Water Engineering Research Ltd. Ashby Road Loughborough Leicestershire 16th November 2015
Managing irector A.N. !ther and "artners #rove Road $irmingham West Mid%ands &'i%%(ay &ystem esign ear &ir)Madam* + am (riting to you to su''%y you (ith the s'i%%(ay system design ,or -o%sterda%e Reservoir* or/shire* or/shire* as reuested. he attached re'ort gives detai%s o, the system %ocation and dimensions* (ith accom'anying ca%cu%ations* ,or the design o, a s'i%%(ay* side channe%* co%%ecting channe%* de%ivery channe% and sti%%ing basin. he design has been 'roduced 'roduced (ith a maimum design discharge discharge o, 113.4m4)s* suiting the 'rovided maimum discharge o, 120m 4)s that (as s'ecied in the brie,. A summary dra(ing detai%ing /ey dimensions o, the e%ements is attached as an A''endi to the re'ort. A %ocation ma' is a%so inc%uded the %ocation o, the system (as 7ustied based on the ground 'ro%e o, the site* (ith the aim o, minimising the cut and %% reuired ,or insta%%ation. -hanne% o'timisation (as underta/en to minimise construction costs and the e8ect on the surrounding environment. esign 'rocedures and the design assum'tions used have been detai%ed in the re'ort so that any engineering decisions made can be ,o%%o(ed and understood. he re'ort s'ecies ,urther detai%s detai%s o, the s'i%%(ay system* ho(ever ho(ever i, any ,urther in,ormation is reuired (ith regards to our design or any other matter* '%ease do not hesitate to contact us. ours ours ,aith,u%%y*
Rebecca Woodhouse (On behalf of Water Engineering Research Ltd)
-!L& -! L&E ERAL RALE E &" &"+L +LL LWA &&EM E&+#N Water Engineering Research Ltd
Rebecca Woodhouse $213919 :enny ynan ynan $21634; $21634; Mariyan ray/ov $224633 Emi% amarov $414<53
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Research Ltd
-ontents 1.0
+ntroducti +ntroduction... on....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ......... ............ .......... ... 1
2.0
Eecutiv Eecutive e &ummary.... &ummary........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ............. ............... ............... ............1 .....1
4.0
Weir esign.... esign........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ......... ............ .............. .......... ... 2
4.1
heory.... heory........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ............ ........... ... 2
4.2
"rocedur "rocedure... e....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ............ ...............2 .......2
4.4
&'i%%(ay &'i%%(ay esign= ;m.......... ;m.............. ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........... ............2 .....2
4.<
+n>o()!ut> +n>o()!ut>o( o( ?ydrogra'h ?ydrogra'h.... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........5 ....5
<.0
&'i%%(ay &'i%%(ay Route.. Route...... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ............; ......;
5.0
-o%%ector -o%%ector and e%ivery e%ivery -hanne% -hanne% esign.. esign...... ........ ........ ........ ........ ........ ........ .......... .............. ............... ............3 .....3
5.1
heory.... heory........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ............ ........... ... 3
5.2
-hanne% -hanne% Width.... Width........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ...........3 .......3
5.4
Water &ur,ace &ur,ace "ro%e... "ro%e....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ..........9 ....9
5.<
-o%%ector -o%%ector -hanne% -hanne% $ac/(ater $ac/(ater "ro%e... "ro%e....... ........ ........ ........ ............ ............... .............. ............... ..............11 ......11
5.5
e%ivery e%ivery -hanne% -hanne% $ac/(ater $ac/(ater "ro%e.... "ro%e........ ........ ........ ........ ........ ............ ............... .............. ............... ..........11 ..11
5.6
-o%%ector -o%%ector and e%ivery e%ivery -hanne%s -hanne%s &ur,ace &ur,ace "ro% "ro%es.... es........ ........ ........ ........ ......... ............ ...........12 ....12
6.0
&ide -hanne% -hanne% esign... esign....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........... .............. ............... ............... ......... ..14 14
6.1
heory.... heory........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... .............14 .......14
6.2
Water &ur,ace &ur,ace " "ro% ro%e e o, a @%at @%at Rectangu%ar ectangu%ar -hanne%..... -hanne%......... .......... ............. .............. .........1< ..1<
;.0
&ti%%ing &ti%%ing $asin esign.... esign........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ......... ...........16 ......16
;.1
heory.... heory........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... .............16 .......16
;.2
&ti%%ing &ti%%ing $asin Length.. Length...... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ..........16 ......16
;.4
!ther s'ecic s'ecications ations.... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ............. ............... ............... ...........13 ....13
3.0
Re,erenc Re,erences... es....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........... .............. .............. ............... .............19 .....19
A''endi A 10m Wide Weir Resu%ts............. Resu%ts........................ ..................... ..................... ..................... ..................... .............. ...1 1 A''endi $ +n>o( ?ydrogra'h.................. ?ydrogra'h............................. ..................... ..................... ..................... .......................... ................ 2 A''endi - Reservoir Etents......................... Etents................................... ..................... ..................... ............................... ..................... 4 A''endi &ite Ma'..................... Ma'............................... ..................... ..................... ..................... ..................... ............................ .................. < A''endi E $ac/(ater "ro%es................ "ro%es........................... ...................... ..................... ..................... ............................ ................. 5 A''endi @ &ide -hanne% -a%cu%ations......... -a%cu%ations .................... ...................... ............................................ ................................. 6 A''endi # &ite E%evations............................ E%evations....................................... ..................... .......................................... ................................ ;
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
List o, @igures @igure 1 B &im'%ied s/etch o, 'ro'osed s'i%%(ay system.....................................1 @igure 2 B "%ot o, N against !ut>o( ,or a ;m (ide (eir.........................................4 @igure 4 B +n>o()out>o( hydrogra'h ,or a (eir (idth o, ;m..................................5 @igure < B "ro'osed s'i%%(ay system route............................................................. ; @igure 5 B @%o( conditions at the connection bet(een the co%%ector and de%ivery channe%s................................................................................................................ 9 @igure 6 B #radua%%y varied >o(........................................................................... 10 @igure ; B -hanne% and (ater sur,ace e%evation...................................................14 @igure 3 B &ide channe% %ayout..............................................................................14 @igure ; B &ide -hanne% &ur,ace Water "ro%e.....................................................15 @igure 3 B &ti%%ing basin........................................................................................16 @igure 9 B #ra'h sho(ing @roude number against L) 2 ,or sti%%ing basin design...1; @igure 10 B &tageBischarge rating curve ,or River $urn......................................1; @igure 11 B ?ydrau%ic 7um' 'ro%e........................................................................13
List o, ab%es ab%e 1 B Ca%ues ,or ?eight above -rest* !ut>o(* &torage and N..........................4 ab%e 2 B Ca%ues ,or average in>o(* N* change in N and the out>o( rate ,or a ;m (ide (eir............................................................................................................... < ab%e 4 B +n>o()out>o( and vo%ume re%ationshi'...................................................6 ab%e < B istance ,rom transition 'oint* (ater de'th and e%evation va%ues..... ...12 ab%e 5 B Eam'%e sur,ace 'ro%e ca%cu%ation= in'utted va%ues and @roude number ............................................................................................................................ 1< ab%e 6 B Eam'%e sur,ace 'ro%e ca%cu%ation= Ne(ton Ra'hson Method.............15 ab%e ; B &ummary o, side channe% (ater sur,ace 'ro%e....................................15
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
1.0
+ntroduction
Water Engineering Research Ltd (ere commissioned by A.N. !ther and "artners to underta/e a s'i%%(ay system design ,or a reservoir (ith an earth dam at -o%sterda%e* or/shire* connecting the dam to the River $urn do(nstream o, the river. his inc%udes 'roducing an eDcient design o, a (eir* side channe%* co%%ecting channe%* de%ivery channe% and sti%%ing basin. he river do(nstream o, the dam is the River $urn. he c%ient 'rovided a >ood in>o( hydrogra'h ,or a storm event at the 'ro'osed reservoir and in,ormed Water Engineering Research Ltd that a maimum design discharge va%ue o, 120m 4)s ,or the River $urn shou%d be ta/en. he storage va%ue ,or the (eir has been given by the euation=
2
(Eq 1.0)
3
S = 988600 h + 20560 h ( m ) (here h (ater de'th ,rom the 'resent (ater %eve%.
he %eve% o, the river do(nstream o, the dam is to be ta/en as 1;1m A! and the 'resent (ater %eve% in the dam is to be ta/en as 250m A!.
2.0
Eecutive &ummary
A sim'%ied s/etch o, the s'i%%(ay system can be seen in @igure 1. A (eir o, (idth ;m has been designed* giving a maimum out>o( o, 113.4m 4)s. his >o(s into a ;m %ong side channe% (ith a (idth o, 6m. he 140m %ong co%%ector channe% has a s%o'e o, 0.0003* and %eads into a de%ivery channe% o, %ength 555m and s%o'e 0.144. o contro% the e8ects o, a hydrau%ic 7um' at the end o, the de%ivery channe%* a sti%%ing basin has been designed. his has a %ength o, 16m. he (ho%e design is to be constructed ,rom concrete. A''endi @ gives a summary o, the /ey dimensions used and e%evations ,or each e%ement o, the system.
Figure 1 - Si!li"ed s#etch of !ro!osed s!ill$a% s%ste
1
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
4.0
Weir esign
4.1
heory
uring a >ood event the (ater %eve% (i%% rise above the reservoir design (ater %eve%. Additiona% (ater (i%% overto' a (eir crest and 'ass through the s'i%%(ay to a%%o( the (ater to sa,e%y trave% do(nstream. he s'i%%(ay system com'rising o, (eir and s'i%%(ay channe%* is designed to ensure that (ater does not reach the crest o, the dam (hich (ou%d %i/e%y cause signicant 'rob%ems and 'otentia% co%%a'se. he system a%so ensures an a''ro'riate discharge ,or the ca'acity avai%ab%e in the river do(nstream.
4.2
"rocedure
he initia% (eir breadth (as set at 10m ho(ever this gave a maimum out>o( va%ue o, 1<1.9m4)s* above the s'ecied va%ue o, 120m 4)s. he ca%cu%ations (ere re'eated and it (as ,ound that a s'i%%(ay (idth o, ;m (as the o'timum dimension. he ,o%%o(ing ca%cu%ations are based on the ;m s'i%%(ay (idth ho(ever ca%cu%ations ,or a 10m (eir are attached in A''endi A.
4.4
&'i%%(ay esign= ;m
Ca%ues ,or time* t FsG* and the corres'onding in>o(* + Fm 4)sG* (ere etracted ,rom the @%ood +n>o( ?ydrogra'h FA''endi $G. hese (ere tabu%ated and Euation 4.1 (as used to determine the out>o(* ! Fm 4)sG ,or de'th va%ues bet(een 0 and 10m. Ca%ues o, u' to 10m (ere chosen as the to' o, the earth dam resides at 260m A! Fcom'ared to a design norma% (ater %eve% o, 250m A!G there,ore i, the (ater (as to rise above this 10m height di8erence* it (ou%d overto' the dam itse%,. Ca%ues ,or increments o, 0.5m (ere ta/en to ensure that an accurate gra'h cou%d be 'roduced.
3
2 3 Outflow ,O = √ 2 g b C d H 2 ( m /s) 3
(Eq &.0)
A -d va%ue o, 0.62 (as chosen ,or the design as suggested by Nova/* Mo8at* Na%%uri H Narayanan. F2001G. &torage ,or each height increment (as ca%cu%ated using Euation 1.1. N (as then ca%cu%ated using Euation 4.2 F(ith t given in seconds* i.e 1 hour 4600 secondsG.
N =
S O + ∆ t 2
he va%ues ,or out>o(* storage and N ,or height increments o, 0.5m (ere tabu%ated as sho(n in ab%e 1. 2
(Eq &.0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
'able 1 - alues for height aboe crest* out+o$* storage and ,.
Height above crest, H (m)
Oufow, O (m3/s)
Storage ,S (m3)
N (m3/ s)
0 0.5 1 1.5 2 2.5 4 4.5 < <.5 5 5.5 6 6.5 ; ;.5 3 3.5
0.0 <.5 12.3 24.5 46.2 50.; 66.6 34.9 102.5 122.4 1<4.4 165.4 133.< 212.< 24;.< 264.2 290.0 41;.6
0 1<1 23; <4; 590 ;<3 909 10;4 12<1 1<14 153; 1;66 19<; 2142 2421 2512 2;0; 2906
9
4<6.0
9.5
4;5.4
10
<05.4
0 <99<<0 1009160 1529160 2059<<0 2600000 41503<0 4;11960 <234460 <3650<0 5<5;000 60592<0 66;1;60 ;29<560 ;92;6<0 35;1000 922<6<0 9333560 10562;6 0 112<;2< 0 119<200 0
410; 4412 4520
A gra'h o, ! against N F@igure 2G (as then '%otted and the trend%ine ,ound* as sho(n by Euation 4.4. he trend%ine (as assumed to 'ass through the origin as height* out>o(* storage and there,ore N* (ere a%% 0 at the start o, the storm event.
4
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd <50.0 <00.0 450.0 400.0 250.0
,FG 0I2 J 0.0;
Outfow, O (m3/s) 200.0 150.0 100.0 50.0 0.0 0
500 1000 1500 2000 2500 4000 4500 <000
N
Figure - lot of , against Out+o$ for a / $ide $eir
4.4
(Eq &.0)
2
O=0.0000145 N + 0.0662981 N
Euations 4.< and 4.5 (ere used to determine the average in,%o( and KN va%ues. he out>o(* !* cou%d be ,ound using Euation 4.4. +n>o( rate (as ta/en at 1 hour increments* in /ee'ing (ith the t used in 'revious ca%cu%ations* ,rom the in>o( hydrogra'h 'rovided.
4.<
´ =0.5 × ( I 1− I 2 ) Average inflow , I
(Eq &.0)
´ −O ∆ N = I 1
(Eq &.0)
4.5
hese va%ues (ere then tabu%ated* as sho(n in ab%e 2.
'able - alues for aerage in+o$* ,* change in , and the out+o$ rate for a / $ide $eir
Time (hours)
Change in time, Δt (s)
0
Infow rate, I (m3/s) 0
4600 1
0.000
4.000
20
0.1 12.301
15.301 40
<0
1.01 23.9<9
<<.;50
<
Outfow rate, O (m3/s)
4.000
1&
4600
ΔN (m3/s)
0.000
6
2
N (m3/s)
4
4600
4
verage infow rate, ! (m3/s)
2.996
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd 4600 <
59 ;3
4600 5
10<
4600
19;.92;
132
;
4<0.24;
22<
3
519.001
2<<
9
;1<.63;
2<3
10
905.393
B<;.<13
<<
9;.640 B54.640
1113.<3 <
43 4600
102.<13
11;2.11 4
50
21
B<2.;95
55
4600
106.;95
1219.54 1
60
20
B4;.695
6<
4600
110.695
1262.42 6
63
19
B44.159
;4
4600
11<.159
1400.02 1
;3
13
B2;.00<
31
4600
11;.00<
1444.13 0
3<
1;
B12.403
90
4600
""'3*
1460.13 <
96
16
10.3<1
106
4600
11;.159
"3%&'# &
""$
15
<;.3;2
123
4600
112.123
1461.65 1
1<0
"#
9;.959
160
4600
102.0<1
1414.;3 0
130
14
149.331
200
4600
33.119
1215.32 1
220
12
1;0.0<1
223
4600
;1.959
10;5.94 9
246
11
5<.;39 191.211
2<2
4600
43.415 195.635
2<6
4600
2<.246 1;3.;6<
24<
4600
14.690 1<2.410
204
4600
6.32; 9;.1;4
156
4600
22
100.;5<
140
6
56.00<
42
B60.294 1053.19 1
26
5
92.294
36.494
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
4.<
+n>o()!ut>o( ?ydrogra'h
!nce out>o( va%ues (ere ,ound* a hydrogra'h sho(ing in>o( and ou>o( va%ues cou%d be '%otted F@igure 4G. his gives us the maimum out>o(* 'ea/ ,or the (eir. he maimum out>o( ,or a ;m (eir (as ,ound to be 113.4m4)s Fat 1< hoursG* and a,ter severa% iterations o, varying (eir (idth* (as discovered to be the o'timum va%ue ,or the 120m4)s %imit. he 'oint at (hich the in>o( is eua% to the out>o( coincides (ith the reservoirs maimum storage. 400 250 200
+ow (m3/s)
+n>o(
150
Moving average F+n>o(G !ut>o(
100
Moving average F!ut>o(G
50 0 0
5
10
15
20
25
Time (hours) Figure & 2n+o$3out+o$ h%drogra!h for a $eir $idth of /
sing the average in>o( and out>o( rate during any given hour* the net change in vo%ume can be ca%cu%ated as sho(n in ab%e 4. his tab%e sho(s a maimum change in vo%ume o, <*;40*000m4. @rom rough ca%cu%ations o, the area change bet(een 250m A! and 260m A! and assuming area changes %inear%y (ith height over the 10m* the vo%ume ca'acity o, the reservoir is 11*;30*000m 4 be,ore overto''ing the dam. ?ence it is 'redicted that the (ater %eve% (i%% reach a maimum o, 25ood event. his gives a to%erance* ensuring that the dam (i%% not be overto''ed in the occurrence o, a 'otentia%%y %arger >ood event or reduction in out>o( due to b%oc/age. Eam'%e ca%cu%ations ,or ab%e 4 va%ues ,or the 2 nd hour are sho(n be%o( by Euations 4.6 4.10. Average in>o( and out>o( rates (ere ta/en ,rom ab%e 2 Fsee numbers in ita%icsG. A''endi - sho(s a ma' o, the area.
Inflow during thehour = Average inflow rate , I´ × 3600
¿ 13 × 3600= 46,800m 3
6
(Eq &.0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
Total volume ∈¿ Inflow during hour 1 + hour 2
(Eq &.0)
¿ 10,800 + 46,800=57,600m 3
Outflow duringthe hour= Averageinflow rate , ´ O × 3600
(Eq &.0)
¿( 0.199 + 1.051 )/ 2 × 3600=2,250m3
Total volume out =Outflow during hour 1 + hour 2 ¿ 358 + 2,250 =2,609
m
(Eq &.0)
3
Change ∈ volume =Total volume ∈−total volume out
(Eq &.0)
¿ 57,600 −2,609=54,991m3
'able & - 2n+o$3out+o$ and olue relationshi!
Hour
Infow -uring the hour (m3)
Tota voume in (m3)
Outfow -uring the hour (m3)
Tota voume out (m3)
Change in voume (m3)
1st 2nd 4rd |
10*300 <6*300 103*000 212*<00 4;<*<00 561*600 ;40*300 3<2*<00 335*600 3;1*200 320*300 ;20*000 5;6*000 <60*300 431*600 42<*000 291*600 262*300 240*<00 193*000 153*<00 115*200
10*300 5;*600 165*600 4;3*000 ;52*<00 1*41<*000 2*0<<*300 2*33;*200 4*;;2*300 <*6<<*000 5*<6<*300 6*13<*300 6*;60*300 ;*221*600 ;*604*200 ;*92;*200 3*213*300 3*<31*600 3*;12*000 3*910*000 9*063*<00 9*134*600
453 2*250 ;*235 1;*631 46*941 63*266 112*590 16;*536 223*1<5 233*149 4<2*23; 435*50< <12*;13 <24*3<1 <24*561 <16*09< <0<*;4; 491*<32 4;6*534 460*036 4<1*361 421*64<
453 2*609 9*394 2;*5;< 6<*505 142*;;2 2<5*462 <12*9<3 6<1*094 929*242 1*2;1*519 1*65;*02< 2*069*;<1 2*<94*532 2*91;*1<4 4*444*24; 4*;4;*9;< <*129*<56 <*506*0<0 <*366*125 5*20;*936 5*529*620
10*<<2 5<*991 155*;0; 450*<26 63;*395 1*131*223 1*;99*<43 2*<;<*252 4*141*;0; 4*;1<*;63 <*194*231 <*52;*;;6 <*691*059 <*;23*013 <*636*05; <*594*964 <*<30*326 <*452*1<< <*205*960 <*0<4*3;5 4*360*<1< 4*654*930
;
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
<.0
&'i%%(ay Route
@igure < be%o( sho(s the 'ro'osed route ,or the s'i%%(ay system.
Figure 4 - ro!osed s!ill$a% s%ste route
!ne o, the 'rimary reasons ,or choosing this route is that it a%%o(s ,or a re%ative%y short de%ivery and co%%ector channe% to be used* there,ore minimising the materia%s reuired ,or construction. +t shou%d be noted that the detai% o, the bend bet(een the co%%ector and de%ivery channe%s has not been designed. his (i%% reuire rein,orcing to account ,or the ,orce o, the (ater hitting the side o, the channe% at this 'oint. o reduce the environmenta% e8ects on the site* the de%ivery channe% is designed to c%ose%y ,o%%o( the contour o, the s%o'e reducing the cut and %% reuired. his ,urther reduces the cost o, the system. -onstructing the s'i%%(ay system to the south o, the dam ensures that the (ood%and to the north (i%% not be %ost. +t a%so avoids the crags north o, the dam. When considering the %ong term durabi%ity and sustainabi%ity o, the 'ro7ect* it (as decided that a%% o, the e%ements (i%% be constructed ,rom concrete. he sti%%ing basin must be constructed o, concrete to resist scour and it is essentia% that a%% connections bet(een e%ements are >ush to ensure no crac/ing or %ea/ing occurs* there,ore ma/ing a ,u%%y concrete design the most sensib%e and eDcient o'tion.
3
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
5.0
-o%%ector and e%ivery -hanne% esign
5.1
heory
A channe% is reuired to trans'ort (ater ,rom the side channe% to river %eve%. his has been bro/en do(n into a co%%ector channe% and de%ivery channe%* (ith a mi%d s%o'e and stee' s%o'e res'ective%y. hey have been designed to t (ith the contours o, the eisting s%o'e and the co%%ector channe% ensures that the (ater >o( is %imited.
5.2
-hanne% Width
A channe% (idth o, 6m (as chosen throughout the design. his va%ue 'rovides an economica% design com'ared to a (ider channe% as it reuires %ess materia%s. A narro(er (idth (ou%d increase the (ater de'th in the channe% and (ou%d there,ore reuire dee'er side (a%%s* increasing construction time* cost and materia% uantity. his (ou%d corres'ond to an increase in the %ength o, the sti%%ing basin reuired and (ou%d %ead to a %ess environmenta%%y ,riend%y design. &evera% iterations (ere carried out at varying (idths to determine norma% height and there,ore the o'timum channe% (idth ,or the system. he ca%cu%ations %ed to the decision to 'rovide a (idth o, 6m. he critica% de'th* yc (as ca%cu%ated at the >o( transition bet(een the co%%ector channe% and the de%ivery channe%* using Euation 5.1.
√ √
2
√
2
2 q 3 ( / ! ) 3 ( 118.3 / 6 ) = = =3.409m y c = g g g 3
Where g 9.31 m 2)s.
(Eq .0)
he eva%uation o, the critica% de'th is reuired ,or the so%ution o, most ra'id%y varied and gradua%%y varied >o( 'rob%ems. As can be seen ,rom Euation 5.1* the critica% de'th is de'endent on discharge so a critica% de'th %ine ,or a given discharge can be dra(n on the (ater sur,ace e%evation dra(ing* as sho(n by the dashed %ine in @igure 5. An abru't change in the geometry o, the channe% resu%ts in the >o( sudden%y changing its ty'e. A high%y su'ercritica% >o(* ,or eam'%e* >o(ing on a very stee' s%o'e and then >o(ing into mi%d or horionta% s%o'e (i%% transition into a subcritica% >o( through a hydrau%ic 7um' mechanism. +n the design o, the co%%ector and de%ivery channe%s* the channe% s%o'e changes ,rom mi%d to stee'. his resu%ts in the transition ,rom subcritica% to su'ercritica% >o(* (ith critica% de'th occurring eact%y at the 'oint o, transition. his is out%ined by @igure 5.
9
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
Figure - Flo$ conditions at the connection bet$een the collector and delier% channels
5.4
Water &ur,ace "ro%e
he rst ste' in dening the mi%d s%o'e o, the channe% (as to ca%cu%ate the critica% s%o'e ,or the given discharge and channe% (idth* (hich (ou%d enab%e the s%o'e to be dened as mi%d. his is sho(n in Euation 5.2. 2
g n g ( 0.012 ) S c = 1/ 3 = 1 /3 3.409 y c 2
=0.00094
(Eq .0)
here,ore* an acce'tab%e s%o'e ,or the co%%ector channe% is &0 0.0003. he horionta% %ength o, the co%%ector channe% is 140m* as ,ound ,rom the ma' Fsee A''endi G. he s%o'e ,or the de%ivery channe% (as then ca%cu%ated. sing the ma' FA''endi G* a horionta% %ength o, 555m is ,ound. $y ta/ing the e%evation o, the transition 'oint to be 2<5m A! and ta/ing a(ay the change in height o, the co%%ector s%o'e F0.0003O140G* this gives a maimum %eve% o, 2<<.9m A! ,or the de%ivery channe%. #iven that the river %eve% is ta/en as 1;1m A! Fas 'er the brie,G* a ,a%% o, ;4.9m F2<<.9B1;1G is 'resent in the de%ivery channe%. his gives a s%o'e o, & 0 K?)L ;4.9)555 0.144 ,or the stee' s%o'e. As 'revious%y e'%ained* the co%%ector channe% has a mi%d s%o'e and that the de%ivery channe% has a stee' s%o'e. he critica% de'th (as ,ound to be 4.<09m and the norma% de'ths (ere ,ound using tria% and error (ith ManningPs euation Fsee Euation 5.4G. he norma% de'th is y n 5.499m ,or the co%%ector channe% and yn 0.354 ,or the de%ivery channe%.
hnew=
[ ][ n √ S f
3 5
b + 2 hold
10
b
]
2 5
(Eq .0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
he 'osition o, the contro% 'oint is the 'oint o, transition bet(een the t(o >o(s as this is the 'oint (here the re%ationshi' bet(een head and discharge is /no(n. Additiona%%y=
. e0t o, this 'oint the >o( is subcritica% and @rQ1. his means that (ater ve%ocityQ(ave ve%ocity and disturbances trave% u'stream and do(nstream. here,ore* the 'ro%es are contro%%ed ,rom a 'oint do(nstream Fi.e. the transition 'ointG.
. 1ight o, this 'oint the >o( is su'ercritica% and @r1. his means that (ater ve%ocity(ave ve%ocity and disturbances trave% do(nstream. here,ore* the 'ro%es are contro%%ed ,rom a 'oint u'stream Fi.e. the transition 'ointG. +t is a%so use,u% to derive the genera% euation o, gradua%%y varied >o(* as sho(n be%o(. @rom $ernou%%i= 2
" # H = y + 2g
+ $ (m)
(Eq .0)
Figure 5 - 6raduall% aried +o$
i8erentiating (ith res'ect to gives Euation 5.5=
(
2
dH d " # = y + d% d% 2g Where &, is the ,riction s%o'e
11
)
+ $ =−Sf
(Eq .0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
(
2
)
− d " # = d$ − S f ,but − d$ = S0 &o y + 2g d% d% d% d 'S d%
=S 0− S f
( ) 2
2 2 2 d 'S d # d A d 1 dA dA = y + =1 + , but = ! &o ( ta(ing" =1 )= y + 2 2g 2g 2 g dy A dy dy dy dy dy
(
)
2
d 'S
( )
2
−2 ! =1 + ! =1 − 3 3 2 g A dy A g 2
2
( )
A%so )r =
d 'S
2 2 2 2 # # A ! = = = hence A A g A 3 √ gy g g ! !
d ' &= dy ( 1 − )r
2
)
2
− =dy 1 )r d% = S 0− S f S 0− S f
No( the direct ste' method is used to nd the distances ,or corres'onding de'ths ,or regu%ar channe%s. @or this 'ur'ose the euation is re(ritten as F-had(ic/ et a%.G=
(
2
1− )r *% = *y S 0−S f
5.<
)
(Eq .0)
mean
-o%%ector -hanne% $ac/(ater "ro%e
he ,o%%o(ing in'ut data has been estab%ished ,or the co%%ector channe%= 113.4 m4)s* $6m* n0.012* & 00.003* yn5.499m* yc4.<09m. he n va%ue ,or a concrete channe% (as chosen to be 0.012 in accordance (ith -had(ic/* Mor,ett H $orth(ic/ F2014G. 20 ste's (ith a de'th change o, 0.1m (ere used to achieve the desired %eve% o, accuracy. he rst ca%cu%ation (as carried out (ith the de'th eua% to y c and the %ast ca%cu%ation (as ,or y 5m. As the %ength o, the de%ivery channe% is 140m* the corres'onding va%ue o, de'th at this %ocation (as ,ound through the direct ste' method (ith additiona% tria% and error ad7ustment in order to obtain the eact va%ue. his (as ,ound to be a va%ue o, <.0<3m* as can be seen in the tab%e in A''endi E.
12
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd +t is (orth noting that had the channe% %ength at norma% de'th been reuired* a 2S increase (ou%d have been added to the norma% de'th va%ue. +t can be seen ,rom the tab%e that y nyyc* &, &0 and @r2Q1* hence the sur,ace 'ro%e occu'ies region 2 ,or a mi%d s%o'e and dy)d is negative. As yTy n* & , T &0 and dy)dT0.
5.5
e%ivery -hanne% $ac/(ater "ro%e
he ,o%%o(ing in'ut data has been estab%ished ,or the de%ivery channe%= 113.4 m4)s* $6m* n0.012* & 00.144* yn0.35<* yc4.<09m. he rst ca%cu%ation (as carried out (ith the de'th eua% to y c and the %ast ca%cu%ation (as at the (ater de'th euiva%ent to 555m. his de'th (as ,ound to be 0.35
5.6
-o%%ector and e%ivery -hanne%s &ur,ace "ro%es
he co%%ector and de%ivery channe%s sur,ace 'ro%es (ere tabu%ated Fsee ab%e
'able 4 - 7istance fro transition !oint* $ater de!th and eleation alues
2istance 0rom transition oint, 4 (m)
5evation ,6 (m)
7ater -eth, 8 (m)
7ater sur0ace eevation, 698 (m)
B129.362 B103.<35 B;1.<6; B<4.425 B22.955 B9.<<< B2.02< 0.000 0.0<4 0.25; 0.634 1.463 2.4;< 4.;35 5.;10 3.402 11.;;; 16.<51 22.304 41.595
2<2.000 2<1.934 2<1.954 2<1.941 2<1.91< 2<1.90< 2<1.393 2<1.396 2<1.390 2<1.362 2<1.305 2<1.;1< 2<1.530 2<1.494 2<1.14; 2<0.;92 2<0.440 249.;03 243.364 24;.69<
<.0<3 <.000 4.900 4.300 4.;00 4.600 4.500 4.<09 4.400 4.150 4.000 2.350 2.;00 2.550 2.<00 2.250 2.100 1.950 1.300 1.650
2<6.0<3 2<5.934 2<5.354 2<5.;41 2<5.61< 2<5.50< 2<5.493 2<5.405 2<5.190 2<5.012 2<<.305 2<<.56< 2<<.230 2<4.9<4 2<4.54; 2<4.0<2 2<2.<40 2<1.653 2<0.664 249.4<<
14
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd <<.126 62.326 92.9<< 1<9.142 40;.204 555.000
246.02; 244.5<0 229.54< 222.061 201.043 163.031
1.500 1.450 1.200 1.050 0.900 0.35<
24;.52; 24<.390 240.;4< 224.111 201.943 163.945
O2 (m)
B1<0
B60
20
100
130
260
4<0
<20
500
Hori:onta arrangement in reation to the transition oint (m)
Figure / - 8hannel and $ater surface eleation
6.0 6.1
&ide -hanne% esign heory
A side channe% is norma%%y incor'orated into a s'i%%(ay system design i, it is not 'ossib%e to have a direct overB,a%% s'i%%(ay. @or this reason* the 'ro'osed system reuires a side channe% due to the 90 degree change in direction bet(een the (eir and co%%ector channe%. A sim'%e s/etch o, a side channe% can be seen in @igure 3. @or the 'ro'osed system* a horionta% rectangu%ar channe% has been designed to sim'%i,y constructabi%ity* saving time and cost.
1<
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
Figure 9 - Side channel la%out
6.2
Water &ur,ace "ro%e o, a @%at Rectangu%ar -hanne%
+n order to nd the (ater sur,ace 'ro%e in the side channe%* the momentum euation bet(een t(o given 'oints (ithin the channe% (as a''%ied* as sho(n in Euation 6.1. A,ter combining a%% re%evant terms momentum 'assing* (eight o, body o, (ater bet(een 'oints* ,riction ,orce and hydrostatic 'ressure at both 'oints and sim'%i,ying by using substitutions and removing neg%igib%e terms* the sur,ace 'ro%e o, a rectangu%ar can be ,ound by Euation 6.2.
+omentum= - (kgm/s)
() ( % .
Wher e
and
?enc e
2
=
)
( )
1 y 1 y 1+ − 2 2 2 ) o y o 2 ) o y o
¿2
2
q . ) o = 2 3 g b y o 2
q
¿
=
(Eq 5.0)
2
) o = 2 3 g b y o
15
(Eq 5.0)
(Eq 5.0)
(Eq 5.0)
.
2
3
(Eq 5.0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd Where ischarge* L&'i%%(ay %ength* b&'i%%(ay (idth* y oRe,erence de'th* ye'th. @or this design yo is the /no(n de'th at the discharge o, the side channe% as ca%cu%ated in &ection 5.< to be <.0<3m. he (idth o, the side channe% is 6m to ensure continuity (ith the co%%ector and de%ivery channe%s* and has %ength ;m eua% to the (idth o, the (eir* as sho(n in &ection 4.4* ,eeding into the side channe%. +n order to obtain a ,u%% 'ro%e a range o, (ater heights (ere obtained at distances ranging ,rom 0B;m a%ong the %ength o, the channe%. he chosen va%ue (as substituted into the ,ormu%a (ith a%% other /no(n va%ues. he Ne(ton Ra'hson method (as then used to com'ute the de'th o, (ater at that corres'onding 'osition. An eam'%e o, this is sho(n in ab%e 5 ,or 0m re%ative to yo at ;m* the ca%cu%ations used to com'ute this are sho(n in A''endi @.
'able - E:a!le surface !ro"le calculation; in!utted alues and Froude nuber
7i-th ength ;
m m m4)s m
6 ; 113.4 <.0<3 0.59;<15 0
B m
'able 5 - E:a!le surface !ro"le calculation; ,e$ton Ra!hson
8 o- (m) 5 6.<0<54621< 6.0429<<<24 5.99;<145; his method (as meter interva%s 5.99;096594 sur,ace 'ro%e to corres'onding 5.99;096563 distance ,rom the channe% are sho(n in ab%e ;.
>? O-
> O-
0.<9252 1 1.0933< 4 0.92490 2 0.90;;2 2 0.90;5; 3 0.90;5; 3
B 0.691;6 0.<0342 1 0.04232 ; 0.00023 3 2.23EB 03 0
8 new (m) 6.<0<54 6 6.0429< < 5.99;<1 < 5.99;09 ; 5.99;09 ; 5.99;09 ;
'able / - Suar% of side channel $ater surface !ro"le
2istance (m)
H (m)
0
6.00
16
re'eated at 1 a%%o(ing a be 'roduced. he heights at each start o, the side
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd 1 2 4 < 5 6 ;
5.9; 5.91 5.;3 5.60 5.44 <.91 <.05
his data has been used to create a gra'h so that the sur,ace can be seen visua%%y* as sho(n in Error= Re,erence source not ,ound.
;.0 6.0 5.0 <.0
7ater height (m)
4.0 2.0 1.0 0.0 0.0
1.0
2.0
4.0
<.0
5.0
6.0
;.0
3.0
2istance (m)
Figure - Side 8hannel Surface Water ro"le
;.0 ;.1
&ti%%ing $asin esign heory
@%o( discharged ,rom the out%et o, the de%ivery channe% is o,ten high%y su'ercritica% and i, this >o( is not contro%%ed* it can %ead to severe erosion at the toe o, the dam. +t is there,ore necessary to dissi'ate the energy and return the (ater %eve% to a norma% de'th a''ro'riate ,or the river %eve% and bed s%o'e. A sti%%ing basin is one (ay in (hich this can be done* and a genera% design can be seen in @igure 10.
1;
Figure 10 - Stilling basin
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
;.2
&ti%%ing $asin Length
+n &ection 5.5 it (as ,ound that ,or the de%ivery channe% design the >o( reaches norma% de'th (ithin its %ength and hence remains at norma% de'th ,or the na% section o, the channe%. his de'th* 10.354m* can be used a%ong (ith its associated ve%ocity as ca%cu%ated in Euation ;.1 in order to nd the @roude number* as sho(n in Euation ;.2.
# 1=
)r =
(Eq /.0)
118.3 = =23.1 m/s b / 1 6 × 0.853
# 1
√ g /1
=
23.1
√ 9.81 × 0.853
=7.99
≅
8
(Eq /.0)
+n order to obtain an initia% estimate o, %ength the & $ureau o, Rec%amation guide (as used. With a @roude number o, 3 and >o( o, 24.1m)s a ty'e ++ sti%%ing basin F,or @r<.5* C20m)sG has been designed* (hich shou%d have a %ength o, <.45y4* (here y4 is the tai%(ater de'th. According to the sti%%ing basin design s'ecied F&hiono* 2015aG a ratio o, %ength to tai%(ater de'th* i.e. de'th a,ter the sti%%ing basin* can be ,ound using @igure 11. #iven a @roude number o, 3 the gra'h out'uts L) 2 <.2* (hich is in %ine (ith our initia% estimate.
Figure 11 - 6ra!h sho$ing Froude nuber against L37 for stilling basin design
13
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd +n order to determine tai%(ater de'th the stageBdischarge rating curve (as used* see @igure 12. ischarge is /no(n to be 113.4 m4)s at the 'oint* and e%evation* at (hich the s'i%%(ay reB7oins the River $urn. @rom @igure 12* this means that the stage* or tai%(ater de'th* is 4.3m. sing the above mentioned ratio the %ength o, the sti%%ing basin (as ,ound to be 15.96m as sho(n by Euation ;.4.
. = 4.2 0 .= 4.2 /2= 4.2 × 3.8=15.96 m / 2
(Eq /.0)
Figure 1 - Stage-7ischarge rating cure for Rier =urn
;.4
!ther s'ecications
he @roude number can a%so be used to determine the 'ro%e o, the hydrau%ic 7um' ,rom @igure 14. @or the 'ro'osed design the ang%e o, the hydrau%ic 7um' (i%% be U9V. he sti%%ing basin (i%% have a series o, chutes and dentated si%%s in order to ,orce the hydrau%ic 7um' (ithin this region* as sho(n in @igure 10. At the u'stream end the chutes (i%% have the ,o%%o(ing dimensions=
h 1= / 1= w 1 =& 1=0.853m
19
(Eq /.0)
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd At the do(nstream end the si%%s are to be dimensioned as sho(n by Euations ;.5B;.;.
& 2= w2=0.15 × / 2 =0.15 ×3.8= 0.57m
(Eq /.0)
Top of sill = 0.002× / 2=0.002 ×3.8= 0.0076m
(Eq /.0)
h2= 0.2 × / 2=0.2 × 3.8= 0.76m
(Eq /.0)
Figure 1& - >%draulic ?u! !ro"le
3.0
-onc%usion
+n order to come u' (ith an integrated design so%ution ,or the >ood ris/ 'osed on the dam* (e had to go through the 'rocess o, designing the individua% 'arts o, the (ho%e conguration= name%y (eir* side channe%* co%%ector channe%* de%ivery channe% and sti%%ing basin. he 'hi%oso'hy behind our so%ution (as to ta/e into account the s'ecics o, the dam and its surroundings and aim to 'rovide a design arrangement (hich is both economica% and ,easib%e. @or this tas/ (e had to im'%ement the /no(%edge and 'rinci'%e in hydrau%ics and (ater engineering acuired throughout our three years o, our course. his meant* rst* (e either 20
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd made an educated guess (e considered to be o'tima% about the design 'arameters or in other cases (e ,ound those 'arameters by tria% and error. hen (e too/ those 'arameters and used them (ith ,ormu%ae and com'utationa% mode%s in order to test the va%idity o, our so%utions. @or each ste' o, the design* (e have given an e'%anation o, the hydrau%ic 'rinci'%es e'%aining the 'henomena (e (ere designing ,or. -onstructabi%ity considerations have a%so been mentioned brie>y throughout the re'ort to and their so%utions (ere given to 7usti,y some o, the design choices (e have ta/en. o conc%ude* (e be%ieve that the design and re'ort (e have 'roduced is a concise e8ort (hich ,u%%y satises the needs and reuirements o, our c%ient.
9.0
Re,erences
&hiono* .* 2015a. S!ill$a% 7esign 8ourse$or# . Loughborough niversity. &hiono* .* 2015b. S!ill$a%s. Loughborough niversity. &hiono* .* 2015c. 6raduall% aried Flo$. Loughborough niversity. -had(ic/* A.:.* Mor,ett* :.- and $orth(ic/* M.* 2014. >%draulics in ciil and enironental engineering. 5th edition. $oca Raton= -R- "ress. Nova/* ".* Mo8at* A.+.$.* Na%%uri* -. and Narayanan* R.* 2001. >%draulic Structures. 4rd edition. &'on "ress.
21
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi A 10m Wide Weir Resu%ts
22
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi $ +n>o( ?ydrogra'h
24
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi - Reservoir Etents
2<
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi &ite Ma'
25
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi E $ac/(ater "ro%es
26
-o%sterda%e &'i%%(ay &ystem esign Water Engineering Research Ltd
A''endi @ &ide -hanne% -a%cu%ations
2;
