wastewater hydraulics || design of sewers

Chapter 3Design of Sewers

Abstract Sewer design in practice is of fundamental significance because thedimensions of sewer systems are specified. Two particular discharges are consid-ered, namely, the minimum and the maximum discharges. The minimum dischargeinfluences the channel slope and therefore the depositional behaviour, whereasthe maximum discharge establishes the sewer dimensions. A design is flexible ifthe minimum and the maximum discharges are close. The circumstances howeverbecome more difficult for large differences between the two extreme discharges. Atthe end of this chapter, the optimum cross-sectional sewer shape is also discussed.

3.1 Introduction

The design of sewers is of paramount importance. Usually the design procedure tobe formulated must be simple and explicit. Calculations must include at least theextreme discharges.

For the maximum discharge (Sect. 3.2) the conveyance capacity of a par-ticular sewer reach for uniform flow must be ascertained. Then, the numericalcalculation for the flowing full condition becomes simple. Normally, the circularcross-section is considered. Because the design does not account for the flow types,uniform flow (Chap. 5) is taken into consideration for the selection of the sewer,and abrupt changes of bottom slope, sewer diameter and discharge are avoided.Computations of backwater and drawdown curves (Chap. 8) involving a significantflow acceleration or flow deceleration indicate that the capacity of a sewer reach isguaranteed.

For the minimum discharge, problems arise for solid transport. It must conse-quently be pointed out that particularly for large ratios of maximum to minimumdischarges, the tractive force necessary for the transport of solids in the sewer ismobilised. In Sect. 3.3 various procedures are outlined first and two proposals arerecommended. Common to both approaches is the concept of minimum wall shearstress which increases the minimum velocity as the sewer diameter increases.

55W.H. Hager, Wastewater Hydraulics, 2nd ed., DOI 10.1007/978-3-642-11383-3_3,C© Springer-Verlag Berlin Heidelberg 2010

56 3 Design of Sewers

Even today the effects of sewer abrasion and sewer aging are evaluated only inexceptional cases. Both aspects cannot be treated in a generalized manner but mustbe analyzed from local data. Although maximum allowable velocities up to about5 ms−1 may be adopted according to Pfeiff (1960), steep sewers with velocities upto 15 ms−1 are in service without any lasting effect due to abrasion.

3.2 Maximum Discharge

3.2.1 Flowing Full Condition

The basis of sewer design is the ‘flowing full’ condition, the state of transitionbetween the free-surface and the pressurized flow. As explained in Chap. 5, this sur-charge free condition is not realized in experiments. Because about 85% part-fullflow corresponds to the full flow discharge, the ‘flowing full’ condition is physicallyset at around 85% part-full stage.

The flowing full condition (subscript v) is distinguished from the part-full flowby its simple geometry. For the common circular cross-section, the cross-sectionalarea is Fv = (π/4)D2, where D is the pipe diameter, Pv = πD the wetted perimeterand Rhv = Fv/Pv = D/4 the hydraulic radius (Chap. 5). Using the resistance law ofColebrook and White (Chap. 2), the relative discharge qr = Qv/(SEgD5)1/2 obtains

qr = − π√2

log

[2.51v

(2gSED3)1/2+ ks

3.71D

]. (3.1)

Here ν is the kinematic viscosity, g acceleration due to gravity, SE the energy lineslope and ks the equivalent sand-roughness height. Eq. (3.1) can be rewritten as

qr = − π√2

log[1.77qrR−1

r + 0.27κs

]. (3.2)

Consequently, the relative discharge qr depends on the diameter Reynolds numberRr = Q/(νD) and on the relative roughness height κs = ks/D. The Reynolds numberreflects the influence of viscosity and the relative sand-roughness height accountsfor the sewer surface boundary material.

The viscosity ν for pure water varies essentially with the sewage temperatureTs. The values adopted by ATV (1988) are reproduced in Table 3.1. Normally theestimated value ν = 1.31×10−6 m2s−1 is taken for sewers. This includes the usuallyhigher sewage temperature and the presence of sewage instead of pure water.

Table 3.1 Kinematic viscosity ν for pure water as a function of sewage temperature Ts

Ts [◦C] 5 10 15 20 25 30ν·106 [m2s−1] 1.52 1.31 1.15 1.01 0.90 0.80

3.2 Maximum Discharge 57

Equation (3.1) involves six parameters, namely, Qv, SE, g, D, ν and ks. If fiveof these are given, the sixth can be determined. In the design procedure for thediameter, D appears in all three relative parameters qr, Rr and κs of Eq. (3.2). Ifthe energy slope SE equals the bed slope So, the corresponding flow is uniform(Chap. 5). As described in Sect. 2.2, the diameter can then be determined closelywith an explicit formulation. Further details on computational procedures are alsopresented in Chap. 5.

3.2.2 Operative Roughness

Whether the equivalent roughness is known exactly or not depends on whether theinfluence of viscosity or of the relative roughness is dominant (Chap. 2). If the effectof viscosity dominates, as in the smooth turbulent flow regime, one does not needto know the exact value of the equivalent sand roughness height ks. If, however,the flow is in the rough turbulent regime for which the effect of viscosity becomesnegligible, exact information on the equivalent sand roughness has to be available inadvance. For the transition regime which often is determining in sewer design, theknowledge of the equivalent sand roughness ks is naturally important.

The wall friction due to fluid viscosity and roughness of boundary material makesup an important part of the energy transfer in sewer flow. Other influences have alsoto be taken into account. There is an additional loss, as discussed in Chap. 2, result-ing from non-prismatic sewer reaches. According to the energy principle, the energylosses are, in calculation, additive to a comprehensive loss coefficient in which thefriction and all other individual losses are taken into account. Conversely, one cancombine all the individual losses with the friction loss and obtain a mean higherroughness, the so-called operative roughness kb (German: Betriebliche Rauheit;French: Rugosité opérationelle) to give the total energy loss. By this model re-presentation the individual losses are differently expressed and distributed overthe entire calculation reach and retained by a representative mean value. The con-cept of operative roughness (ATV 1988; Howe 1989) has the advantage to lumpthe loss effects, and the necessity to specify detailed information on individualeffects is avoided. It has, however, the disadvantage that for long nearly prismaticsewers, higher losses are accounted for not always corresponding to hydrauli-cally economic solutions, therefore. On the whole, the effort required for workingout the individual information may be offset by the increased cost of conduitmaterial.

The operative roughness kb contains the following influences (ATV 1988):

• Wall roughness,• Inexact and altered layout,• Conduit joints,• Shape of inlet transition, and• Manhole structures.


For standard sewers the operative roughness height is ks = 0.1 mm for the effectivewall roughness, including the operational conditions of the sewer system againstthe original new conduit conditions. This lumped value does not contain theinfluences of:

• Reduction of nominal width,• Combining flow in junction manholes, and• Inlet and outlet structures of throttle conduits, pressurized conduit flows and

inverted siphons.

Reductions of the nominal diameter are to be estimated, according to ATV (1988),from the effective mean discharge measurement. Small amounts of reduction canbe ignored. The evaluation of performance, however, has to be carried out withbasically 95% of the nominal diameter provided the actual effective diameter cannotbe ascertained individually.

With regard to junction structures (Chap. 16), the losses are to be individuallyestimated. According to ATV (1988) the proof can be renounced in case either abottom drop of height D/20 is built on the channel floor or the discharge in thedownstream sewer is limited to 85% instead of 90% of the flowing full discharge,as mentioned in Sect. 3.2.1.

Deviations from these prescribed values for the lumping concept is permitted bythe kb values presented in Table 3.2 in the form of an individual design concept.The respective losses due to the equivalent wall roughness ks and the individuallyarising losses are assigned in proportion of their contributions with a lower limitvalue of ks ≥ 0.1 mm. Changes from the original conditions are to be taken intoaccount. ATV (1988) recommends the lumping concept both for the size determi-nation and the discharge capacity estimation using the kb values listed for standardsewers. This procedure is to be considered as the normal case and further referenceto individual items is not required. For non-standard sewers described in Chap. 6 andin-situ concrete channels without specific information, the effective wall roughnesscorresponds to the operative wall roughness kb = 1.5 mm.

Table 3.2 Lumped values for the operative roughness kb [mm] after ATV (1988)

Application kb [mm]

Conduit throttle,a Pressure conduit,a,b Inverted siphonsa and relined reaches(re-inspected) without manholes

0.25

Conveyance sewers with manholes 0.50Intercepting sewers and pipelines with manholes, likewise with unformed

manholes as also conveyance sewers with special manholes0.75

Intercepting channels and pipelines with special manholes, masonry channels,in-situ concrete channels, sewers of non-standard conduits without specificinformation about roughness

1.50

aWithout outlet and bend losses, bwithout pressurized network

3.3 Minimum Discharge 59

3.3 Minimum Discharge

3.3.1 Design Considerations

Vicari (1916) suggested that two conditions must be satisfied for the minimum(subscript m) discharge Qm in sewers:

• Minimum flow depth hm = 3 cm and• Minimum tractive force Sm = 2.5 N/m2.

It is from these considerations that the required maximum diameter is calculated.Ackers et al. (1964) conducted an extensive study of aging of sewers. Their most

essential conclusions were:

• The sewer coating development varies strongly with the condition and thematerial content of the sewage. The coating develops rapidly to an end thickness,

• For higher velocities but otherwise similar conditions, the sewer coating is thinnerthan for lower velocities,

• For sewer coating thicknesses smaller than 3 mm, the same resistance as fornew conduits may be adopted. Beyond this limit thickness, the resistance effectincreases sharply,

• Sewers whose inverts are covered with gravel and which carry discharges withFroude numbers of about 0.5 develop standing waves leading to considerablyhigher resistance,

• The recommended equivalent roughness height amounts to ks = 1.5 mm for sewercoatings smaller than 5 mm thick in normal condition, for good condition ks =0.5 mm, and for bad condition ks = 3 mm. These values become as high as about25 mm for crusted conditions and even about ten times higher for sewers withgravel deposition.

According to Smith (1965) a sewer should pass the maximum discharge safely aswell as maintain self-cleansing for the minimum discharge. His design procedure isbased on a minimum velocity.

3.3.2 Yao’s Procedure

According to Yao (1974) the minimum sewer velocity depends on the characteristicsof the flow boundary surface, the deposited material and the depth of flow. The con-cept of minimum velocity is replaced by the concept of minimum wall shear stress.

In order that a particle in the lower zone of the cross-section settles, the angleof inclination is to be smaller than the angle of repose of the particle material.According to Lysne (1969) the average natural angle of repose may be taken as35◦ which would cause deposition below the 10% part-full depth in a circularcross-section.


The mean shear stress τo for uniform flow in open channels is

τo = ρgRhSo (3.3)

with ρ as fluid density, g as gravitational acceleration, Rh as hydraulic radius and So

as bottom slope. The local boundary shear stress τ varies along the perimeter, fromthe maximum at the invert to the minimum at the free surface. For sewers with asmall filling ratio, the effect of the variation in the value of τ is negligible.

The minimum shear stress τom relates to the initiation of motion and is estimatedfor sand from Shields’ diagram (Graf 1971, Raudkivi 1993). Yao recommends inseparate sewer systems for particles of diameters from 0.2 mm to 1 mm a minimumbed shear stress τom = 1 to 2 N/m2. For combined sewer systems, values between 3and 4 N/m2 are mandatory. Applying the formula of Manning and Strickler with K =1/n as the roughness coefficient then gives, for the full flowing sewer (subscript v),

Qv = 0.62(1/n)(τo/ρ)1/2D13/6. (3.4)

A comparison of the concepts of constant minimum velocity Vm and the constantbottom shear stress results, for a particular value of Vm, in smaller self-cleansing forlarger sewer diameters.

Equation (3.3) can also be expressed as a relationship between the bottom slopeSo, the sewer diameter D and the bottom shear stress τo as

So = τo/(ρD). (3.5)

For constant value of τ o/ρ, the larger the diameter the smaller is the bottom sloperequired. A relationship between the flowing full velocity Vv, the sewer diameter Dand the bottom shear stress (τ o/ρ) obtains as

Vv

(1/n)D1/6(τo /ρ)1/2= 0.79. (3.6)

Example 3.1 What is the minimum velocity in a 500 mm sewer, for 1/n =85 m1/3s−1, if a minimum bed shear stress of 2 N/m2 must be guaranteed atthe flowing full stage?From Eq. (3.6) follows Vv = 0.79·85·0.51/6(0.2/1000)1/2 = 0.85 ms−1. Thecorresponding discharge is Qv = 0.85 (π/4)0.52 = 0.167 m3s−1.

For part-full discharge (subscript t) the hydraulic radius must be used andaccording to Eq. (3.3), the part-full velocity is

Vt = 1/n(τo/ρ)1/2R1/6h . (3.7)

3.3 Minimum Discharge 61

For small part-full conditions defined by y = h/D < 1/2, the relation

Rh/D = 2

3y

(1 − 1

2y

)(3.8)

approximates the hydraulic radius to within 1% of the exact value. From Eqs. (3.7)and (3.8) one obtains for the part-full velocity Vt

Vt

(1/n)D1/6(τo/ρ)1/2= 0.935y1/6(1 − 0.08y) (3.9)

Example 3.2 How large is the minimum velocity for a 15% part-full flow inExample 3.1?With y = 0.15, the right hand side of Eq. (3.9) yields 0.935·0.151/6

(1–0.08·0.15) = 0.67 and for Vt = 0.67·85·0.51/6(0.2/1000)1/6 = 0.72 ms−1.This is only about 15% less than the flowing full velocity.

Table 3.3 gives the ratios of the velocities for part-full and flowing full conditionsfor a representative number of part-full stages. It can be observed that beyond 40%part-full filling there is practically no further influence on the minimum velocity.

Table 3.3 Ratio of minimum velocities μt = Vt/Vv for part-full and full flow conditions in circularsewer

Part-full stage y 0.05 0.1 0.2 0.4 0.6 0.8 1Ratio μt 0.72 0.80 0.89 0.98 [1.09] [1.13] 1

For a minimum part-full flow of 5%, it follows from Eq. (3.9)

Vt

(1/n)D1/6(τo/ρ)1/2= 0.57. (3.10)

For a minimum bottom shear stress of τ o = 2 N/m2 and (1/n) = 85 m1/3s−1, thevalues of Vt calculated from Eq. (3.10) for a range of diameters are compiled inTable 3.4. The velocity of 0.50 ms−1 for the smallest possible diameters increases

Table 3.4 Minimum velocity Vt for 5% part-full flow with 1/n = 85 m1/3s−1 according toEq. (3.10)

D [mm] 150 200 250 300 400 500 600 700 800Vt [ms−1] 0.50 0.52 0.54 0.56 0.59 0.61 0.63 0.65 0.66

900 1000 1200 1400 1500 1600 1800 2000 25000.67 0.69 0.71 0.72 0.73 0.74 0.76 0.77 0.80


by only a small amount to 0.80 ms−1 for the largest size recommended in practice.For usual sewer diameters one may adopt roughly a minimum velocity of about 0.60to 0.70 ms−1, therefore.

Further research on the minimum slope required to avoid deposition of sand andgravel in sewers has been conducted by Novak and Nalluri (1978), Mayerle et al.(1991), Butler et al. (1996), and Nalluri and Ab Ghani (1996). A review of recentworks is also available (Hager 1998).

3.3.3 ATV Procedure

The ATV (1988) refers mainly to the works of Macke (1980, 1983) and Sander(1994). A table for various sewer diameters and 50% part-full flow containing theminimum velocities Vm and the corresponding minimum bed slopes Som to avoiddeposition of material is presented. The relation between the sewer diameter D, Vm

and Som is reproduced in Table 3.5. The relation between D and Vm can also beexpressed by

Vm[ms−1] = 0.5 + 0.55D [m]. (3.11)

Values of Vm obtained from Eq. (3.11) agree with those of Table 3.5 for nominaldiameters smaller than 300 mm. Beyond that, the ATV recommends higher veloci-ties. For 10% part-full flow, the minimum velocities obtained from Eq. (3.11) shouldbe increased by an additional amount of about 10%.

Schütz (1985) underlined the effect of backwater. All relations derived previ-ously are valid strictly for uniform flow; for control manholes with lateral inflowin particular, attention should be paid to backwater effects into the lateral branch.Schütz further recommended the empirical formula

Som[−] = 1/D [mm], (3.12)

according to which the minimum sewer slope for a diameter of 1000 mm amountsto 0.1%. For a sewer diameter of 250 mm a minimum sewer slope Som = 0.4% issufficient, however.

Table 3.5 Minimum velocity Vm and corresponding minimum slope Som as functions of conduitdiameter D for 50% part-full flow. For 10–20% part-full flow, Vm increases by about 10% (ATV1988)

D [mm] 150 200 250 300 400 500 600 800 1000Vm [ms−1] 0.48 0.50 0.52 0.56 0.67 0.76 0.84 0.98 1.12Som [%] 0.27 0.20 0.16 0.15 0.14 0.14 0.14 0.13 0.13

1200 1400 1500 1600 1800 2000 2200 2400 30001.24 1.34 1.39 1.44 1.54 1.62 1.72 1.79 2.030.12 0.12 0.12 0.12 0.12 0.11 0.11 0.11 0.11

3.4 Sewer Cross-Sections 63

Sander (1994) observed an average particle size of d = 0.35 mm. Further, thedetermining minimum filling ratio should be 10%, and a minimum bottom shearstress is 0.8 Nm−2. For sewers smaller than D = 1 m, the minimum bottom sloperequired against long term sedimentation is

Som = D–1 )31.3(.]m[1.2‰

For D > 1 m, the absolute minimum bottom slope So = 1.2‰ should be used.Equation (3.12) is thus modified for both small and large sewer diameters.Equation (3.13) has been tested with selected sewer systems and found appropriatefor common sewage.

3.4 Sewer Cross-Sections

Sewers built in older times had been developed in a variety of shapes. Carson et al.(1894) described, as an example, the pipe handle cross-section (similar to a horse-shoe cross-section with vertical intermediate walls and semi-circular soffit), thegothic section with a pointed arch and the egg-shaped cross section besides thecircular cross-section.

French (1915) compared the above mentioned four sections regarding the veloc-ities by application of Kutter’s formula for equal discharge. The egg-shaped sectionwas identified as the best capacity cross-section up to 35% part-full flow andfor larger flow depths all sections are hydraulically similar within 5%. Overall,the circular section performs best. The egg-shaped section shows in service moredeposition than the corresponding circular section. The study defined thirty of thesections then in use in the USA and specified their cross-sectional characteristics forfull flow conditions.

Donkin (1937) compared the circular with the egg-shaped and the U-shapedsections both hydraulically and economically. The U-shaped section constructedin brickstone was found to be narrowly optimum compared to the other two sec-tions. The techniques used in these investigations may not be considered sufficientin current standards.

Thormann (1941) introduced the standardisation of cross-sectional types of sew-ers. Fifteen cross-sections were proposed all of which are axis-symmetric and eitheregg-shaped or horseshoe shaped. Denoting the width of the section as B and theheight from invert to soffit T, six different axis ratios B:T = 2:αp were proposed,with αp = 3.5, 3, 2.5, 2, 1.5 and 1. The cross-sectional forms include:

• Extra-high, normal, transposed, depressed and transposed-depressed egg-shapedsections,

• Extra-high and normal circular sections,• Cap- or hood-shaped cross-section with αp = 2.5 and 2,• Parabolic cross-section 2:2,• Kite-shaped cross-section 2:2, and• Horseshoe-shaped cross-sections for αp = 1.5 and 1.


These cross-sections form the basis of ATV 110 (1988). The standard construc-tion technique for the cross-sections was established by Schoenefeldt et al. (1943).Thormann (1944) defined the cross-sectional geometry of fifteen standard sections.Roske (1958) referred to the dimensionless representation of the cross-sectionalsizes only to the circular, the egg-shaped and the horseshoe-shaped sections.

Kuhn (1976) concluded that neither the circular nor the egg-shaped nor the horse-shoe sections possess definite advantage over the other sections recommended, sothat no general recommendation can be given. Because of the industrial finish tech-nique the circular cross-section is employed in a wide variety of situations for whichthe section is often referred to as the standard sewer cross-section.

Schmidt (1976) compared the standard egg-shaped section with the circular sec-tion. For the same cross-sectional area the relation between the diameter DE of thenormal 2:3 egg-shaped section and the diameter Dk of the circular section is given byDk = 1.2DE. As long as the discharge is Q/Qv ≤ 0.22, the velocity in the egg-shapedsection is higher than that in the corresponding equal area circular section. It is statedthat for a night minimum discharge of around 1% of the storm water flow, around7% part-full stage establishes in the egg-shaped section while it is only about 4% inthe circular section. To produce the same velocity, the circular section would requireabout 30% more bottom slope than the egg-shaped section. According to Schmidt(1976), the standard egg-shaped section is suited for slopes which are unfavourablyplaced with regard to the avoidance of deposition during dry weather flow.

Sartor and Weber (1990) followed the opinion of Schmidt and recommendedspecially the egg-shaped section because of its advantages in maintenance and water

Fig. 3.1 Cross-sections of sewers used in the city of Paris, after Dupuit (1854)

3.4 Sewer Cross-Sections 65

Fig. 3.2 Sewer cross-sections of Thormann (1944)

quality. A quantification of these advantages requires comparative accounting ofthe pollutions carried by the sewers. Egg-shaped sections having cross-sectionaldimensions smaller than 500/750 are of special interest.

According to ATV (1988) the standard cross-sections are (Chap. 5):

• Circular section,• Egg-shaped section 2:3, and• Horseshoe section 2:1.5.

The remaining twelve cross-sectional forms, standardized by Thormann referredto previously and described in Chap. 5, can be alternatively described with thepart-full flow characteristic curves of their normalized sections. For the determina-tion of the full flow quantities, the so-called form factor must be known. The formfactor describes the influence of cross-sectional geometry on the discharge. What


the relevant reports in the literature do not state is whether in the future only thethree standard sections have to be considered. Having this in mind, only the circularsection is usually considered herein. On questions of sewer flow, the standardizedegg-shaped and the horseshoe sections are also accounted for. Pecher et al. (1991)follow this treatment also, whereas Unger (1988) considers solely the circular andthe standard egg-shaped sections.

Notation

B [m] width of cross-sectional profiled [m] particle size diameterD [m] pipe diameterF [m2] cross-sectional areag [ms−2] acceleration due to gravityh [m] flow depthkb [m] operative roughness heightks [m] equivalent sand roughness heightK [m1/3s−1] coefficient of roughnessP [m] wetted perimeterqr [−] relative dischargeQ [m3s−1] dischargeRh [m] hydraulic radiusRr [−] Reynolds number with respect to DSE [−] energy line slopeSo [−] bottom slopeT [m] height from invert to soffit of cross-sectionTs [◦C] sewage temperaturey [−] filling ratioαp [−] ratio of the axesκs [−] relative roughnessμt [−] velocity ratioν [m2s−1] kinematic viscosityρ [kgm−3] densityτ [Nm−2] shear stress

Subscripts

m minimumo bed, bottom part-fullv full flow condition

References 67

References

Ackers, P., Crickmore, M.J., Holmes, D.W. (1964). Effects of use on the hydraulic resistance ofdrainage conduits. Proc. Institution Civil Engineers 28: 339–360; 34: 219–230.

ATV (1988). Richtlinien für die hydraulische Dimensionierung und den Leistungsnachweis vonAbwasserkanälen und -leitungen (Guidelines for the hydraulic design of sewers). RegelwerkAbwasser – Abfall, Arbeitsblatt A110. Abwassertechnische Vereinigung: St. Augustin [inGerman].

Butler, D., May, R.W.P., Ackers, J.C. (1996). Sediment transport in sewers. Proc. Institution CivilEngineers Water, Maritime & Energy 118(6): 103–120.

Carson, H., Kingman, H., Haynes, T., Collison, H.N. (1894). Cross-sections of sewers and dia-grams showing hydraulic elements of four general types, Metropolitan Sewerage Systems.Engineering News 30(5): 121–123 (incl. supplement).

Donkin, T. (1937). The effect of the form of cross-section on the capacity and cost of trunk sewers.Journal Institution of Civil Engineers 7: 261–279.

Dupuit, J. (1854). Traité théorique et pratique de la conduite et de la distribution des eaux(Theoretical and practical treatment of the pipe and water distribution). Carilian-Goeury etDalmont: Paris [in French].

French, R. de L. (1915). Circular sewers versus egg-shaped, catenary and horseshoe cross-sections.Engineering Record 72(8): 222–223; 72(20): 608–610.

Graf, W.H. (1971). Hydraulics of sediment transport. McGraw-Hill: New York.Hager, W.H. (1998). Minimalgeschwindigkeit und Sedimenttransport in Kanalisationen (Minimum

velocity and sediment transport in sewers). Gas Wasser Abwasser 78(5): 346–350 [in German].Howe, H. (1989). Grundzüge des neuen ATV-Arbeitsblattes A110 (Fundamentals of the new ATV

A110 guideline). Korrespondenz Abwasser 36(1): 28–29 [in German].Kuhn, W. (1976). Der manipulierte Kreis – Gedanken zur Profilform bei Abwasserkanälen (The

manipulated circle – Thoughts on the sewer profile shape). Korrespondenz Abwasser 23(2):30–37 [in German].

Lysne, D.K. (1969). Hydraulic design of self-cleaning sewage tunnels. Journal SanitaryEngineering Division ASCE 95(SA1): 17–36.

Macke, E. (1980). Über Feststofftransport bei niedrigen Konzentrationen in teilgefülltenRohrleitungen (On sediment transport for low concentration in partially filled pipes). Mitteilung69. Leichtweiss-Institut für Wasserbau, TU Braunschweig: Braunschweig [in German].

Macke, E. (1983). Bemessung ablagerungsfreier Strömungszustände in Kanalisationsleitungen(Design of depositionless flows in sewers). Korrespondenz Abwasser 30(7): 462–469 [inGerman].

Mayerle, R., Nalluri, C., Novak, P. (1991). Sediment transport in rigid bed conveyances. JournalHydraulic Research 29(4): 475–495.

Nalluri, C., Ab Ghani, A. (1996). Design options for self-cleansing storm sewers. Water Scienceand Technology 33(9): 215–220.

Novak, P., Nalluri, C. (1978). Sewer design for no-sediment deposition. Proc. Institution CivilEngineers 65(2): 669–674; 67(2): 251–252.

Pecher, R., Schmidt, H., Pecher, D. (1991). Hydraulik der Abwasserkanäle in der Praxis(Hydraulics of sewers in practise). Parey: Hamburg, Berlin [in German].

Pfeiff, S. (1960). Mindest- und Höchstfliessgeschwindigkeiten in Entwässerungsnetzen (Minimumand maximum velocities in sewer networks). gwf Wasser/Abwasser 101(4): 83–85 [in German].

Raudkivi, A.J. (1993). Sedimentation – Exclusion and removal of sediment from diverted water.IAHR Hydraulic Structures Design Manual 6. Balkema: Rotterdam.

Roske, K. (1958). Dimensionslose Grössen in der Hydrodynamik der offenen Gerinne(Dimensionless quantities in the hydrodynamics of open channels). Stuttgarter Bericht 5. Inst.Industrie und Siedlungswasserwirtschaft, TU Stuttgart. Oldenbourg: München [in German].


Sander, T. (1994). Zur Dimensionierung von ablagerungsfreien Abwasserkanälen unter beson-derer Berücksichtigung von neuen Erkenntnissen zum Sedimentationsverhalten (The designof depositionless sewers under particular attention of new results relative to sedimentation).Korrespondenz Abwasser 32(5): 415–419 [in German].

Sartor, J., Weber, J. (1990). Die Wiederentdeckung des Eiprofils aufgrund von Schmutz-Frachtbetrachtungen (The re-discovery of the egg-shaped profile based on contaminantdischarge considerations). Korrespondenz Abwasser 37(6): 689–693 [in German].

Schmidt, H. (1976). Die Verwendung von Eiprofilen aus hydraulischer Sicht (The use of egg-shaped sewers based on hydraulic considerations). Korrespondenz Abwasser 23(7): 209–212[in German].

Schoenefeldt, O., Thormann, E., Conrads, A. (1943). Einheitliche Leitungsquerschnitte für dieStadtentwässerung (Uniformized sewers for city drainage). Gesundheits-Ingenieur 66(16):192–200 [in German].

Schütz, M. (1985). Zur Bemessung weitgehend ablagerungsfreier Strömungszustände inKanalisationsleitungen nach Macke (On the design of practically depositionfree flows in sewersbased on Macke). Korrespondenz Abwasser 32(5): 415–419 [in German].

Smith, A.A. (1965). Optimum design of sewers. Civil Engineering and Public Works Review 60(2):206–208; 60(3): 350–353; 60(9): 1279–1283.

Thormann, E. (1941). Einheitliche Leitungsquerschnitte für Entwässerungsleitungen (Fillingcurves of drainage pipes). Gesundheits-Ingenieur 64(8): 103–110 [in German].

Thormann, E. (1944). Füllhöhenkurven von Entwässerungsleitungen (Filling curves for drainagepipes). Gesundheits-Ingenieur 67(2): 35–47 [in German].

Unger, P. (1988). Tabellen zur hydraulischen Dimensionierung von Abwasserkanälen und-leitungen, DN100-4000 und DN300/450 –1400/2100 (Tables for hydraulic design of sewers).Ingwis-Verlag: Lich [in German].

Vicari, M. (1916). Kleinste Sohlgefälle für Schmutzwasserkanäle (Minimum bottom slopes forsewers). Gesundheits-Ingenieur 39(51): 537–540 [in German].

Yao, K.M. (1974). Sewer line design based on critical shear stress. Journal EnvironmentalEngineering Division ASCE 100(EE2): 507–520; 101(EE1): 179–181; 101(EE4): 668–669.

wastewater hydraulics || design of sewers

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