Effect of Biofilm Formation on Roughness Coefficientand Solids Deposition in Small-Diameter PVC Sewer PipesKarloren Guzmán1; Enrique J. La Motta2; J. Alex McCorquodale3; Soli Rojas4; and Maria Ermogenous5

Abstract: The purpose of a sanitary sewer is to carry the peak discharge at the end of the design period, and to transport suspendedmaterials under all flow conditions to prevent deposition of solids, and hence, sewer blockages. To accomplish the latter, the liquid mustprovide for sufficient shear stress to suspend and transport the particles along the sewer. Published design criteria for critical shear stressin sanitary sewers vary significantly. However, the effect of biological film development on the internal pipe surface has been neglected.Experiments conducted utilizing a pilot-scale sanitary sewer installed in the Hydraulics Laboratory at the University of New Orleans, La.,provide evidence that the shear stress to move particles of a given size is independent of slope and pipe diameter, but does depend on theeffect of biological film on increasing the roughness coefficient. This critical shear stress, to achieve self-cleansing in sanitary sewers, wasfound to be in the range of 1.1–1.4 N/m2, depending on the integrity of the biofilm. Based on this principle, a design procedure applicableto small-diameter PVC pipes with slopes between 0.1 and 0.5% was developed.

DOI: 10.1061/�ASCE�0733-9372�2007�133:4�364�

CE Database subject headings: Biofilm; Roughness; Sewer pipes; Solid wastes; Waste management.

Introduction

Effective management of a community’s wastewater requires theefficient collection and conveyance of the different types ofwastewater under variable flow conditions. For this reason, asewer must be designed to convey the minimum flow withoutdeposition of suspended solids, or with occasional deposition inamounts and in locations where resuspension will take placeunder the next increase in flow. In other words, solids must becarried in suspension at self-cleansing, yet nondestructive veloci-ties. Among the problems experienced in sewer systems con-structed in flat areas, a deficiency frequently reported is the lackof self-cleansing action in small-diameter sewers.

The Manning equation, most commonly used for the design ofsanitary sewers, expresses the velocity as a function of a rough-ness coefficient n, the hydraulic radius, and the pipe slope. Ac-cording to Manning’s formula, the fluid velocity varies inverselywith n. Standard sanitary sewer design references �ASCE 1982;Brater and King 1976; Tchobanoglous 1981� give ranges of val-

1Research Assistant, Dept. of Civil and Environmental Engineering,Univ. of New Orleans, New Orleans, LA.

2Professor, Dept. of Civil and Environmental Engineering, Univ. ofNew Orleans, New Orleans, LA �corresponding author�. E-mail:elamotta@uno.edu

3Professor, Dept. of Civil and Environmental Engineering, Univ. ofNew Orleans, New Orleans, LA.

4Engineer, Montgomery, Watson, and Harza, Tampa, FL.5Research Assistant, Dept. of Civil and Environmental Engineering,

Univ. of New Orleans, New Orleans, LA.Note. Discussion open until September 1, 2007. Separate discussions

must be submitted for individual papers. To extend the closing date byone month, a written request must be filed with the ASCE ManagingEditor. The manuscript for this paper was submitted for review and pos-sible publication on February 16, 2005; approved on October 1, 2006.This paper is part of the Journal of Environmental Engineering, Vol.133, No. 4, April 1, 2007. ©ASCE, ISSN 0733-9372/2007/4-364–371/

$25.00.

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ues of n for different pipe materials and surface conditions, whichare applicable to pipes flowing full.

Yarnell and Woodward �1920�, Wilcox �1924�, and Camp�1940�, recognized the effect of depth of flow on the roughnesscoefficient, and presented experimental data that have beenwidely used by design engineers �ASCE 1982�. Working with twolarge reinforced concrete-arch combined-trunk sewers that werenot covered with biological film, Schmidt �1953� demonstratedthat when the depth of flow changed from about 0.45 to 1.5 m,the roughness coefficient changed from 0.0123 to 0.0131; thepresence of 0.14-m deep grit increased the value of n to 0.0175.

Working with clean 200-mm clay and asbestos sewer pipes,laid on 0.25 and 0.4% slopes, with velocities �0.3 m/s, anddepth-to-diameter ratios �y /d0� ranging from 0.1 to 1.0, Cosens�1954� observed a wide scattering of n values, ranging from0.0075 to 0.0108, to the extent that no function to describe thevariability of n with the depth-to-diameter ratio could have beenproposed. Nevertheless, Cosens �1954� concluded that n “prob-ably” changes with slope.

Bloodgood and Bell �1961� worked with a carefully built testinstallation provided with 100- and 200-mm vitrified clean claypipes, 100-mm centrifugally spun clean cast iron pie, and 100-and 200-mm clean cement–asbestos pipes, laid on 0.25 and 0.4%slopes, using municipal water and a wide range of flow depths.Although they did not report the variability of Manning’s n withthe depth-to-diameter ratio, these researchers concluded that y /d0

is the principal factor in the selection of an n value for a particularpipe.

In carefully controlled tests with 200- and 300-mm cleanpipes, Neale and Price �1964� found that Manning’s formula isnot applicable to flows in smooth-walled polyvinylchloride �PVC�sewer pipe. Rather, the Von Karman smooth pipe curve,1 /�f =2 log �fNR−0.8, provided a good fit to their experimentalobservations. Similar observations were made by Demetriou andNanou-Giannarou �1988� who worked with PVC pipes provided

with artificial roughness.

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Observations on the variability of n with depth performed byPomeroy �1967� in sanitary sewers revealed that the roughnesscoefficient increases with the relative depth of flow.

Factors that affect the choice of Manning’s n coefficient arethe conduit material, size, shape, depth of flow, Reynolds number,and Froude number. In addition to these factors, the deposits insewers, particularly grit accumulation on the invert, and the typi-cal slime layer growing on the internal pipe surface, should affectthe value of the roughness coefficient. In fact, field tests per-formed by Pomeroy �1967� in small-diameter asbestos–cementsanitary sewers yielded values of Manning’s roughness coefficientas high as 0.0409 in sewers with sediments.

Additionally, it has been generally accepted that to avoid sedi-mentation of grit in sanitary sewers, the minimum velocity shouldbe greater than 0.6 m/s �2 ft/ s� when the pipe is flowing full, andthat it would be desirable to maintain a self-cleansing velocityunder partially filled conditions �La Motta 1996�. Because thebasic mechanism of self-cleansing action is the hydrodynamicshear exerted on the sewer boundary by the flowing wastewater, ithas been suggested that a more rational approach would be to usethe critical shear stress as the basis for the design of self-cleaningsewers. Based on characteristics of suspended particles in waste-water, a critical shear stress in the range of 0.95–1.90 N/m2

�0.02–0.04 lb/ ft2� has been proposed for designing self-cleansingsanitary sewers �Yao 1976�. Novak and Nalluri �1984� showedthat the nature of the packed bed had a significant effect on thecritical shear stress; thick packed bed was well represented by theShields curve while a tin veneer of particles could have criticalshear stresses that are an order of magnitude lower.

A generally accepted design procedure for sanitary sewers laidon flat slopes was suggested several decades ago in Manuals 37and 60 �ASCE 1966, 1982�, and by Fair et al. �1968�, whichconsists of using a slope that at any depth of flow generates ashear stress equal to or greater than that existing in a sewer run-ning full with a minimum velocity of 0.6 m/s.

Another design alternative was proposed by Pujol �2000�,which consists of assuming that the shear stress to move particlesof a given size is constant for a given pipe diameter and wouldonly depend on the slope.

Even though the occurrence of biological films in a sanitarysewer is very important in defining its operation characteristics,there is very little basic research available on this topic. Designengineers often handle the transport of sediments in sanitary sew-ers using empirical rules that do not adequately account for thehydrodynamics, sediment transport mechanisms, and the biologi-cal factors present in these systems.

The formation of biological films on the channel surfaces notonly affects the characteristics of the surface, such as the rough-ness coefficient, but may also promote the accumulation of or-ganic and inorganic particles because of its adhesive properties.These particles, in turn, can contribute to sediment buildup, thusincreasing the roughness coefficient n of the channel surface.

The main objectives of this research project were to determinethe Manning’s roughness coefficient in small-diameter PVCpipes, with and without biological film on the internal pipe sur-face, and to determine the effect of shear stress on sediment trans-port in small-diameter clean PVC sewer pipes and PVC pipescoated with a biological film.

Research Approach

The research project reported herein was developed at the pilot-

scale sanitary sewers installed in the Hydraulics Laboratory at the

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University of New Orleans, La. Preliminary work was carried outusing opaque PVC pipes �Betancourt 2001; Colmenares 2001�.Difficulties associated with imperfect pipe alignment and pipedeflection between supports led to inconsistent results. To elimi-nate these problems and to minimize uncertainties associated withflow regimes in subsequent research, it was decided to use clearPVC pipes so that the actual flow behavior and the growth of thebiological film inside the pipe could be observed. Two pipe diam-eters were used �150 and 200 mm�.

System Description

The equipment used to conduct this research project consists of amultipurpose tilting flume 0.61 m wide, 0.91 m deep, and21.95 m long with a PVC pipe installed inside. The tilting flumeis made of stainless steel with Plexiglas walls. Two storage tanksare located at each end of the flume, one upstream and one down-stream. An extra 1.89 m3 storage tank was interconnected withthe pumps and the flume to store extra water to start the system. A150-mm PVC pipe under the flume was used to convey the waterfrom the pumps to the upstream head tank. Acoustic sensors wereattached to the supply pipe and also to the digital Controlotronflow meter �Model 1010WP� used to measure the flow. Two PricePump Company pumps, Model RC300AI, of 2.24 kW, with acapacity of 1,635 m3/d were connected to the downstream end topump water into the system. The pumps were equipped with abutterfly valve for flow control.

A 13-m long, 200-mm diameter opaque PVC was connectedpermanently by a flange to the head tank. A 9.14-m long, 200-mmclear PVC Schedule 40 test pipe was connected to the permanentPVC pipe using a rubber coupling; this was the testing pipe.Opaque PVC collar connections were used between the three seg-ments of the test pipe to provide rigidity. The experimental PVCclear Schedule 40 pipe was placed on wooden beams that weresupported on scissor jacks riveted with steel plates to avoid pipedeflection. After completion of the tests with the 200-mm PVCpipe, a 17.68-m long, 150-mm clear PVC replaced the wholesystem. Opaque connections were used between the six segmentsof the new pipe. The same support method used for the 200-mmPVC pipe was implemented for the 150-mm PVC pipe setup.

Piezometer taps were installed along the invert of the clearpipe. Transparent tubing was connected to the taps and also tomanometer board tubes that were attached to the flume wall nextto stainless-steel scales marked in mm. A total of nine taps wereused to measure the water level in the 200-mm PVC testing pipeand 17 taps in the 150-mm clear PVC pipe. The first tap wasplaced at 0.61 m from the beginning of the test pipe, the othertaps were located at 0.91 m intervals. Fig. 1 shows the experi-

Fig. 1. Sketch of the system and its components

mental setup.

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Experimental Approach

The general experimental approach was as follows: �1� the fric-tion properties of each pipe were measured without biofilm�clean�; �2� the grit transport tests for each pipe without biofilmwere performed; �3� the friction tests were repeated for each pipewith biofilm present; and �4� the grit tests were repeated with abiofilm present. The test program is summarized in Table 1.

Determination of Manning’s n Coefficient, Self-CleansingVelocity, and Shear StressThe following experimental data were recorded during each runof the system: flow rate, water temperature, piezometric readingat each tap, and pipe slope �fixed at the beginning of each run�. Todetermine the self-cleansing velocity and shear stress, experi-ments were performed by injecting sand for different shear stressconditions.

Both a tracer procedure �using a NaCl solution� and the ultra-sonic flow meter were used to determine the flow rate. The flowrates by the two methods were compared to confirm or correct theflow readings obtained. At low flow rates the ultrasonic flowmeter gave inaccurate readings, so the tracer test results wereadopted. The water temperature and conductivity were measuredusing a Jenway conductivity/temperature meter Model 4150 be-fore each run. Temperature was used to determine the respectivevalue of water viscosity and also to make sure the temperature didnot increase to undesirable values that could affect the biologicalfilm.

For each flow, the piezometric levels corresponding to thewater surface elevation in the pipe at each tap were read to thenearest 0.5 mm using an automatic surveyor’s level �Topconmodel AT-G2�. Before making the readings, the air waspurged from the piezometers by backwashing them through themanometer board tubes.

Table 1 summarizes the test program. The 200-mm PVC test-ing pipe was evaluated using slopes of 0.1 and 0.5% slope forclean pipe. After biological film was developed, the same pipe

Table 1. Testing Program

Series

Pipediameter

�mm�Slope�%� Surface Grit

Numberof runs

A-I 200 0.1 Clean PVC No 44

A-2 200 0.5 Clean PVC No 6

B-1 200 0.1 Biofilm No 20

B-2 200 0.5 Biofilm No 46

Cool 200 0.1 Clean PVC Yes 6

C-2 200 0.5 Clean PVC Yes Supercritical

D-1 200 0.1 Biofilm Yes 13

D-2 200 0.5 Biofilm Yes Supercritical

E-1 150 0.1 Clean PVC No 26

E-2 150 0.3 Clean PVC No 26

E-3 150 0.5 Clean PVC No 26

Fool 150 0.1 Biofilm No 11

F-2 150 0.3 Biofilm No 9

G-1 150 0.1 Clean PVC Yes 7

G-2 150 0.3 Clean PVC Yes 7

G-3 150 0.5 Clean PVC Yes 9

H-1 150 0.1 Biofilm Yes 2

H-2 150 0.3 Biofilm Yes 6

was evaluated at the same slopes, namely, 0.1 and 0.5%. Simi-

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larly, the 150-mm clear PVC pipe without film was evaluated atthree different slopes, namely, 0.1, 0.3, and 0.5%. Slopes greaterthan 0.5% were not considered since the results obtained in pre-vious experiments showed that the flow was supercritical. Slopesless than 0.1% were not considered because the self-cleansingcapacity was very low at these flat slopes.

As indicated in Table 2, Betancourt �2001� found that the LakePontchartrain beach sand has similar particle-size distribution tothe sewer grit removed from two different municipal locations�Bridge City Wastewater Treatment Plant in Jefferson Parish, La.,and East Bank Wastewater Treatment Plant in New Orleans, La.�.Therefore, Lake Pontchartrain beach sand was used in the experi-ments reported herein.

To conduct the sediment transport experiment, a 5-cm holewas cut at 0.91 m from the beginning of the 200-mm PVC testpipe, and at 0.61 m from the beginning of the 150-mm PVC pipeto inject the sand necessary for the test.

In every run, a sample of 100 g of sand was introduced and thetime of injection was recorded. The system was run for 1 h toprovide adequate opportunity for grit transport. While the systemwas running, the piezometers were flushed at approximately15 min intervals to avoid the entrapment of sand in the taps. Afterthat, the flow was shut off and the pipe was allowed to drainslowly. Then, the pipe was flushed with a Karcher electric pres-sure washer Model K240 �1,300 psi� to remove all the sand thathad settled on the bottom of the pipe. All of the flushed effluentwas passed through a No. 60 or finer sieve at the end of the testpipe to capture all the sediment. The collected sample was ovendried to determine the mass retained on the respective sieve.When the pipe was covered with biofilm, the pressure washerremoved the biofilm, and the mass collected at the sieve wascomposed of the sand remaining in the pipe and all the organicmatter washed. To determine the mass of sand collected in thesample, the sieve was first dried at 105°C for at least 2 h, and thedried solids were inserted in a muffle furnace at a temperature of550°C to ignite the organic matter. Finally, the mass of the sandwas measured, and then the mass of the transported sand wascalculated. This experiment was repeated several times at variousflow rates and shear stresses until a flow condition was reachedwhere at least 90% of the sediment was transported during the 1 htest. At least 1 week was required between runs to allow forbiological film regeneration on the wetted pipe surface.

Spreadsheets were developed to process all the data as theywere collected in the experiments; this permitted some qualitycontrol while the experiments were in progress. These spread-sheets automatically calculate the values of the water depth, area,wetted perimeter, hydraulic radius, top width, mean depth, Froudenumber, Reynolds number, velocity, total energy line, frictionslope, Manning’s roughness coefficient n, and finally, shear stress.In addition, graphs of the water depth and the total energy line foreach flow were plotted to check the consistency of the piezometerreadings. The gradually varied flow concept was used to treat

Table 2. Particle-Size Distributions of Actual Municipal Grit and BeachSand Used in the Experiments

NumberMunicipal grit

�mm�Beach sand

�mm�

D16 0.15 0.13

D50 0.20 0.25

D84 0.42 0.38

small changes in the water surface slope. The energy equation

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was written for a subreach defined between successive test sec-tions with the friction slope represented by the velocity and depthat the initial and final sections of each subreach. The roughnesscoefficient n was solved from the resulting equation.

Biological Film DevelopmentTo maintain an aerobic biological film in the test pipe an airdiffuser was installed in the bottom of the head tank. The air wassupplied by a compressor. Similarly, air was supplied to the stor-age tanks to avoid odors. Carbon filters were attached to the tapwater to remove any residual chlorine from the drinking waterused to fill the system. To maintain an active biological film at-tached to the pipe wall, a substrate was added to the head tank.The substrates used were methanol �CH3OH� and glucose. Theconcentration of the substrate in the system was approximately800 mg COD/L. Total chemical oxygen demand �COD� testswere performed to monitor substrate concentration and consump-tion. Total suspended solids and volatile suspended solids testswere performed to determine if the consumption of the substratewas due to the biological film or to suspended bacteria. Every twoweeks the system water was replaced with fresh water tominimize growth of suspended bacteria and to prevent the watertemperature from exceeding 28°C. The system was operated con-tinuously with the addition of the substrate for 45 days until asignificant biological film development was observed on the pipewall.

Results

This section presents the results of several experiments that wererun to determine the Manning’s n coefficient, self-cleansing ve-locity, and critical shear stress for self-cleaning in clear PVC pipewith and without biofilms.

Manning’s n Coefficient

Results Using 200-mm SDR 40 PVC Pipe, 0.1% Slope,with and without Biological FilmWith a 200-mm SDR 40 PVC pipe coated with a biological filmand laid on a slope of 0.1%, the predominant flow regime wasfound to be subcritical, corresponding to Froude number valuesbetween 0.20 and 0.60. Fig. 2 includes the values of Manning’s nin the same PVC pipe with and without biofilm. It can be ob-served that without biofilm the average roughness coefficient was0.011, and Manning’s n did not show a clear dependence on rela-tive depth although the ratio of computed roughness coefficient tothat corresponding to the pipe running full, n /nf, fell in a similarrange �1–1.3� to that found by Camp �1940�.

Fig. 2 also illustrates a range of values of n observed withbiofilm �between 0.014 and 0.043�, corresponding to relativedepths between 0.18 and 0.97. There is an inverse relationshipbetween Manning’s n and the relative depth. These data weregathered from Day 34 to Day 40, and correspond to different filmthicknesses, and demonstrate that in these tests there was no de-tectable effect of biological film age on the average value of n.These observations on the effect of biofilm on the roughness co-efficient differ significantly from those made by Bishop and Jepp-son �1975� who, after performing field measurements of theroughness coefficient in 200-mm PVC sanitary sewers that hadbeen in operation for 4–5 years, reported n values ranging from

0.0079 to 0.0097, with an average of 0.0088. Based on the obser-

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vations reported herein, the low magnitude of the values pre-sented by Bishop and Jeppson �1975� would seem to indicate thatthere was no significant biofilm development in those sewers.

Fig. 2 also includes the values of n when sand was added tosimulate what happens in real sewers. After the sand was intro-duced, a portion of it was scattered and attached to the biologicalfilm and another portion accumulated forming small mounds atseveral pipe locations. Surprisingly, the values of n did notchange with respect to those corresponding to the pipe coatedwith biofilm only.

DataFit version 8.0.32 was used to generate a best-fit functionto predict Manning’s n coefficient as a function of the Reynoldsnumber, NR as follows:

n = 0.477NR−0.3183 �1�

with R2=0.915, as shown in Fig. 3. In Eq. 1

NR = VRh/� �2�

where Rh�hydraulic radius; ��kinematic viscosity; andV=Q /A.

Eq. 1 has theoretical support, since n=Rh1/6�f /8g�1/2, which

shows that n�function of the friction factor, f , and the pipe hy-

Fig. 2. Comparison of Manning’s n coefficient with and withoutbiological film for 0.1% slope, d0=200 mm. “With biofilm aftersand application” means that sand was injected to the pipe andimmediately Manning’s n values were measured. “Biofilm anddeposited sand” means that the n values were measured after thesystem was running for several hours.

Fig. 3. Manning’s n coefficient versus Reynolds number with biofilmfor 0.1 and 0.5% slopes, d0=200 mm

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draulic radius. Since, f is a function of the inverse of theReynolds number, NR �e.g., the Blasius Eq. f �0.223/NR

1/4�, andrelative pipe roughness, it can be concluded that n should be afunction of the Reynolds number, NR. However, Eq. �1� shows astronger dependency on the Reynolds number than the theorywould support, which is probably because the relative roughnessdue to the biofilm increases as the flow depth and Reynolds num-ber decrease.

Results Using 200-mm SDR 40 PVC Pipe, 0.5% Slope,with Biological FilmWhen the slope was increased to 0.5%, the majority of the pointshad a Froude number �1, indicating supercritical flow condi-tions. Fig. 4 illustrates the effect of biological film on the Man-ning’s n coefficient. It can be seen that in the early stages ofbiofilm development, the value of n was not affected by the pres-ence of film. Then, as the biological film grew and covered moreof the wet pipe surface, Manning’s n increased to between 0.015and 0.020. There is a clear effect of biofilm on increasing theroughness coefficient. For supercritical and transitional flow con-ditions, with an undulating liquid surface, a significant scatteringof the data was observed. As a result, no best-fit function is pro-posed to predict n. The n values and observations of the patchynature of the film indicated that there was periodic shearing andsloughing of the biofilm under the higher shear stresses associatedwith the steeper slope.

Fig. 3 presents a summary of the experimental data showingthe effect of biological film on the Manning’s n coefficient basedon the Reynolds number at different slopes, namely, 0.1 and0.5%. The critical values of n that should be used for small-diameter PVC sewer design clearly exceed the clean pipe values.

Results Using 150-mm SDR 40 PVC Pipe, 0.1, 0.3, and 0.5%Slope, Clean SurfaceThe results corresponding to 28 different ratios of depth using150-mm SDR 40 PVC pipe laid at slopes of 0.1, 0.3, and 0.5%,without biofilm, are presented in Fig. 5. For the 0.1% slope, theaverage value of the roughness coefficient was calculated to be0.0096, with individual values ranging from 0.0086 to 0.0104 atrelative depths ranging from 0.1641 to 1. No strong dependencyof n on relative depth can be detected. For the 0.3% slope, theaverage value of the roughness coefficient was calculated to be0.0093, with individual values ranging from 0.0089 to 0.0098 atrelative depths ranging from 0.133 to 1. For the 0.5% slope, the

Fig. 4. Manning’s n calculated at different ratios of depth with film atdifferent ages and without biofilm for 0.5% slope, d0=200 mm

same procedures with slopes of 0.1 and 0.3% were carried out.

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The Manning’s n values obtained can be seen in Fig. 5 as well.For this slope, the average value of the roughness coefficient wascalculated to be 0.0089, with individual values ranging from0.0084 to 0.0099 at relative depth ratios ranging from 0.1281 to0.9755. From Fig. 5 it is clear that the values obtained with slopesof 0.1, 0.3, and 0.5% are very similar and nearly constant. There-fore, it can be concluded that when the pipe is clean within therange of this experiment there is no dependency of the roughnesscoefficient on the slope or relative depths of flow. It is noted thatthe full pipe n based on a hydraulic smooth surface is approxi-mately 0.0076, which suggests that the pipe used in this test wasnot hydraulically smooth. The Manning’s n for the 150-mm pipetended to be less than for the 200-mm pipe, which suggests thatthe 150-mm pipe had a lower relative roughness. The n versusy /d0 relationship does not follow the Camp curve, although theratio n /nf is in range 1–1.27. No correlation between n and y /d0

can be detected because of the scatter in the data. These resultssupport the conclusion that for fully turbulent subcritical flow inclean PVC pipes the roughness coefficient can be assumed to benearly constant, around 0.01.

Results Using 150-mm SDR 40 PVC Pipe, 0.1%, 0.3% Slopewith Biological FilmThe same method and procedures used with the 200-mm PVCpipe covered with biological film were repeated with the 150-mmPVC pipe with film. Fig. 6 illustrates a range of values of nbetween 0.0134 and 0.0185, corresponding to relative depths be-tween 0.84 and 0.18. It can be seen that although the value ofManning’s n coefficient increases with decreasing depth, thisvariation is not as large as the one observed in the case of the200-mm pipe, in which the n values ranged from 0.014 to 0.043.A possible reason for this is that the effective roughness intro-duced by the biofilm was less in the 150-mm pipe than in the200-mm pipe. It is noted that the n values for the 150-mm pipewithout biofilm were also less than the corresponding value forthe 200-mm pipe.

Determination of Self-Cleansing Velocity and CriticalShear Stress

Fig. 7 summarizes the values of the percent of sand transportedwithin 60 min after injection, as a function of fluid velocity forthree different slopes �0.1, 0.3, and 0.5%�, with and without bio-logical film on the pipe surface, for two pipe diameters, 150 and200 mm. It can be seen that in order to transport at least 90% of

Fig. 5. Manning’s n calculated at different ratios of depth withoutbiofilm for 0.1, 0.3, and 0.5% slopes, d0=150 mm

the sand in pipes with biofilm coating their inner surface, the

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minimum fluid velocity should be around 0.55 m/s, whereasclean pipes require lower velocities, around 0.45 m/s to transport90% of the sand. The same chart reveals that some depositionoccurs at fluid velocities as high as 0.86 m/s regardless ofwhether there is biofilm or not coating the inner pipe surface.

Fig. 8 shows the shear stress needed versus percent of sandtransported within 60 min after the injection. It can be seen thatthe minimum shear stress necessary to transport at least 90% ofthe sand is between 1.1 and 1.4 N/m2. Without biofilm, values ofshear stress and critical shear stresses were in the range of0.4–0.55 N/m2 to transport 90% of the sand. The shear stresswas calculated using Eqs. �5� and �7� presented below.

Proposed Design Criteria for Small-Diameter PVCSewers Laid on Minimum Slopes

Published design criteria for critical shear stress in sanitary sew-ers vary significantly. Based on the experimental observationspresented herein, applicable to PVC pipe diameters of 150 and200 mm laid at slopes between 0.1 and 0.3%, a reasonable designalternative consists of assuming that the shear stress to transportparticles of a given size is independent of slope and pipe diam-

Fig. 6. Manning’s n calculated at different ratio of depths withbiofilm on 0.1 and 0.3% slopes, d0=150 mm

Fig. 7. Percent of sand transported versus velocity with and withoutbiofilm for 0.1, 0.3, and 0.5% slopes, d0=200 and 150 mm

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eter, and would only depend on the increased value of the rough-ness coefficient due to the biological film growing attached to thepipe surface.

Basic Equations

To ensure self-cleansing, the shear stress generated under thesewer operating conditions should be equal to or exceed the criti-cal shear stress needed to carry particles of given characteristics.Therefore, the basic design criterion is the following:

�0 � �c �3�

where �0�shear stress for specific pipe diameter, depth of flow,and slope; and �c�critical shear stress needed to carry a certaingrain size, e.g., at least 90% of the sediments �D90�, obtainedthrough experimental observations.

The Shields–White equation �Graf 1971� for critical shearstress is

�c = Cs��Ss − 1�D �4�

where ��specific weight of water at the prevailing temperature;Cs�Shields-White coefficient; Ss�specific gravity of the sedi-ment particles; and D�particle diameter. If �c has been deter-mined experimentally, then Cs can be computed as

Cs =�c

��Ss − 1�D�5�

These coefficients were determined for D=D90=0.4 mm for thecase of PVC pipes with and without biofilm and are presented inTable 3.

Manning’s equation can be expressed as follows:

Table 3. Summary of Critical Shear Stresses �D90=0.4 mm� Applicableto 150- and 200-mm PVC Sewer Pipes

MeasurementCleanPVC

Biofilm-coatedPVC

� �Pa� 0.4–0.55 1.1–1.4

Uncertainty �Pa� 0.075 0.15

Uncertainty % 15 15

V self-cleaning m/s 0.45 0.55

Shields–White coefficient 0.062–0.085 0.17–0.22

Fig. 8. Percent of sand transported versus shear stress with andwithout biofilm for 0.1, 0.3, and 0.5% slopes, d0=200 and 150 mm

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Q =A · Rh

2/3 · S1/2

n�6�

in which Q�mean flow; Rh�hydraulic radius; S�slope; andn�coefficient of roughness.

The shear stress is given by �Fair et al. 1968�

�0 = � · Rh · S �7�

If the central angle defined by the liquid surface in a circular pipeis defined by

� = 2 arccos�1 −2y

d0� �8�

the wet area, A, and the hydraulic radius, Rh, can be expressed interms of the depth of flow �through Eq. �8�� as follows �Fair et al.1968�:

A = �2� − sin ���d02

8� �9�

Rh =�� − sin ��d0

4��10�

The Reynolds number can also be expressed as a function ofthe flow velocity and the hydraulic radius by

Nr = VRh/� �2��

The data generated in this research suggest that Eq. �1� can beused to predict the effect of the biological film growth on theroughness coefficient of 200-mm PVC sewers under subcriticalflow conditions

n = 0.477 · Nr−0.3183 �n � 0.013� �1��

Combining Eqs. �3�, �7�, and �10�, and solving for the slope yields

S �

�c��

2�

�d0�� − sin ���11�

To design sanitary sewer pipes, the peak wastewater flow�PWWF� at the end of the design period and the average dailywastewater flow �ADWWF� at the beginning of the design periodshould be known. The PWWF is used to determine the value ofthe pipe diameter whereas the minimum, self-cleansing slope isdetermined using the ADWWF.

Some design parameters must be assumed. For instance, themaximum value of y /d0 can be assumed to vary between 0.75 and0.8. According to results obtained earlier, the critical shear stressthat should be used for designing small-diameter PVC sewers, toprevent significant solids deposition, is 1.4 N/m2. Table 3 sum-marizes the most probable critical shear values from this studyand generalizes the results in the form of a Shields–White coef-ficient, Cs, that can be used with Eq. �4� to determine the criticalshear for grit with different Ss or D.

Procedure for Small-Diameter PVC Sewer Designunder Subcritical Flow Conditions

1. Select the pipe diameter and calculate a tentative slope usingthe peak flow at the end of the design period. This design

flow rate is given by the sum of the following flows:

370 / JOURNAL OF ENVIRONMENTAL ENGINEERING © ASCE / APRIL 200

• Peak sanitary flow at the end of the design period�average domestic flow rate � peaking factor;

• Peak infiltration flow; and• Allowance for illicit storm water connections.

The assumption usually made is that the pipe will flow atthe maximum value of y /d0 under this flow rate; Eq. �6� willbe used using the roughness coefficient observed at the maxi-mum depth of flow.

2. Check if the slope calculated in Step 1 is sufficient to provideself-cleansing conditions at the beginning of the design pe-riod. The flow rate to be used in this case is the averagedomestic sewage flow rate at the beginning of the designperiod �no infiltration�. This flow �minimum flow rate� issignificantly smaller that the peak flow rate. The procedurewould be the following:• The depth of flow can be found by combining Eqs. �6�

and �10�, using the minimum flow rate, the slope calcu-lated in Step 1, and a roughness coefficient expressed as afunction of the depth of flow �Eq. �1�� or NR �Eq. �2��.

• This depth of flow can be used to find the shear stressthrough Eq. �7�.

• Find the shear stress for the specific site using Eq. �4�with the grit characteristics and Cs in Table 3; the higherlimit of Cs is recommended.

• If the shear stress is greater that the critical shear stress�Eq. �4��, accept the slope as the design slope.

• If the shear stress is less than the critical shear stress,calculate the new slope with Eq. �11�. Since changingthe slope will change the depth of flow, calculate thenew depth of flow using Eqs. �6� and �9�, and repeat theprocedure until the selected slope provides a shear stress�0��c.

• Calculate the Manning’s coefficient based on the Rey-nolds number from Eq. �1� for maximum and minimumflow.

Conclusions

The following conclusions can be drawn from the research de-scribed in this paper:1. For clean 150- to 200-mm PVC pipes, the average value

of Manning’s roughness coefficient is around 0.01, and itwas found to be independent of water depth, slope, and pipediameter.

2. The development of a biological film on the internal surfaceof a sewer pipe significantly affects the roughness coeffi-cient. In the experiments performed herein, the followingexpression provided good statistical correlation for the upperenvelop of n for 200-mm PVC pipes with biofilm under sub-critical flow conditions:

n = 0.477NR−0.318

3. Considering that actual sanitary PVC sewer pipes are mostlikely covered with biological film, design recommendationscommonly found in the literature regarding the value of n�i.e., n=0.013�, can significantly underestimate the trueroughness coefficient. Thus, if the depth of flow is less than50% of the pipe diameter, the design value of n could belarger than 0.02.

4. For small-diameter PVC pipes, covered with biofilm, andflowing partially full, the minimum velocity to carry 90% of

sand is around 0.55 m/s.

7

5. For small-diameter PVC pipes coated with biofilm, the mini-mum shear stress to carry 90% of sand is around 1.4 N/m2

and the Shields–White coefficient CS=0.2 N/m2. For therange of slopes studied, between 0.1 and 0.5%, and for thepipe diameters used in this research �150 and 200 mm�, theshear stress required to move particles of a given size isindependent of slope and pipe diameter.

6. The design criteria suggested several decades ago by ASCEManual 60 �ASCE 1982� and by Fair et al. �1968�, whichyield different values of the minimum self-cleansing shearstress, depending on the pipe diameter and slope, are notsupported by the experimental data reported in this paper.The design approach outlined herein, which is applicable tosmall-diameter PVC sewer pipes, is more realistic.

Acknowledgments

This research was supported by the University of New OrleansSchlieder Urban Environmental Systems Center through an EPAGrant. The writers would like to acknowledge the contribution ofM. J. Pujol of the University of La Plata, Argentina, and of theother research team members: Juan C. Josse, Freddy Betancourt,and Pablo Colmenares.

Notation

The following symbols are used in this paper:A � wet area;

Cs � Shields–White coefficient;D � particle diameter;d0 � inside pipe diameter;

f � Darcy–Weisbach friction factor;NR � Reynolds number;

n � Manning’s coefficient;Q � mean flow rate;Rh � hydraulic radius;S � pipe slope;

Ss � specific gravity of the sediment particles;V � fluid velocity, computed as the ratio Q /Ay � depth of flow.� � specific weight of water at the prevailing temperature;� � central angle to the liquid surface;� � kinematic viscosity;

�0 � shear stress for specific pipe diameter, depth of flow,and slope; and

�c � critical shear stress needed to carry a certain grain size,obtained through experimental observations.

JOURNA

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