There are no changes in grade and alignment.

CORRUGATED ALUMINUM PIPE TESTS

In April 1971, a report was published titled FurtherStudies of Friction Factors for Corrugated AluminumPipe Flowing Full by Edward Silberman and Warren 0.Dahlin, St. Anthony Falls Hydraulic Laboratory, Universityof Minnesota. Laboratory tests were conducted on pipewhich ranged in diameter from 12 inches to 66 inches

and lengths from 100 feet to 220 feet using both annularand helical corrugated aluminum pipe. The tests wereconducted with a head of 20 feet so that the pipe wouldflow full.

The conclusions reached by the authors are Theexperiments described in this report have been conductedusing corrugated aluminum pipes flowing full. The mea-surements were made following an entry region of 20 ormore pipe diameters, and although this distance appears


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converted to Mannings nvalues results in nvalues of0.010 to 0.013.

In the corrosion process (tuberculation), growths ormounds form on the walls of the iron pipe. These growthsare often so large and numerous that the frictional re-sistance is greatly increased and, in addition, a seriousreduction in the effective cross sectional area of the pipe

is produced. The result is a tremendous reduction in hy-draulic capacity. In order to offset the destructive effectsof tuberculation, the cast iron and ductile iron pipe manu-facturers generally supply pipe with either cement mortarlinings or polyethylene linings. These are relatively thinlinings, and it is quite probable that the linings will lose theirprotective capabilities within a few years, due to leachingand scrubbing action, and permit the start of tuberculation.For cast iron or ductile iron sewers an nvalue of 0.013should be used regardless of the type of lining.

AGENCY POLICIES ON n

Beginning in 1953, many governmental agencies

made policy statements relating to the Manning nvaluesfor use on work under their jurisdictions. Policy statementsare listed in Table 9. Since these policy statements wereso similar, the selection of the proper nvalue for differentpipe types appeared to be settled. In the FHWAsHydraulicDesign Series Number 5, all nvalues are lab values. Inall other policy statements, the fact that the nvalues forconcrete pipe have a built in safety factor, however, wasnot considered and a corresponding safety factor is notapplied to the laboratory values for some other smoothwall pipe nor for corrugated metal pipe.


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DD 10 October 2007Technical data herein is considered reliable, but no guarantee is made or liability assumed.

Agency Year Publication Values of Manning's Roughness Cofficients

HeadquartersDepartment ofthe Army

Office of Chiefof Engineers

Technical Manual TM 5-820-3 Drainage andErosion-Control Structures

for Airfields and Heliports

Type of Pipe

All smooth wallCorrugated metal pipe

2 2/3 by 1/2 inch3 by 1 inch6 by 2 inch9 by 2 1/2 inch

n

0.012

0.0240.027

0.028-0.0330.033

19781978

HeadquartersDepartment ofthe ArmyOffice of Chiefof Engineers

Technical Manual TM 5-820-4 Drainage forAreas Other ThanAirfields

Type of Pipe

All smooth wallCorrugated metal pipe

2 2/3 by 1/2 inch3 by 1 inch6 by 2 inch9 by 2 1/2 inch

n

0.012

0.0240.027

0.028-0.0330.033

1983

US Departmentof TransportationFederal HighwayAdministration

Hydraulic Flow ResistanceFactors for CorrugatedMetal Conduits

Corrugation

2 2/3" x 1/2"3" x 1"6" x 1"6" x 2" struct. plate9" x 2 1/2 struct. plate

n

.0263 to .0235

.0281 to .0260

.0260 to .0270

.0330 to .0300

.0338 to .0318

DiameterRange (ft.)

1 - 83 - 83 - 83 - 217 - 15

1980

US Departmentof TransportationFederal HighwayAdministration

Hydraulic DesignSeries Number 5,Hydraulic Design ofHighway Culverts

For helically corrugated pipe - use the samevalues as an annular corrugated pipe

The Manning's nvalue ranges indicated in this table

are laboratory values. In general, it is recommendedthat the annular resistance factors be used for

corrugated metal pipes with helical corrugations.

Type of Pipe

Concrete Pipe

Concrete Box CulvertsSpiral Rib Metal PipeCorrugated Metal Pipe

2 2/3" x 1/2"6" x 1"5" x 1"3" x 1"6" x 2"9" x 2 1/2"

Corrugated Metal Pipes,Helical Corrugations,Full Circular Flow

2 2/3" x 1/2

n

0.010 - 0.011

0.012 - 0.0150.012 - 0.013

0.022 - 0.0270.022 - 0.0250.025 - 0.0260.027 - 0.0280.033 - 0.0350.033 - 0.037

0.012 - 0.024

2001

Table 9 Policy Statements

Documents

Coeficienti Manning