An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 1
EXPERIMENTAL APPROACH TO THE HYDRAULICS OF VERTICAL SLOT FISHWAYS
By J. PUERTAS1, A . Membe , ASCE, L. PENA2, T. TEIJEIRO3
h ps://ascelib a y.o g/doi/10.1061/%28ASCE%290733-9429%282004%29130%3A1%2810%29Abs ac :
“This ma e ial may be downloaded o pe sonal use only. Any o he use equi es p io pe mission o he Ame ican
Socie y o Ci il Enginee s. This ma e ial be ound a URL/link o abs ac in he ASCE Lib a y o Ci il Enginee ing
Da abase”
Fishways a e hyd aulic s uc u es ha enable ish o go h ough ans e se obs uc ions o con inue hei ups eam mig a ions.
This pape p esen s he esul s o a scale model o a e ical slo ishway. The pe o mance o wo pa icula designs o e ical
slo ishways o wo di e en slopes was s udied in a wide ange o discha ges. Wa e dep hs we e measu ed in almos he
whole su ace o pools. A linea ela ion be ween dimensionless discha ge and dep h o low, and he same low pa e ns o
each design we e ound. Wi h an acous ic Dopple elocime e (ADV), h ee-dimensional eloci ies we e measu ed a se e al
le els in he en i e pool o de ec he s uc u e o he low and quan i y eloci y dis ibu ion. Two di e en egions in low
pa e ns we e ound: a di ec low egion cha ac e ized by maximum eloci ies; and a eci cula ion egion, de ined by low
eloci ies and ho izon al eddies. Fo a gi en slope, he eloci y a any poin o he pool (pa icula ly a he slo ) may be
conside ed independen o he discha ge and cons an wi h he dep h. Some sugges ions on kine ic u bulen ene gy a e also
made.
INTRODUCTION
Fish popula ions in i e s a e highly dependen on he cha ac e is ics o hei aqua ic habi a , since i p o ides he
suppo o all hei biological unc ions. This dependency is mo e c i ical in he case o mig a o y ish which equi e di e en
habi a s o comple e hei li e cycle (La inie e al. 1998). Anad omous ish species (Salmonidae, Clupeidae,
Pe omyzon idae...) ha e o o e come se e al obs acles in hei mig a ion ups eam which may p e en hei ee ascension o
he spawning a eas. These obs uc ions, which can be o na u al o igin (go ges, apids, wa e alls) o man-made (usually
hyd aulics wo ks o di e en ypes: dams, ba ie s, wa e mills...), p e en , as a di ec consequence, he na u al mig a ions o
ish up and in some cases downs eam. This es ic ion o he “ ee ci cula ion” o ish is known as he ba ie e ec , which
makes i impossible o he mig a o y ish o comple e hei li e cycle. I also isola es and sepa a es ish popula ion, d as ically
diminishing he numbe o local species. Fish passage s uc u es and e ical slo ishways in pa icula y o minimize he
An expe imen al app oach o he hyd aulics o e ical slo ishways.
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1 P o ., Ci il Enginee ing School, A Co uña Uni e si y, Campus de El iña, s/n, 15912, A Co uña, Tel: (+34)981 167000 Ex . 5185, Fax:
(+34) 981167179, E-mail: [email p o ec ed]c.es
2 Res., CITEEC, A Co uña Uni e si y, Campus de El iña, s/n, 15912, A Co uña, Tel: (+34)981 167000 Ex . 5185, Fax: (+34) 981167179, E-
mail: ci [email protected]
3 P o ., EPS, San iago de Compos ela Uni e si y, Be na dino Pa do Ou o, s/n, 27002, Lugo, Tel: (+ 34) 982 223 325 Ex 23250, Fax: (+ 34)
982 241 835, E-mail: [email protected]
nega i e e ec s caused by ans e se hyd aulics cons uc ions and o acili a e he exploi a ion o species o e a wide
ex ension (La inie e al. 1999). Fo any ishway o be conside ed e ec i e, i mus allow ish o easy access o he ishway
inle , as well as le ing ish go h ough he ishway wi h no delay, s ess o inju y, so ha hey can head o hei spawning a eas
in a na u al way.
Al hough biological and hyd aulic aspec s a e essen ial o de eloping a good design o a speci ic ishway and,
he e o e, being able o minimize nega i e impac s on mig a o y i e auna, i mus be emembe ed ha all damages ha migh
be caused by an obs acle can ne e be ully compensa ed by ishways.
The ea lies e ical slo ishways was de eloped by Milo C. Bell and buil a he Hell´s Ga e on F ase Ri e , Canada
(Clay, C.H. 1995). A e ical slo ishway consis s o a ec angula channel wi h a sloping bed di ided by ba les in o a numbe
o pools. Wa e a els down he channel h ough e ical slo s, passing om one pool o he nex one below (Wu e al., 1999)
un il i inally eaches he i e pas he obs acle. The di e ence in wa e le el be ween he uppe and lowe end o he ishway
is di ided in o a numbe o small alls (Raja a nam e al. 1986). Wa e lows h ough he slo like a je and i s ene gy becomes
dissipa ed by he mixing o he je in he pool.
Fishways mus a ac ish owa ds he inle and le hem ascend, so ha he wa e eloci y in he lume mus no
o e come he ish bu s speed (Beach, B.H., 1984). Ve ical slo ishway mus also p o ide es ing zones in he pools o he
mig a o y ish so ha hey may eco e hei swimming abili y a e his g ea exe ion. Ve ical slo ishways a e widely used
in small dams (<5 m.) and na u al obs uc ions whe e discha ges a e uncon ollable o unde go g ea a ia ions. The
o e whelming ad an age o e ical slo ishways is hei adap abili y o a ia ions in wa e le els while hei hyd aulic
pe o mance emains s able.
A s udy o hyd aulic cha ac e is ics o e ical slo ishways in labo a o y model was pe o med. A he same ime, no
included he e, a nume ical simula ion o he low was conduc ed using he expe imen al da a ob ained o calib a e a signi ican
model based on he Fini e Volume Me hod, including u bulence e ms.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
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P e ious expe imen al esea ch on he hyd aulics o e ical slo ishways was aken in o accoun . In he esea ch
p ojec ca ied ou a he Uni e si y o Albe a (Canada) by Raja a nam e al. (1986, 1992, 1999) 18 di e en designs we e
s udied o he ollowing ange o slopes So=5, 10 and 15%. In all o hem i was ound a linea ela ionship be ween
dimensionless discha ge Q* and a ela i e low dep h yo/bo exis ed, whe e Q* was de ined as 5*
oobgSQQ , Q being he
discha ge o he ishway, So he geome ical slope o he ishway and bo he slo wid h; yo is he a e age dep h o low measu ed
a he cen e o he pools. Taking in o accoun hyd aulic c i e ia such as u bulence le els, he ci cula ion pa e ns in he pool,
he je eloci ies and ene gy dissipa ion and some o he ac o s like simplici y o design o inancial cos , hey concluded ha
o 8bo wide and 10bo long pool designs, he ishway pe o mance was sa is ac o y. On he basis o he designs s udied,
Raja a nam e al. (1992) ecommended designs 6, 16 and 18 o p ac ical use (Fig. 1). The ecommenda ions o La inie e al.
(1998) o pool dimensions also en ail a leng h o 8-10b and a wid h o 6-8b, and a e e y simila o he ones p oposed by
Raja a nam e al. (1992). Wu e al. (1999) wen u he in he s udy o design 18, and concluded ha o a slope o 5%, he
main low a els om one slo o he nex h ough he pool as a 2D cu ed je wi h wo eci cula ion egions, one on each side.
Fo slopes o 10% and 20% he main low is 3D. The low a he slo was no pe pendicula o he slo . The maximum eloci y
a he slo was app oxima ely equal o hg2.
This pape , in an a emp o con inue he line o he esea ch begun by Wu e al. (1999) on he de ailed s udy o he
designs ecommended as e ec i e by Raja a nam e al. (1992), ocuses on an expe imen al hyd aulic cha ac e iza ion o a scale
model o he o he wo pa icula e ical slo ishway designs: he so-called design T1 (simila o design 16) and design T2
(simila o design 6). Sligh changes we e made in hei cons uc ion in o de o adap hem o he exis ing acili ies a he
hyd aulic esea ch labo a o y. The con igu a ions and dimensions o pools a e shown in Fig. 2b and Fig. 2c.
To s udy low pa e ns o bo h design, an expe imen al p og am was planned and a de ailed s udy o dep h and
eloci y ields was conduced, since hese a e he wo mos impo an pa ame e s on he hyd aulic pe o mance o e ical slo
ishway. The ela ionship be ween he discha ge and he dep h is he main ac o used o de e mine he hyd aulic pe o mance
o he ishway. Dep h pa e ns a e impo an in es ablishing he wa e dis ibu ion in pools o ensu e a minimum wa e le el,
enough o allow he passage o he species in ques ion, as well as in adop ing design c i e ia o he ishway heigh . In addi ion,
he eloci y alue mus be compa ible wi h swimming capabili ies o he species conce ned and i should de e mine low
eloci y low zones and c i ical zones which ish will equi e bu s speed (Beach, M.H. 1984).
An expe imen al app oach o he hyd aulics o e ical slo ishways.
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EXPERIMENTAL ARRANGEMENT
The expe imen al wo k was ca ied ou a he CITEEC (Cen o de Inno ación Tecnolóxica en Edi icación e Enxeñe ía
Ci il) a he Uni e sidade da Co uña (Spain). The ishway scale model consis ed o a me allic s uc u e 12 m long wi h a 1x1
m2 ec angula sec ion. The ishway scale model was cons uc ed in such a way as o be able o adop di e en slopes. The
ishway was di ided in o ele en pools: a head ank ecei ing he wa e om an ups eam ese oi , nine ac i e pools and a
ail ank. The i s ou pools p esen ed a T2 con igu a ion, he nex we e ansi ion ype pools and he las ou pools had a T1
con igu a ion. The lume bed, side walls and he ba les sepa a ing he pools we e made o anspa en plexiglass shee s (1 cm
hick) making i possible o obse e he low. Ba les we e always e ical, despi e o he slope in he ishway model. The
expe imen al measu emen s we e eco ded in pools numbe 3 and 7 (Fig. 2a). Wa e was supplied by a hyd aulic closed ci cui .
Discha ges was measu ed by means o an elec omagne ic lowme e . All he elemen s in he hyd aulic ci cui we e au oma ed
and hei ope a ion was cen alized in a con ol compu e .
Th ee a iables we e de ined o he a angemen o he expe imen al s udy: ishway slope, discha ge, and bounda y
condi ion. The slopes mos equen ly used a hese ypes o s uc u es a y be ween 5-10% (Clay, C.H. 1995 and La inie e
al. 1998), hence i was decided o e alua e he ishway o wo o hem, he i s nea he lowe limi , (So=5,7%) and he
second, in he icini y o he uppe limi (So=10,054%).
The slope alue and physical dimensions o he pools de e mine he limi s o discha ge ange ha he model is able o
assume; he maximum discha ge employed was 125 l/s, o a slope o So=10,054%. The minimum discha ge p o iding enough
wa e dep h o he unc ioning o he measu emen ins umen s was se close o 15 l/s and 35 l/s o So= 5,7% and So=10,054%
espec i ely. Tes discha ges di e ed app oxima ely by 10 l/s be ween hem.
A concep ual s a e o uni o m low (Raja a nam e al. 1986, 1992) was used, so ha he mean dep h measu ed a he
middle ans e se sec ion was he same in all he pools. A he lowe end o he lume a ailga e, causing o e low was used o
each he necessa y bounda y condi ions o he uni o m low in each discha ge-slope ela ionship.
A ca esian posi ione was placed o e he expe imen al pools in o de o au oma e he posi ioning o he measu emen
ins umen s (Fig. 3). The MAC (Mul iuse Axis Con ol) uns he mo emen o he elec ic mo o s (one on each ca esian axis,
X and Y) which d aw he suppo ing me allic beam on which he measu emen ins umen s a e ixed. This suppo ing beam can
also be d awn e ically (axis Z). The measu emen ins umen s can, he e o e, be se au oma ically a any poin in he pool (3D
mesh). Two measu emen de ices we e placed on he ca esian posi ione , bu no simul aneously: a dep h p obe and ADV
elocime e .
An expe imen al app oach o he hyd aulics o e ical slo ishways.
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Veloci ies we e measu ed by means o a Dopple e ec elocime e (Mic oAcous ic Dopple Velocime e SonTek).
The Mic oADV is a emo e sensing de ice which has he ad an age o being inhe en ly d i - ee and does no equi e ou ine
ecalib a ion. The p obe is subme ged in he low and he ecei e s a e slan ed a 30º om he axis o he ansmi ansduce
and ocus on a common sampling olume, o a o al measu emen olume o 0.08 cm3 . The olume is loca ed a 5 cm om he
p obe o educe low in e e ence. The maximum Mic oADV sampling a e is 50 Hz. Th ough he Mic oADV Da a Acquisi ion
Sys em he speci ic eloci y o he h ee ca esian axis (Vx,Vy,Vz) was ob ained o each da a poin (K aus e al. 1994; Niko a
e al. 1998).
Veloci y measu emen s we e ca ied ou in planes pa allel o he lume bed wi h 10 cm in be ween, s a ing a 5 cm
om he channel bed up o as close as possible o he wa e su ace. In each plane, da a poin s we e dis ibu ed o ming a 10x10
cm mesh, educed o 5x5 cm in c i ical zones. The e o e a h ee-dimensional mesh o 10x10x10 cm o he measu emen o
eloci y was main ained. An example o he mesh in one o he planes pa allel o he bed o a T1 con igu a ions is shown in
Fig. 2d.
Wa e su ace heigh in he pools was measu ed by means o a conduc i i y-based dep h p obe, DHI Wa e Gauge
Type 202. The DHI Wa e Gauge is comp ised o wo hin pa allel s ainless s eel elec odes. A condi ioning signal module
(DHI Wa e Me e Condi ioning Module Type 102E) ecei es, p ocesses and ampli ies he elec ic sign sen by he wa e gauge.
Dep h measu emen s in he pools we e e alua ed ollowing a bidimensional mesh wi h da a poin s a a 10x10 cm maximum
sepa a ion in be ween. Calib a ion es s we e pe o med p io o each wo king day.
A summa y o expe imen al measu emen s is shown in Table 1. I mus be aken in o accoun ha he numbe o
measu emen planes o he eloci y ield a e a iable, hus in he T1 con igu a ion wi h a slope o 5,7% and a discha ge o 35
l/s, 3 planes pa allel o he bed we e measu ed; while in he T1 con igu a ion wi h a slope o 10,054% and a discha ge o 125
l/s, 6 planes pa allel o he bed we e measu ed.
A e a p e ious expe imen al es s, a measu emen equency o 15 Hz was chosen. The ins umen s ayed a each da a
poin o 10 and 15 seconds o collec da a on dep h and eloci y, espec i ely. Da a s o age was ca ied ou by a da a
acquisi ion p og am (Vi ualBench-Logge , Na ional Ins umen s). Conside ing an a e age o 4 planes pa allel o he bed wi h
an a e age o 132 da a poin s o eloci y in each plane (1 da a poin =675 single da a o eloci y), 356400 eloci y da a o each
discha ge o a gi en slope and ype we e measu ed, all o which p o ided a la ge amoun o collec ed da a.
ANALYSIS OF THE EXPERIMENTAL RESULTS
The i s ela ionship o be analyzed is he one be ween dimensionless discha ge and dep h. Subsequen ly, some o he
ela ionships be ween he di e en cha ac e is ic dep hs (maximum, minimum, mean, a he slo ) a e shown, as well as dep h

An expe imen al app oach o he hyd aulics o e ical slo ishways.
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dis ibu ion a he su ace o he pool and in some longi udinal e ical sec ions. As a consequence, each indi idual pa e n o
e e y con igu a ion should be known, as well as he e ec s o h slope and discha ge on he dep h dis ibu ion.
When analyzing eloci y ields, he dis ibu ion o he wa e eloci y has been ep esen ed o e planes pa allel o he
bed in o de o cha ac e ize he di e en egions in o which he eloci y ield can be di ided: eci cula ion egions and di ec
low egion. La e , he e ical dis ibu ions o eloci y alues a e displayed in o de o e alua e hei dependence on discha ge
and eloci y. A speci ic s udy o he eloci y a he slo was done o unde s and he limi a ion ha his eloci y imposes on he
design o e ical slo ishways, as hese alues will be compa ed wi h swimming abili y o ish.
The passage o mig a o y ish h ough he ishway is di ec ly ela ed o he u bulence and ae a ion in pools. The
global ene gy dissipa ion pe olume uni was used adi ionally as an indica o o he u bulence le els in he pools. Also
p esen ed is he u bulen kine ic ene gy om he expe imen al eloci y measu emen s.
Fo he ep esen a ion o he expe imen al esul s, he ollowing dimensionless a iables we e chosen: So, geome ic
slope o he ishway, Yo/b, ela i e low dep h a he ans e se middle sec ion, QA, dimensionless discha ge. In p e ious
s udies he ollowing dimensionless discha ges we e p oposed:
Raja a nam e al. (1986) 5*
oobgSQQ   1 
Kamula (2001) 32** LbSgQQ oo
  2 
whe e Q* and Q** a e dimensionless discha ges, and L is he pool leng h. I was conside ed impo an no o make he
dimensionless discha ge dependen on he ishway slope in o de o de ec he indi idual pe o mance o he ishway o each
slope. On he o he hand, i he cha ac e is ic leng h L emains in a iable (L=1.2 m) o all he designs in ou es s, he e is no
poin in including i in he dimensionless pa ame e s. Hence, a new de ini ion o he dimensionless discha ge is p oposed:
P esen Da a 5
bgQQA  3 
Due o i s u ili y, he dimensionless Q* was used o make he o e all compa ison o he esul s ob ained in he di e en
designs and o he di e en slopes including hese da a and hose o Raja a nam e al. (1992). I mus be aken in o accoun ha
he cha ac e is ic leng h o he slo bo was used by Raja a nam e al. (1986,1992) in some cases, o de ine he eal wid h o he
slo and in o he cases, me ely a e e ence wid h. In his s udy b has always been se o he eal wid h o he slo (Fig. 1 and Fig.
2).
A summa y o he mos signi ican da a om he expe imen s pe o med is gi e n in Table 2, whe e, Yb is he dep h a
he slo and Ym is he a e age dep h in he pool, being Ymax and Ymin being he maximum and minimum dep h in he pool
An expe imen al app oach o he hyd aulics o e ical slo ishways.
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espec i ely (all he dep h measu es ep esen he e ical dis ance be ween he bed and he wa e ee su ace). Vb is he
eloci y a slo ,

bbd VbYQC  is a discha ge coe icien which is p o ided o pe mi a compa ison wi h hose gi en by
Raja a nam e al. (1992) and

0
LWYgQSE o

is he ene gy dissipa ion a e in he pool.
DEPTH-DISCHARGE EQUATION
Following he indica ions by Raja a nam e al. (1986), a simple analysis was ca ied ou o de e mine he low
equa ions which es ablish he ela ionship be ween he discha ge and he dep h:








b
Y
QA0  4 
whe e 5
bgQQ A is he dimensionless discha ge in he ishway model, Yo/b is he ela i e low dep h, and ,  a e
coe icien s ela ing he dimensionless discha ge and he ela i e low dep h. I has been e i ied ha he alues ob ained o all
he di e en cases es ed ma ched a linea ela ionship, ha is o say, in e e y case whe e =1, and ha he  coe icien
depended on he con igu a ion o ba les and he slope. The i ial condi ion is Yo=0 when Q=0 has been imposed on he
eg ession s aigh line, which implies ha he independen e m does no exis .
The expe imen al esul s: ela i e dep h Yo/b e sus he nondimensional discha ge a e gi en in Fig. 4a, and he
co esponding low equa ions a e shown in Table 3. The  alues a e p opo ional o he slope. A highe alue o he
p opo ionali y ac o (s eepes line) means ha o he same discha ge he dep h eached is lowe and he e o e he eloci y
p o iles should inc ease, which implies a g ea e e iciency in con eyance.
The designs we e also compa ed by g ouping he expe imen al esul s ob ained o bo h slopes; o his eason So was
included in he nondimensional discha ge Q* (Equa ion 1). The alues in he ishway model and in he equa ions a e p esen ed
he Fig. 4b and he Table 3, espec i ely. Al hough he pe o mance o bo h designs was e y simila o each slope, i was also
obse ed ha gi en he same dep h alue in bo h designs, i was he T1 con igu a ion ha had he lowe discha ges.
A compa ison be ween ou esul s and he ones ob ained by Raja a nam e al. (1992) was ca ied ou including designs
6, 16 and 18 (Fig 1). The discha ge was non-dimensionalized by Q* Eq.1 and he esul s we e con e ed o an s anda d
p o o ype alues (Clay, C.H. 1995) wi h 0.305 m wide slo (b=0.305 m) using F oudian scaling o mulae. The cha ac e is ic
leng h bo, was ede ined in he esul s by Raja a nam (1992), using he eal slo leng h, b. The expe imen al obse a ions
con e ed o he s anda d p o o ype a e shown in Fig. 5. The discha ge-dep h equa ions we e ound wi h he condi ion o Yo=0
when Q=0 (Table 4) which also includes he alues p o ided by Wu e al. (1999) o he D18 design. The esul s ob ained show
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 8
ha o designs D16 and T1, which a e e y simila in cons uc ion, he discha ges equa ions a e also e y simila , while o T2
design (simila o D6 in cons uc ion) he alue o i s p opo ional cons an is no ably la ge . The simplici y o T2 design e sus
T1 design p o ides a g ea e con eyance capaci y which explains he highe alues in he p opo ionali y coe icien . The lowe
alue o he discha ge coe icien in D6 design e sus D16 design does no appea o ha e a physical explana ion.
DEPTH DISTRIBUITON
The a e age dep h a he middle ans e se sec ion has been chosen o e i y he pe o mance o he design, bu i is
also impo an o know he alues o o he cha ac e is ic dep hs as Ymax, Yb, Ym and Ymin. Each o hese p o ides us wi h
in o ma ion on a pa icula ea u e o he ishway: wall design c i e ia (Ymax), he limi a ions ha dep h may impose on he
passage o ish (Ymin) as well as gi ing he dep h a c i ical sec ions (Yb).
A linea ela ionship has been ound be ween each o he di e en cha ac e is ic dep hs and he ela i e low dep h a
he middle ans e se sec ion Yo/b,

´
0
´

 bYbY  5 
whe e Y s ands o any o he cha ac e is ic dep hs, ´,´ a e coe icien s which depend on he ela ed cha ac e is ic dep hs, as
well as on he slope and on he con igu a ion o he ba les. These ela ionships can be ound in Table 3. The dep h a he slo
was ound o ha e a alue ha was qui e simila o he a e age dep h in he pool.
In Fig. 6, he expe imen al esul s o he di e en cha ac e is ic dep hs e sus Yo/b a e shown, along wi h he
co esponding equa ions (s aigh lines g aphs) o T2 design o a slope 5,7%. I is sugges ed ha he expe imen al ela ions
be ween he di e en dep hs should no be ex apola ed o e y low dep h alues, since, o he nea ze o discha ge alues, all
dep h alues will con e ge a a null alue. Addi ional e ec s such as su ace ension o ces will come in o play when
discha ges a e so small.
WATER SURFACE
Typical le el con ou s can be obse ed in Fig. 7, in he ou expe imen al si ua ions s udied and wi h a single discha ge
o 0.065 m3/s. The e is always a egion o g ea dep hs jus ups eam o he slo as well as in he egion downs eam o he pool,
nea es o he la ge ba les. A he slo poin i sel he e is a sha p d op in he dep h and con inuing along down he slo , in he
di ec ion o he je , he e is a egion o minimum dep hs as a consequence o such decay. Dep h pa e ns a e qui e independen
o low a es.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 9
Since he con igu a ions pa e ns o he wa e su ace a e independen o discha ges, he pe o mance o he e ical
slo ishway emains s able wi h a ia ions in low a es. This s abili y is one o he mos impo an cha ac e is ic in e ms o he
applica ion o e ical slo ishway.
In spi e o simila pe o mance o he wo con igu a ions, we mus emembe ha he shallowes egion is loca ed in
he T1 design nea he longi udinal cen al line. This is due o he di e en o ien a ion o he main low when i comes ou o
he slo , app oxima ely pa allel o he sidewalls in he T2 con igu a ions and mo ing diagonal up o he a co ne in he T1
con igu a ion. Ano he no iceable di e ence is seen in he di e en con igu a ions o he le el lines joining hese wa e su ace
poin s wi h he same dep h, which in design T2 a e pe pendicula o he longi udinal axis (Fig 7c, p o ile AA´) while in design
T1 hey a e pe pendicula o diagonal line (Fig. 7a, p o ile BB´).
Wa e dep hs measu ed in he sec ion pa allel o he longi udinal axis, joining bo h slo s (AA´) and wi h a discha ge o
0.065 m3/s, a e shown in Fig. 8. In bo h designs he la ges dep h alues we e eached o he slope o So=10,054%. The e is a
apid d op o dep h which co esponds o he ansi ion om he slo o he dep ession egion immedia ely below, and a g adual
inc ease un ill he nex slo is eached. The g ea es ela i e d op in he dep ession pe ained o a slope o 10,054%.
VELOCITY FIELD AND FLOW PATTERNS
The con igu a ions o he eloci y ields in he pools a e one o he main ac o s used o de e mine he cha ac e is ics
o he low. Veloci y ields aken in planes pa allel o he bed a e shown in Fig. 9, whe e ho izon al componen s (Vx and Vy) o
he eloci y ec o s can be seen. A e e ence ec o is included in o de o make he comp ehension o he igu es mo e
in ui i e.
Gene ally, wo di e en kinds o egions a e o med: one, which will be e e ed o as he di ec low egion, whe e he
low ci cula es in a cu ed ajec o y a a high speed om one slo o he nex downs eam; and he o he s, which will be e e ed
o as eci cula ion egions, cha ac e ized by slowe eloci ies, low in he opposi e di ec ion, owing o he exis ence o e ical
axis eddies. Two eci cula ion egions o di e en sizes and sepa a ed by he di ec low egion, a e shown in he low pa e ns;
he la ge one is loca ed close o he long ba les and he smalle one, nea he sho ba les.
In design T1 he s eam ace o he main low a els owa ds he cen e o he pool con inuing up un il i eaches he
slo downs eam in a cu ed ajec o y, whe eas in design T2 he s eam ace o he main low a els in a s aigh e di ec ion,
pa allel o he lume sidewalls om one slo o he nex , c ea ing, as a consequence, a mino mixing o he je coming om he
slo and he wa e olume in he pool. This di e ence in he con igu a ions o he main low ajec o y is one o he main
easons why i is necessa y o explain he di e en hyd aulic pe o mance o bo h designs.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 16
APENDIX II. NOTATION
The ollowing symbols a e used in his pape :
b = slo eal wid h;
bo = slo cha ac e is ic wid h om Raja a nam e al. 1992;
Cd = coe icien o discha ge;
E = ene gy dissipa ion;
g = accele a ion due o g a i y;
h = e ical dis ance om he bed;
k, kA = u bulen kine ic ene gy and dimensionless u bulen kine ic ene gy;
L = leng h o pool;
Q = discha ge;
Q* = dimensionless discha ge om Raja a nam e al. (1992,1986);
Q** = dimensionless discha ge om Kamula, R. (2001);
QA = dimensionless discha ge om p esen da a;
S0 = bed slope;
Vm = dep h-a e age eloci y;
Vb = eloci y a slo ;
Vmb = dep h-a e age eloci y a slo ;
Q
mb
V = discha ge and dep h-a e ge eloci y a slo ;
Vx ,Vy ,Vz = eloci y a a poin on X,Y,Z axis;
Y = dep h o low (measu ed in e ical) ;
Yo = uni o m low dep h, mean dep h a middle a e se sec ion (measu ed in e ical);
Yb = low dep h a slo (measu ed in e ical);
Ym = mean low dep h a pool (measu ed in e ical);
Ymax = maximum low dep h a pool (measu ed in e ical);
Ymin = minimum low dep h a pool (measu ed in e ical);
W = wid h o pool;
h = di e ence be ween ups eam and downs eam dep h a slo ;
 = densi y o luid;

An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 17
Table 1. Summa y o p esen expe imen s.
Dep h Veloci y
Design T1 T2 T1 T2
So 5,7% 10,054% 5,7% 10,054% 5,7% 10,054% 5,7% 10,054%
Range Q 16-85 35-115 25-85 35-125 16-85 35-125 25-185 35-125
Nº Discha ge 8 9 7 9 8 9 7 9
Poin s/Le el 89 111 109 109 101 140 132 132
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 18
Table 2. Summa y o expe imen al esul s. All measu emen s a e model da a wi h b=0.16 m in he T1 design and b=0.15
m in he T2 design.
Des. So Q (m3/s) QA Y
o (m) Yb (m) Ym (m) Ymax (m) Ymin (m) Vb
(m/s)
Cd
Ed
(W/m3)
T1 5,7 0.0159 0.4945 0.125 0.158 0.130 0.175 0.107 0.86 0.73 71.81
T1 5,7 0.0209 0.6529 0.176 0.195 0.179 0.215 0.143 0.85 0.79 67.13
T1 5,7 0.0246 0.7669 0.190 0.230 0.197 0.236 0.167 0.79 0.85 72.99
T1 5,7 0.0341 1.0624 0.253 0.306 0.262 0.313 0.212 0.88 0.80 75.94
T1 5,7 0.0458 1.4277 0.379 0.406 0.386 0.425 0.356 0.84 0.83 68.25
T1 5,7 0.0540 1.6827 0.437 0.476 0.445 0.483 0.400 0.87 0.82 69.74
T1 5,7 0.0641 1.9983 0.488 0.529 0.495 0.540 0.453 0.89 0.85 74.18
T1 5,7 0.0741 2.3104 0.604 0.604 0.608 0.652 0.562 0.88 0.87 69.35
T1 5,7 0.0859 2.6791 0.665 0.697 0.674 0.711 0.628 0.85 0.91 72.97
T1 10.05 0.0348 1.0847 0.155 0.201 0.171 0.253 0.093 1.25 0.86 223.25
T1 10.05 0.0445 1.3879 0.247 0.278 0.262 0.357 0.178 1.20 0.83 179.76
T1 10.05 0.0551 1.7174 0.314 0.371 0.331 0.420 0.242 1.21 0.77 174.88
T1 10.05 0.0643 2.0059 0.366 0.406 0.378 0.469 0.288 1.19 0.83 175.00
T1 10.05 0.0751 2.3425 0.436 0.505 0.452 0.541 0.363 1.25 0.75 171.72
T1 10.05 0.0849 2.6482 0.489 0.553 0.507 0.597 0.429 1.00 0.96 172.94
T1 10.05 0.0945 2.9478 0.526 0.561 0.541 0.634 0.443 1.17 0.90 179.16
T1 10.05 0.1044 3.2554 0.581 0.621 0.596 0.690 0.513 1.05 1.01 179.11
T1 10.05 0.1150 3.5856 0.641 0.681 0.656 0.755 0.556 1.06 1.00 178.79
T2 5,7 0.0160 0.5855 0.102 0.109 0.152 0.061 0.682 0.95 1.05 88.18
T2 5,7 0.0250 0.9153 0.169 0.180 0.225 0.122 1.125 0.93 0.97 83.64
T2 5,7 0.0350 1.2811 0.263 0.274 0.323 0.214 1.750 0.99 0.84 75.23
T2 5,7 0.0453 1.6585 0.350 0.362 0.408 0.298 2.336 1.00 0.81 72.96
T2 5,7 0.0540 1.9772 0.439 0.449 0.497 0.376 2.928 0.97 0.82 69.39
T2 5,7 0.0639 2.3405 0.524 0.531 0.577 0.475 3.495 1.09 0.72 68.82
T2 5,7 0.0741 2.7131 0.606 0.613 0.660 0.552 4.040 0.87 0.92 69.02
T2 5,7 0.0840 3.0785 0.670 0.679 0.732 0.615 4.468 0.96 0.82 70.81
T2 10.05 0.0253 0.9277 0.134 0.138 0.208 0.080 0.892 1.14 0.75 188.43
T2 10.05 0.0352 1.2912 0.206 0.202 0.276 0.132 1.375 1.23 0.79 170.20
T2 10.05 0.0453 1.6601 0.248 0.251 0.329 0.152 1.656 1.32 0.79 181.73
T2 10.05 0.0549 2.0100 0.307 0.311 0.405 0.212 2.048 1.32 0.80 177.95
T2 10.05 0.0645 2.3644 0.371 0.372 0.461 0.275 2.471 1.27 0.85 173.48
T2 10.05 0.0746 2.7325 0.431 0.432 0.515 0.330 2.873 1.31 0.83 172.42
T2 10.05 0.0838 3.0718 0.483 0.480 0.569 0.380 3.222 1.33 0.83 172.81
T2 10.05 0.0954 3.4955 0.536 0.539 0.623 0.437 3.577 1.30 0.85 177.17
T2 10.05 0.1048 3.8398 0.578 0.578 0.657 0.483 3.853 1.30 0.87 180.66
T2 10.05 0.1151 4.2177 0.615 0.612 0.714 0.505 4.100 1.46 0.80 186.50
T2 10.05 0.1248 4.5739 0.650 0.649 0.745 0.536 4.332 1.28 0.91 191.39
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 19
Table 3. Flow equa ions, ela ionship be ween dimensionless discha ge and ela i e dep hs. In pa en heses, co ela ion
coe icen ( 2).
Design So QA Y
min/b Yb/b Ymax/b Ym/b Q*
T1
5,7%
0.631Yo/b
(0.9946)
0.9739Yo/b-0.1409
(0.9986)
0.9758Yo/b+0.2512
(0.9944)
0.9993Yo/b+0.3018
(0.9992)
1.015Yo/b
(0.9998)
2.7289Yo/b
(0.9872)
10.054%
0.8888Yo/b
(0.9889)
0.9742Yo/b - 0.3822
(0.9979)
1.0008Yo/b+0.2918
(0.9933)
1.021Yo/b+0.6133
(0.9996)
1.033Yo/b
(0.9987)
T2
5,7%
0.6867Yo/b
(0.9903)
0.9789Yo/b-0.2871
(0.9994)
1.031Yo/b+0.0407
(0.9983)
1.0065Yo/b+0.3583
(0.9997)
1.0183Yo/b
(0.9994)
3.0382Yo/b
(0.9783)
10,054%
0.9988Yo/b
(0.9903)
0.9196Yo/b-0.4069
(0.9965)
0.9949Yo/b+0.2826
(0.9949)
1.0323Yo/b+0.4811
(0.9982)
1.0002Yo/b
(0.9997)
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 20
Table 4. Rela ionship be ween dimensionless discha ge and ela i e dep h wi h 5*
oobgSQQ . In pa en heses,
co ela ion coe icen ( 2).
P esen Da a Raja a nam e al. (1992) Wu e al. (1999)
bYQ oT 7289.2
*
1
(0.9872)
bYQ oD 6878.2
*
16 
(0.9981)
bYQ oD 7745.3
*
18 
(0.9761)
bYQ oD 75.3
*
18 
bYQ oT 30382.3
*
2
(0.9783)
bYQ oD 2787.2
*
6
(0.9406)
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 21
Table 5. Discha ge-a e aged mean eloci y a slo .
Q
mb
V (cm/s)
Desi
g
n So=5,7% So=10.054%
T1 85.63 115.21
T2 96.99 126.47

An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 22
Table 6. Ene gy dissipa ion a e o ishway model and o s anda d p o o ype wi h a slo wid h b=0.305 m.
E
(W/m3)
Model
Desi
g
n So=5,7% So=10.054%
T1 71.44 177.49
T2 70.57 181.06
P o o ype (b=0.305 m)
Desi
g
n So=5,7% So=10.054%
T1 98.63 245.05
T2 100.63 258.18
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 23
Table 7. Speci ic alues o u bulen kine ic ene gy.
k (cm2/s2)
Q=65 l/s Q=75 l/s Q=85 l/s
T
y
pe, So h Zlow Z
in e Z
high Zlow Z
in e Z
high Zlow Z
in e Z
high
hbed 148 529 1958
342 677 1797
122 722 1818
T1, 5% h 25 cm 168 810 863
194 889 1554
238 915 1281
hsu ace 331 927 1734
328 653 2211
249 565 3329
hbed 123 224 598
133 208 689
149 243 774
T2, 5% h 25 cm 142 498 355
103 222 378
160 219 464
hsu ace 216 371 1810
137 361 2955
184 580 1989
hbed 351 675 8890
298 797 3440
234 1000 3501
T1, 10% h 15 cm 232 1586 5450
363 1321 2035
382 1099 2822
hsu ace 171 1554 3404
181 1310 2983
285 998 3938
hbed 92 472 1080
167 384 1268
131 521 1643
T2, 10% h 15 cm 293 767 727
190 592 815
260 447 810
h
su ace 255 581 651
277 880 1389
287 1130 919
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 24
Fig. 1. De ails o designs 6, 16 and 18, ecommended o p ac ical use by Raja a nam e al. (1986, 1992).
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 25

b


b

 




b T2=150 bT1=160 Uni : milime e s
Fig. 2. a) Dimension o he labo a o y model o a e ical slo ishway. b and c) De ails o T1 and T2 designs. d) Da a
poin mesh in a pa allel plane o he bed o T1 design and a slope o 10,054%.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 32
0Cm 50 100 150
0Cm
5
0
100
Axis Y
Axis X
R
e
e
e
n
c
e
e
c
o
:1m
/
s
e
g
Flow
a)
0cm 50 100
100
5
0
0cm
Axis X
Axis Y
R
e
e
e
n
c
e
V
e
c
o
1m
/
s
c)
Flow
Fig. 9. Ho izon al eloci y ields, Vx-Vy in planes pa allel o he bed o se e al expe imen al si ua ions: a) Design T1,
S=5,7%, Q=85 l/s, h=35 cm; b) Design T1, S=10,054%, Q=105 l/s, h=5 cm; c) Design T2, S=5,7%, Q=54 l/s, h=25 cm; d)
Design T2, S=10,054%, Q=75 l/s, h=25 cm
0Cm 50 100 150
0Cm
5
0
100
Axis Y
Axis X
Re e ence Vec o : 1 m/seg
Flow
b)
0cm 50 100
100
5
0
0cm
Axis X
Axis Y
R
e
e
e
n
c
e
V
e
c
o
1m
/
s
d)
Flow

An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 33
a) b) c)
Fig. 10. Flow pa e ns in pools: a) Design T1, So=5,7%; and So=10.054% wi h QA<2.75. b) Design T1, So=10.054% wi h
QA>2.75. c) Design T2.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 34
a) b)
Re e ence Vec o : 1 m/s
X
Z
020 40 60 80 100 120
0
10
20
30
40
50
60
70
Uni : cm.
Fig. 11. Veloci y ields, Vx-Vz in e ical planes pa allel o longi udinal axis o ishway. a) T1 design, So=5,7%, Q=0,065
m3, Y=72 cm b) T2 design, So=10,054%, Q=0,0746 m3, Y=86 cm
R e e e n c e V e c o : 1 m / s
X
Z
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 35
a) b)
0
10
20
30
40
50
60
0 50 100 150 200
Vx (cm/s)
h (cm)
Q=65 l/s
Q=85 l/s
Q=95 l/s
Q=105 l/s
Q=125 l/s
P . 2 P . 3P . 1
Fig. 12. Ve ical dis ibu ions o eloci y alues a some poin s o se e al discha ge. a) T2 design, S0=10,054% in: P . 1
x=76 cm, y=46 cm; P . 2 x=76 cm, y=11 cm; and P . 3 x=56 cm, y=86 cm. b) T1 design, So=5.7% in: P . 4 x=36 cm, y=12
cm; and P . 5 x=36 cm, y=62 cm.
0
10
20
30
40
50
60
70
0 50 100 150 200
Vx (m/s)
h (cm)
Q=85 l/s
Q=75 l/s
Q=65 l/s
Q= 55 l/s
Q=45 l/s
Q=35 l/s
P .4
P . 5
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 36
a)
0
20
40
60
80
100
120
30 40 50 60 70 80 90 100 110 120
Q (l/s)
Vm(cm/s)
x=46 cm, y=64cm
x=6 cm, y=79 cm
x=6 cm, y=84 cm
x=56 cm, y=9 cm
x=116 cm y=46.5 cm
x=26 cm,y=84 cm
b)
0
20
40
60
80
100
120
140
10 20 30 40 50 60 70 80 90
Q (l/s)
Vm (cm/s)
x=16 cm, y=86 cm
x=6 cm,y=91 cm
x=66 cm,y=11 cm
x=36 cm,y=36 cm
x=86 cm, y=56 cm
Fig. 13. Veloci y e olu ion agains discha ge a se e al expe iemen al da a poin s. a) T1 design, So=10.054; b) T2 design,
So=5.-7%.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 37
a)
0
20
40
60
80
100
120
0 10203040506070
h (cm)
Vb (cm/s)
Q=15,85 l/s Q=20,94 l/s Q=24,6 l/s Q=34,1 l/s Q=45,8 l/s
Q=54 l/s Q=64,1 l/s Q=74,1 l/s Q=85,9l/s
b)
0
20
40
60
80
100
120
140
160
0 102030405060
h (cm)
Vb (cm/s)
Q=35.2 l/s Q=45.3 l/s Q=54.8 l/s Q=64.5 l/s Q=74.6 l/s
Q=83.8 l/s Q=95.4 l/s Q=104.8 l/s Q=124.8 l/s
Fig. 14. Values o he slo eloci y agains dis ance o he bed o se e al discha ges. a) T1 design, So=5.7%; b) T2
design, So=10.054%.

An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 38
0
20
40
60
80
100
120
140
160
0 20406080100120140
Q (l/s)
Vmb (cm/s)
Design T1, So=5,7%
Design T1, So=10,054%
Design T2, So=5,7%
Design T2, So=10,054%
Fig. 15. Dep h a e age slo eloci ies e sus discha ge.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 39
0
50
100
150
200
250
0.00 0.03 0.05 0.08 0.10 0.13 0.15
Q (m3/s)
E (W/m3)
Design T1, So=10,054%
Design T2,So=10,054%
Design T1, So=5,7%
Design T2, So=5,7%
Fig. 16. Ene gy dissipa ion alues e sus ci cula ing discha ge in he model.
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 40
0cm 50 100
100 50 0cm
Eje X
Eje Y
Re e ence Vec o 100 cm/s
k
1500
1333
1167
1000
833
667
500
333
167
0
Zlow
Zin e
Zhi
g
h
0Cm 50 100 150
0Cm
50
100 Eje Y
Eje X
Re e ence Vec o 100 cm/s
k
1500
1333
1167
1000
833
667
500
333
167
0
Zlow
Zin e Zhigh
a) b)
Fig. 17. Con ou lines o u bulen kine ic ene gy (cm2/s2) o a discha ge o Q=0.085 m3/s. a) Design T1,
So=10.054%, h=30 cm; b) Design T2, So=5.7%, h=60 cm .
An expe imen al app oach o he hyd aulics o e ical slo ishways.
Page 41
Fig. 18. Dimensionless u bulen kine ic ene gy, a e aged on he e ical o design T1 and So=10.054%.
Kine ic Tu bulen Ene gy, Design T1, So=10,054%
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
25 35 45 55 65 75 85 95 105 115
Q (l/s)
KA
Zlow Zin e Zhigh