Abu Dhabi-Sewerage pipe theories and calculation.doc

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CHAPTER

3

THEORIES AND

CALCULATIONS

3.1 INTRODUCTION

This chapter presents the theories and standards that were used to design a sewage and

drainage system in general. In Section 3.2, the wastewater flow sewer and drainage

being designed is described. The Colebrook-hite e!uation for the "elocity of flow in

a sewer is presented in Section 3.3. The design limitations of the sewerage system

such as depth of flow, pipe gradients, pipe depths, pipe si#es and manholes are gi"en

in Section 3.$. %inally, Section 3.& sets out the detailed sewerage design process, from

the decision to adopt a sewerage system to the de"elopment of the o"erall sewerage

layout whiles ample of calculations for the detailed design for sewers is represented in

Section 3.'.

3.2 WASTEWATER FLOW

This pro(ect in"ol"es two systems, a sewage system and drainage systems. The sewer

system is designed to con"ey the wastewater from workshops, commercial

establishments and industries, while the drainage system discharges the e)cess surface

water from streets and roofs of buildings.

3.2.1 Sewage Wastewater Flow

The flow rate of the wastewater flow used for the design of the main trunk sewer was

based on the water consumption and the population according to the *bu-+habi

+esign anual, 2. This can be estimated as follows



nConsumptioater/opulation/.%.0 ××= A

13.

here

0 4 wastewater flow 156day

*./.% 4 *bu-+habi /eaking %actor.

In this pro(ect, a water consumption figure of 27 15pcd was used for the year 22

based on *bu-+habi +esign anual, 2.

The peaking factor was applied to all sewage flows to identify re!uired pipe and

pump station si#es. The *bu-+habi peaking factor 1*/% is a "ariation of the 8abbit

formula. The formulation for *bu-+habi is

−

×=−---

population'

$.2&%actor3/eaking+habi*/%1*bu

13.2

The */% is used to pro(ect ma)imum sewage flows from a tributary area. The

tributary area should include a contributing population e!ual to or greater than &

persons. %or tributary populations with fewer than & persons, an alternati"e method

of estimating peak flows should be used.

3.2.2 Poplat!o" Sr#e$



* population sur"ey is essential for sewer design, in order to come up with a

sufficient peaking factor for acceptable design in real life9 also to achie"e the purpose

of sewerage system, the design should use reasonable data relating to e)isting or

e)pected population in the future. The sur"ey is a collection of building types because

the population intensity differs from one type to another. The number of floors also

increases the population intensity.

The /opulation sur"ey was determined through se"eral site "isits to obser"e the

population at a certain factory or block. Then a suitable factor was obtained according

to the population per s!uare meter. :ach area was multiplied by that factor to obtain

the population for different blocks.

3.2.3 Dra!"age Wastewater Flow

The actual amount of runoff flow can be determined by using the ;ational method

1Steel and c<hee, =>=. This can be estimated as follows

*IC2$-0 ×××= 13.3

here

0 4 peak runoff rate 1m36day

C 4 runoff coefficient 1dimensionless

I 4 a"erage rainfall intensity 1mm6hr

* 4 drainage area 1ha



The rainfall intensities for different durations and return period storms for *bu-+habi

are presented in Table 3. 1*bu-+habi +esign anual, 2. In this pro(ect, the

return period is & years will be adapted and the storm duration is 2 hr, gi"ing '.3&

mm6hr of rainfall intensity, whereas in Table 3.2, typical runoff coefficients for areas

of "arious characteristics are gi"en 1*bu-+habi +esign anual, 2.

;unoff coefficients to be used with design storms to estimate storm water runoff

"olumes. These coefficients are established on a sit-specific basis to reflect actual

catchment characteristics. In this pro(ect, the runoff coefficient used in designing the

storm water is .'.

Ta%le 3.1 Ra!"&all I"te"s!t$ Drat!o" Fre'e"($

Retr" Per!o) I"te"s!t$ *++,-r %$ Drat!o" *-r

.& . .& 2. 2.& ' 2$

?ear 3.$$ >.== &2.$ $3.'3 3$.= 2.& >.'2

2 ?ear 73.>7 &>.7 $2.>3 3&.& 27.$ '.$3 '.2

?ear >&.3 &2.2 37.&' 3.== 2&.&= $.'' &.$7

>& ?ear >.>> $=.>& 3'.72 3.&3 2$.$3 3.=3 &.2

$ ?ear '$.3 $$.&' 33. 2>.33 2.7> 2.32 $.'2

2 ?ear &&.$ 37.>7 27.>7 23.>> =.2 .&3 3.=>

?ear $'.'3 32.7= 2$.$' 2.$ '. 7.> 3.3

& ?ear 3>.$7 2'.>& =.=' '.3& 3.7 '.7 2.'

2 ?ear 23.'& >.$7 3.' .'$ 7.& 3.=$ .&'

Ta%le 3.2 T$p!(al R"o&& Coe&&!(!e"ts

Area Des(r!pt!o"Coe&&!(!e"t

Categor!es %$ sr&a(e

8rick .> @ .7&

Concrete and *sphalt .> @ .=&

Sandy Soil .& @ .2

Categor!es %$ se

Cemeteries, /arks and /laygrounds . @ .2&



8usiness districts .> @ .=&

Res!)e"t!al

*partments .& @ .>

I")str!al

5ight .& @ .7

Aea"y .' @ .= Bote that for preliminary calculation of runoff, these coefficients are consistent with

those used with the ;ational method for estimating runoff.

3.3 /ELOCIT0 OF FLOW

3.3.1 Cole%rooW-!te E'at!o"

Throughout this pro(ect, the Colebrook-hite e!uation will be used to determine the

"elocity of the calculated flows presented pre"iously in section 3.2, either for sewer

flows or drainage flow. This can be estimated as follows

×+×−= 2g+S+

2.&C

3.>+

Dslog2g+SE 13. $

here

E 4 "elocity of flow at d6+ 1m6s

g 4 gra"itational acceleration 1m6s2

+ 4 pipe diameter 1mm

S 4 hydraulic gradient, 1mm6mm

1In"ert slope for full pipes, water surface slopes for open channels, m6m

k s 4 linear measure of effecti"e roughness 1mm

4 kinematics "iscosity of fluid 1m26s



The roughness coefficient is a measure of the "ariation and magnitude of

protuberances on the interior surface of the pipe. The roughness, therefore, is a

function of the pipe material, age and condition. Typical coefficients for the "arious

pipe materials are gi"en in Table 3.3 1*bu-+habi +esign anual, 2.

Bote that poor sewer pipe conditions are to be assumed for *bu-+habi system designs

1F s4.& where drainage design should be based on 1F s4.' assuming asbestos-

cement pipes.

Ta%le 3.3 T$p!(al Rog-"ess Coe&&!(!e"ts For P!pes

P!pe ater!al

Cole%rooW-!te4 5 s *++

6oo) Nor+al Poor

G/EC .3 .' .&

<;/ .3 .' .&

Coated Cast Iron .= .& .3

Gncoated Cast Iron .& .3 .'

+uctile Iron .& .3 .'

*sbestos cement .& .3 .'Eitrified Clay .3 .' .&

Concrete .& .3 .'

3.3.2 !"!++ a") a7!++ Flow /elo(!t!es

+esign flow "elocities should be within the limits presented in Tables 3.$ and 3.&

1*bu-+habi +esign anual, 2. inimum "elocities are based on pro"iding self-

cleansing "elocities and pre"enting solids sedimentation in the sewer and drainage

pipes.



a)imum "elocities are set to pre"ent manhole corrosion and minimi#e sewer gases

in the sewer system and minimi#e the negati"e effects of abrasion on the drainage

pipes and manholes.

Ta%le 3.8 a7!++ a") !"!++ /elo(!t!es !" Sewers.

P!pe Des(r!pt!o" !"!++ *+,s a7!++ *+,s Des!g" *+,s

<ra"ity line .' 2.& .>&

/ressure 5ine . 3. .&

Ta%le 3.9 a7!++ a") !"!++ /elo(!t!es !" Dra!"age.

P!pe Des(r!pt!o" !"!++ *+,s a7!++ *+,s Des!g" *+,s

<ra"ity line .>& 2.& .>&

/ressure 5ine . 3. .

3.8 DESI6N LIITATIONS OF THE SEWERA6E S0STE

3.8.1 Dept- o& Flow

The design criteria for depth of flow in sewer lines are presented in Table 3.' 1*bu-

+habi +esign anual, 2. Sanitary sewers should be checked for percentage full

at all times.

Ta%le 3.: a7!++ P!pe Per(e"tages Fll !" Sewer P!pes.

P!pe Des(r!pt!o" a7!++ ),D !"!++ ),D

Trunk sewer lines .>& .&

ain and lateral sewer lines .7& .&

d6+ is ratio of flow depth to 1d nominal pipe diameter 1+.

3.8.2 P!pes Dept-s





inimum gradients based on the Colebrook-hite formula

3.8.8 P!pes S!=es

The current standard for the minimum si#e of sewer mains is 2 mm. The minimum

pipe si#e recommended for house connections is & mm or ' mm outside

diameter. The minimum pipe si#e permissible on drainage pro(ects is 2& mm.

Hne e)ception is pipe used for land drains. The land drain minimum is ' mm.

Aowe"er, slotted carrier pipes, ser"ing as both land and carrier drain, must meet the

2& mm minimum.

3.8.9 a"-oles

anholes should be of sufficient si#e to permit access for maintenance acti"ities. In

addition, their design and material should be such to guarantee ma)imum

performance for an e)tended ser"ice life.

Bote that this pro(ect was not deal with designing manholes or studying the manholes

criteria. It was (ust indication of their locations in the system.

3.9 DETAILED DESI6N PROCESS

The theories introduced pre"iously allow a sewer system to be analy#ed in order that

sewer and drainage flows and "elocities can be determined. This is only one part of

the o"erall design process. +etailed design re!uires a combination of hydraulic

calculations and the application of standard designs, procedures and details.



* sanitary sewer has two main functions to con"ey the designed peak discharge and

to transport solids so that deposits are kept to a minimum. It is essential9 therefore,

that the sanitary sewers ha"e sufficient capacity for the peak flow and that it function

at minimum flows without e)cessi"e maintenance and generation of odors as well as

sufficient "elocity of that flow to transport the solids.

8ased on the criteria and the design limitation stated pre"iously throughout this

chapter, the detailed design procedure is as follows

. 5abel each manhole based on the flow direction. SA and +A are an

e)ample of manholes labels where SA refers to sewer manhole Bo. as

well as +A refers to drainage manhole Bo. and so on.

2. +etermine the co"er le"el 1C.5 in m for each manhole from the contours

le"els shown in %igure 2. in *ppendi) *.

3. *dditional depth 4 .2 m is added to the C.5 of future pa"ements or

construction in the unpa"ed areas. Therefore, C.5 can be estimated as follows

-.2<.5C.5 +=

1$.



$. +etermine the first manhole in"ert le"el 1I.5 in m from the sur"ey study of

the location which will be designed, where the second I.52 will be calculated

as follows

( )I.55---

SI.52 −×

−×=

1$.2

here

S 4 pipe gradient 1

5 4 pipe 5ength 1m

&. Calculate the depth to in"ert for each manhole 1+.I as follows

I.5C.5+.I

−=

1$.3

'. +etermine the pipes diameters 1proposed, lengths and gradients according to

the design limitation based on the *bu-+habi +esign anual, 2.

>. +etermine the (unction population, the number of persons ser"ed for each

manhole and the increment population. Bote that increment population is an

accumulati"e summation between the (unction population and the number of

person ser"ed for each manhole.

7. Calculate the pecking factor 1/.% using the 8abbit formula, :!uation 13.2.



=. Calculate the total flow in 56s using :!uation 13..

. Calculate the full flow "elocity in m6s using Colebrook-hite formula,

:!uation 13.$.

. Calculate the flow full in 56s based on the "elocity calculated in the pre"ious

step and the area of the pipe as follows

*E0 ×= 1$.$

2. Calculate the ratio between the partial flow 1total flow of the pipe and the full

flow of the pipe as follows

0%ull

0/artial;atio =

1$.&

3. +etermine the ratio between the actual "elocity and the full "elocity of the

pipe 1E6Ef and the actual ratio between the flow depth and the pipe diameter

1d6+ based on the partial flow to full flow ratio calculated in the pre"ious

step. The "alues of E6Ef and d6+ are represented in Table 3.7 in *ppendi) 8

1*bu-+habi +esign anual, 2.



$. %ind the "alue of the actual "elocity based on the E6Ef . Then compare the

actual "elocity and the actual d6+ with design limits represented in Table 3.$

and Table 3.' to be sure that the design is acceptable.

*ll the pre"ious steps are followed in designing sewer pipes, whereas the following

steps are re!uired for designing drainage pipes. Steps from to ' are same as sewer

design where the remaining steps are as follows

>. +etermine the catchments area, the (unction area for each pipe, the total area

and the cumulati"e catchment areas. Bote that total area is the total of the

catchments areas and the (unction area for each pipe.

7. +etermine the rainfall intensity using Table 3.2.

=. +etermine the runoff coefficient using Table 3.3.

. Calculate the runoff flow in m36s using ;ational method, :!uation 13.3. Then

calculate the accumulati"e runoff flow.

The remaining steps from to $ are the same as for sewer design. Bote that in step

3 you must use Table 3.= in *ppendi) 8 instead of Table 3.7 for determining the

"alues of E6Ef and actual d6+ for drainage pipes.

3.: SAPLES OF CALCULATIONS



T-e &ollow!"g ass+pt!o"s w!ll %e se) !" %ot- sewer a") )ra!"age s$ste+s>

• + 4 $ mm

• S 4

• * 4 3>.& mm2 1the width of street 4 & m and the length 4 >.& m

Sa+ple 1> Sewer )es!g" (al(lat!o" &ro+ SH12,?,3 to SH12,?,3A as

s-ow" !" Ta%le 9.8.

-.2<.5C.5 +=

m-$.--.2-3.=S,A26763 =+=

m-$.--.2-3.=S,A26763* =+=

( )I.55---

SI.52 −×

−×=

( ) m-.=>-2.=>-----

S,A26763* =−×

−×=

I.5C.5+.I −=

m-3.2->.-2-.-$S,A26763 =−=

m3.2-.=>-$.-S,A267637 =−=



−

×=−---

population'

$.2&%actor3/eaking+habi*/%1*bu

*ssuming population intensity is persons

2&.$

---

---'

$.2&%actor3/eaking+habi*/%1*bu =

−

×=−

nConsumptioater/opulation/.%.*0 ××=

56s >>.3

---

3'--2$

27-2&.$0 =

×

××=

×+×−= 2g+S

+

2.&C

3.>+

Dslog2g+SE

1+ownward m6s -.$2&

-.---.$=.7->2-.$

&-.$2.&

-.$3.>

.&log

---

1

---

$--1=.7->2E

=

××××

××+

×

×××−=

*E%G55

0 ×=



56s $.3&21-.$$

J----.$2&

%G550 =××=

2'.-$.&3

>>.3

0%ull

0/artial;atio ===

Fro+ Ta%le 3.? !" Appe")!7 @>

-.3&+

d

m6s -.3'-.$2&-.7$3E

-.7$3Ef

E

=

=×=

=

Comparing the actual "elocity and the actual d6+ with the design limits presented in

Table 3.$ and Table 3.', we found the following

• E 4 .3' m6s K Emin 4 .' m6s.

• d6+ 4 .3& K d6+ min 4 .&

This means that the design is not acceptable. So, the pipe dimensions must be

changed, either the pipe diameters or the pipe gradients.



Sa+ple 2> Dra!"age )es!g" (al(lat!o" &ro+ DH:,1?,;,8 to

DH:,1?,;,3 as s-ow" !" Ta%le 9.9.

-.2<.5C.5 +=

m>-.-3-.2-3.&$S,A'676>6 =+=

m>-.-3-.2-3.&3S,A'676>6 =+=

( )I.55---

SI.52 −×

−×=

( ) m$.-2&.-2-----

S,A2 =−×

−×=

I.5C.5+.I −=

m2.&.-2>-.-3$+,A'676>6 =−=

m3.$.-2>-.-33+,A'676>6 =−=

*IC2$-0 ×××=

56s $.&23>.&)3'--

3&.''.-2$-0 =××=



×+×−= 2g+S

+

2.&C

3.>+

Dslog2g+SE

1+ownward m6s -.$2&

-.---.$=.7->2-.$

&-.$2.&

-.$3.>

-.'log

---

1

---

$--1=.7->2E

=

××××

××+

×

×××−=

*E%G550 ×=

56s $.3&21-.$$

J----.$2&

%G550 =××=

$'.-$.&3

&.2$

0%ull

0/artial;atio ===

Fro+ Ta%le 3. !" Appe")!7 @>

-.$7+

d

m6s -.$2-.$2&-.=72&E

-.=72&Ef

E

=

=×=

=

Comparing the actual "elocity and the actual d6+ with the design limits presented in

Table 3.& and Table 3.', we found the following



• E 4 .$2 m6s K Emin 4 .>& m6s.

• d6+ 4 .$7 K d6+ min 4 .&

This means that the design is not acceptable. So, the pipe dimensions must be

changed, either the pipe diameters or the pipe gradients.

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Abu Dhabi-Sewerage pipe theories and calculation.doc