Worked Example 9: Sample Water System Design Numerical Example Figure 22 below shows the topographic survey results for a proposed gravity flow water system.
Figure 22 Assuming that the allowable pipe pressure head is 100m, the safe yield from the the spring is 0.25L! and that the design parameters from "ordan are adhered to #see Appendi$ %.&, design a system that will supply water to the community for the minimum cost. Answer 'he design of this water system will be approached in the following phases( 1. )e*uirement for an and pl placement of of br brea+ pr pressure ta tan+s. 2. esign of pipe wor+. -. hec+ ch chosen pi pipe wo wor+ fo for lo low pr pressure he head pa parameter. 1. Requirement for and placement of break bre ak pressure tanks onsider the control valve at the reservoir tan+ be ing closed to begin with. 'his is the ma$imum static head condition #Appendi$ % /o. 1&. All the static heads can be calculated from *uation #-5& below( onsider the section of the system from the spring #point 1& to low point 2. 'he static head is(
which e$ceeds the 100m allowable pipe pressure head given above. onsider the section of the system from the spring #point 1& to high point -. 'he static head is( which is within the above limit. onsider the section of the system from the high point - to the reservoir tan+ #point %&. 'he static head is( which e$ceeds the 100m allowable pipe pressure head given above. t is clear that the pipes at points 2 and % will blow unless we introduce brea+ pressure tan+s to relieve the pressure. 'he first break pressure tank #hereafter 1& must relieve the pressure at point 2 but still allow the water to flow over point -. 'he ma$imum height #h 1& we can place 1 at is given by( so( and therefore( and( so( and therefore( !o the height of 1 must be less than or e*ual to 150 and greater than 125, to satisfy the conditions. As there will be frictional losses in the pipes we should situate 1 at its ma$imum allowable height, which is in this case 150m. 'his corresponds to a location appro$imately 225m from the spring tan+. 'he second break pressure tank #hereafter 2& must relieve the pressure at point % but not e$ceed the pressure head limits in the pipe wor+ between it and 1. 'he ma$imum height #h 2& we can place 2 at is given by(
so( and therefore( And so( and therefore( !o the height of 1 must be greater than or e*ual to 50 and less than or e*ual to 100, to satisfy the conditions. !o it will be placed at a height of 70m. 'his corresponds to a location appro$imately 2500m from the reservoir tan+. 'he two brea+ pressure tan+ locations are added to the topographic survey, and shown below in Figure 2-.
Figure 2y inspection of Figure 2-, the ma$imum static heads #after the introduction of the two brea+ pressure tan+s& are as follows( At 1( At oint 2(
At oint -( At 2( At oint %( All of which are acceptable. 2. Design of pipe work 'he safe yield of the water source is 0.25L!. !o in general we want to ma+e sure that at no point in the system is more than 0.25L! being drawn, as this will either empty a brea+ pressure tan+ or the spring tan+, allowing a ir into the system. 3e can do this in two ways. 1. esign the natural flow situations such that 4ust less than 0.25L! is being drawn. 2. se control valves at the brea+ pressure tan+s and reservoir tan+ to limit the flow to 4ust less than 0.25L!. 3e will consider the second option because the calculations are simpler and the control of the system easier. onsider the section of pipe between the spring tank (point 1) and !1( 'his section of pipe is 225m long and the ma$imum static head is 50m #see above&. From the friction tables for a controlled flow of 0.25L! we get the following data. Pipe Frictional head loss Frictional head loss for 22m of Diameter (m/100m) pipe (m)
!elocit" (m/s)
67
1-.81
-0.82
1.29
:;
-.%<
<.91
0.<-
1=
1.0<
2.%1
0.%5
1> ;
0.29
0.8-
0.28
t is clear that we can use "# dia. pipe $ere, as it will not reduce the ma$imum static head below the 10m low pressure head limit #see Appendi$ %. /o. -& and the velocity of the water lies within acceptable parameters #see Appendi$ % /o. %&. 'he residual head at the 1 valve #?@1& is given by *uation #-%&( !ubstituting the numerical values into this e*uation for 67 dia. pipe we get(
'his is an acceptable residual head based up on the limits set in Appendi$ % /o. 8. onsider the section of pipe between !1 and !2 ( 'his section of pipe is 2500 225 B 2-<5m long. 'he main feature we have to contend with is the topographical pea+ at point -. 'his only lies 25m below 1, so we canCt afford to ;burn off7 too much frictional head between 1 and point - or else the residual head will drop below the limit of 10m #see Appendi$ %. /o. -&. !o we need to bu rn off no more than 25 10 B 15m of head between 1 and point -. 'he distance between 1 and point - is from Figure 2-, 1900 225 B 15<5m. From the friction tables for a controlled flow of 0.25L! we get the following data. Pipe Frictional head loss Frictional head loss for 1#m of diameter (m/100m) pipe (m)
!elocit" (m/s)
67
1-.81
21%.-8
1.29
:;
-.%<
5%.85
0.<-
1=
1.0<
18.95
0.%5
1> ;
0.29
%.%1
0.28
3e clearly cannot use 67 and :7 diameter pipes here as they ;burn off7 far more than 15m of head. 3e could use 1> 7 dia. pipe here, but there are two problems. Firstly the water velocity is very low at 0.28 mDs #see Appendi$ % /o. %& and secondly it is a little more costly than 1= dia. pipe #Appendi$ % /o. 9&. !o consider using 1= dia. pipe. 'he water velocity is still below the limit of 0.< mDs #see Appendi$ % /o. %&, but the head loss is almost acceptable. 'here seems to be only one solution. %se 1& pipe between !1 and point ' and place a was$ out at t$e lowest point between !1 and point ' w$ic$ $appens to be point 2. 'he pressure head at point - #@-& is given by *uation #-%&( !ubstituting the numerical values into this e*uation for 1= dia. pipe we get (
'his is a little less than the minimum low pressure head limit of 10m #see Appendi$ % /o. -& but is acceptable in the circumstances. /ow consider the second section of pipe bet ween point - and 2. 'he remaining pressure head is 9.15m #from above& and so we can add this to the remaining head between point and 2 to get the overall head. 'he most desirable residual head #Appendi$ % /o.8& at a valve or tap is around 15m. !o we are loo+ing to ;burn off7 something li+e ( 'he distance between point - and 2 is from Figure 2-, 2500 1900 B <00m. From the friction tables for a controlled flow of 0.25L! we get the following data. Pipe Frictional head loss Frictional head loss for #00m of diameter (m/100m) pipe (m)
!elocit" (m/s)
67
1-.81
E5.2<
1.29
:;
-.%<
2%.2E
0.<-
1=
1.0<
<.%E
0.%5
1> ;
0.29
1.E8
0.28
3e clearly cannot use 67 diameter pipe here as it ;burns off7 far more than %9.15m of head. # dia. pipe $ere looks good , as although it only burns off appro$imately half of the re*uired head, it produces a water velocity within the parameters re*uired #Appendi$ % / o. %& and is cheaper than the 1= dia. pipe #Appendi$ % /o. 9&. 'he residual head at the 2 valve #?@2& is given by ( !ubstituting the numerical values into this e*uation for : 7 dia. pipe we get ( 'his is in the high end of the residual head range based upon the limits set in Appendi$ % /o. 8. 3e can improve on this and reduce costs by using a combination of :7 dia. pipe and 67 dia. pipe. onsider the combination pipes *uation #%1&.
3here( B Length of smaller diameter pipe, to give desired frictional head loss #m&. @ B esired frictional head loss #m&. f hl B Frictional head loss due to larger diameter pipe #mD100m&. f hs B Frictional head loss due to smaller diameter pipe #mD100m&. L B 'otal length of pipe #m&. n this case our desired head loss #@& is %9.15m, L B <00m, f hl B -.%
'his close to 200m, and as the pipe usually comes in 100m lengths, we should emplo* 200m of "# dia. pipe and 500m of # dia. pipe. 'his combination of pipes will produce a total frictional head loss #f hcomb& of ( !o the residual head at the 2 control valve will be ( 'his very close to the desired residual head based upon the limits set in Appendi$ % /o. 8. onsider the section of pipe between !2 and t$e reser+oir tank (point ,) ( 'his section of pipe is -200 2500 B <00m long and the ma$imum static head is at point % and is <0m #see above&. From the friction tables for a controlled flow of 0.25L! we get the following data. Pipe diameter
Frictional head loss (m/100m)
Frictional head loss for #00m of pipe (m)
!elocit" (m/s)
67
1-.81
E5.2<
1.29
:;
-.%<
2%.2E
0.<-
1=
1.0<
<.%E
0.%5
1> ;
0.29
1.E8
0.28
f we try to achieve the desired residual head at the reservoir tan+ valve of 15m #see Appendi$ % /o. 8& then we need to ;burn off7 <0 15 B 55m of head through friction. !tudying the data above suggests that a combination of 67 and : 7 pipe would be the optimum solution. sing the combination pipes *uation #%1& as previously(
n this case our desired head loss #@& is 55 m, L B <00m, f hl B -.%
'his close to -00m, and as the pipe usually comes in 100m lengths, we should emplo* '00m of "# dia. pipe and ,00m of # dia. pipe. 'his combination of pipes will produce a total frictional head loss of ( 'he residual head at the reservoir tan+ control valve #?@ %& is given by e*uation #-%& ( !ubstituting the numerical values into this e*uation for the combination of 67 dia. and : 7 dia. pipe we get( 'his is an acceptable residual head based up on the limits set in Appendi$ % /o. 8. '. -$eck c$osen pipe work for low pressure $ead parameter At this stage of the design we need to chec+ that we have not reduced the pressure head in the pipe below the 10m limit set in Appendi$ % /o. -. 3e can do this most simply by plotting the @ydraulic Grade Line #see $ordan& onto the topographic survey. 'o do this we need to tabulate all the chosen pipe sections, their lengths and their respective friction head losses based upon a controlled flow of 0.25L!. 'his data is shown below( %ectio Pipe 'enth Frictional head loss otal frictional head loss n dia& (m) (m/100m) (m/100m) 11 67
225
1-.81
-0.82
1- 1=
15<5
1.0<
18.95
-2 :7
500
-.%<
1<.-5
%ectio n
Pipe dia&
'enth (m)
Frictional head loss (m/100m)
otal frictional head loss (m/100m)
-2 67
200
1-.81
2<.22
2H%
:7
%00
-.%<
1-.99
2H% 67
-00
1-.81
%0.9-
'hese lines are plotted onto the topographic survey as shown in Figure 2%. $amination of the @GL shows that it the pressure head never becomes negative #i.e. the @GL never goes below the ground surface& and its minimum is at point -, which we have already considered. 'herefore the chosen pipe wor+ design is acceptable.
Figure 2% I revious /e$t J • • • • • •
Fluid *echanics For +ra,it" - Flow .ater %"stems and Pumps reface art 1( ntroduction art 2( General oncepts art -( erivation of the ontinuity *uation art %( 'he ontinuity *uation for Kultiple ipe !ystem art 5( nergy in a erfect !ystem 'he ernoulli *uation
art 8. mperfect !ystems Friction and the ernoulli *uation art <( umps and 'urbines 'he ernoulli *uation art 9. 'ypical !cenarios art E( !pecial !cenarios Appendi$ 1( inetic nergy of a Fluid Appendi$ 2( otential nergy of a Fluid Appendi$ -. Friction Losses and the )eynolds /umber Appendi$ %. 3ater !ystem esign arameters Appendi$ 5( nterpolation Appendi$ 8( Frictional @ead Loss hart 3or+ed $ample 1( /atural Flow 3or+ed $ample 2( /atural Flow 3ith ipes of ifferent iameters and Lenghts 3or+ed $ample -( !imple 'ap !yatem #'ap Mpen& 3or+ed $ample %( !imple 'ap !ystem #'ap losed& 3or+ed $ample 5( ump )e*uirement 3or+ed $ample 8( istribution!ystem 'he General *uation 3or+ed $ample <( arallel ipes 3or+ed $ample 9( !ources at ifferent levations 3or+ed $ample E( !ample 3ater !ystem esign
• • • • • • • • • • • • • • • • • • •
i. Glossary erm Description
nits
a
Acceleration
KetresD!econd2
A
Area
Ketres2
At
)eservoir !upply ipe Area
Ketres2
,d
ipe iameter
KetresDinches
nergy
"oules
+
inetic nergy
"oules
p
otential nergy
"oules
F
Force
/ewtons
f
Friction Factor
f AHn
Frictional @ead Loss in 'ap !upply ipe
Ketres
f h
Frictional @ead Loss
Ketres
f hl
Frictional @ead Loss in Larger iameter ipe
Ketres
f hn
Frictional @ead Loss in ipe n
Ketres
f hs
Frictional @ead Loss in !maller iameter ipe
Ketres
f p
Frictional Loss #ressure&
/ewtonsDKetre2
f tHA
Frictional @ead Loss in )eservoir !upply ipe
Ketres
g
Gravitational Acceleration
KetresD!econd2
h
@eight
Ketres
@
esired Frictional @ead Loss
Ketres
h A
@eight of "unction A
Ketres
@ A
@ead at oint A
Ketres
h
@eight of "unction
Ketres
@ma$
Kai$imum !tatic @ead
Ketres
hn
@eight of nth 'ap
Ketres
@n
)esidual @ead at 'ap n
Ketres
ht
)eservoir @eight
Ketres
lectrical urrent
Amps
L
Length
Ketres
Ln
nth 'ap !upply ipe Length
Ketres
Lt
)eservoir !upply ipe Length
Ketres
K
Kass
ilogrammes
n
/umber of 'aps
/)
)eynolds /umber
ressure
/ewtonsDKetre2
A
ressure at "unction A
/ewtonsDKetre2
ressure at "unction
/ewtonsDKetre2
+
inetic nergy as a ressure
/ewtonsDKetre2
n
)esidual ressure at nth tap
/ewtonsDKetre2
p
ump ressure
/ewtonsDKetre2
p
otential nergy as a ressure
/ewtonsDKetre2
t
'urbine ressure
/ewtonsDKetre2
N,*
Oolumetric Flow )ate
Ketre-D!econd
* A
Oolumetric Flow )ate at "unction A
Ketre-D!econd
!
istance
Ketres
t
'ime
!econds
v
Oelocity
KetresDsecond
O
Oolume
Ketre-
O
Ooltage
Oolts
v A
Oelocity of 3ater in )eservoir !upply ipe
KetresD!econd
vav
Average Oelocity
KetresD!econd
vn
Oelocity of 3ater in n th 'ap !upply ipe
KetresD!econd
3
ower
3atts
3e
lectrical ower
3atts
3in
ower !upplied to ump
3atts
3out
ower !upplied by ump
3atts
?h
'otal ifference in @ead between 'an+s
Ketres
?@
)esidual @ead
Ketres
?
)esidual ressure
/ewtonsDKetre2
P
ump fficiency
Q
inematic Oiscosity
Ketres 2D!econd
R
ensity #ro&
ilogrammesDKetre-
ii. Scope 'his manual is intended to aid the water pro4ects wor+er or volunteer in the following ways ( 1.
'o e$plain, from first principals and using basic physical relations, the origin of the e*uations that design water systems. 2. 'o systematically outline the +ey e*uations and e$plain how to apply them to scenarios where there is no te$t boo+ method readily available. -. 'o give step by step numerical solutions to some of the more common and also some special scenarios.
%.
'o systematically lay down the design parameters for gravity flow water systems and show how they should be applied to a design. !ections 2H< e$plain the basic concepts, show how the core e*uations are derived, e$plain perfect and imperfect systems and cover the analysis of pumps and turbines. !ections 9 and E show how to apply the core e*uations to a series of common and special scenarios. 'he wor+ed e$amples 1H9 show how to simplify the e*uations developed in !ections 9 and E for practical use and give step by step numerical e$amples for each scenario. n addition wor+ed e$ample E shows the design process applied to a sample gravity flow water system design. Appendices 1H8 give more comple$ derivations of the core relations, e$planations of useful processes in the calculations and additional technical data. For the e$perienced water system designer would suggest reading through !ections 9 and E, Appendi$ % and 3or+ed $ample E in particular. Any *uestions about this manual should be addressed to odger at dodgerSirational.org.
iii. References 1.
/andbook of ra+it*low 3ater 4*stems ( 'homas ."ordan "nr. ( ntermediate 'echnology ublications 1EE8. 2. asic ngineering 4ciences and 4tructural ngineering for ngineerin6raining aminations ( Apfelbaum T Mttesen ( @ayden oo+ ompany 1E<0. -. %. riction 8oss -$aracteristics -$art ( !ol*et$*lene (!) 4DR!ressure Rated 6ube ( !'A T Gustavo rbano.
iv. Notes 1.
n the numerical calculations for the 3or+ed $amples, the asteris+ #U& denotes the multiplication sign and the slash #D& the divide sign. 2. n general, metric fundamental units #Ketres, ilogrammes and !econds& have been used in the 3or+ed $amples, the two main e$ceptions being inches for pipe diameters and LitresD!econd #L!& for flow rates.
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