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UNIVEBSITY OF MINNESOTA
ANTHONY FALTS HYDRAUTIC TABORATORYTORENZ G. STRAUB, Director
Techniccl Paper No. 15, Series B
Straight Drop Spillway Stilling Basinby
Chcsles A. Donnelly qnd Fred W. Blcisdell
Hydraulic Engineers, USDA, AnS
November, 1954
Study conducted by
uNrrED sTATES DEpARTMEiw or AcnlcutrunEAGRICUTTURAT RESEARCH SERVICE
SOIL AND WATER CONSERVATION NESEANCH BRANCH
,r in coopercrtion with the
Minnesots Agriculturcl Experiment Station
crnd the
St. Anthony Folls Hydrculic Lcborctory
ST.
EDB
UNIVERSITY OF MINNESOTA
ST. ANTHONY FALLS HYDRAULIC LABORATORY
LORENZ G. STRAUB, Director
Technical Paper No. 15, Series B
Straight Drop Spillway Stilling Basin by
Charles A. Donnelly and Fred W. Blaisdell
Hydraulic Engineers, USDA, ARS
November, 1954
Study conducted by
UNITED STATES DEPARTMENT OF AGRICULTURE
AGRICULTURAL RESEARCH SERVICE
SOIL AND WATER CONSERVATION RESEARCH BRANCH
in cooperation with the
Minnesota Agricultural Experiment Station
and the
St. Anthony Falls Hydraulic Laboratory
ST.UNIVERSITY OF MINNESOTA
ANTHONY FALLS HYDRAULIC LABORATORYTORENZ G. STRAUB, Director
Techniccl Pcper No. 15, Series B
Straight Drop Spillway Stilling Basinby
Chcrles A. Donnelly qnd Fred W. Blqisdell
Hydrculic Engineers, USDA, ARS
November, 1954
Study conducted by
UNITED STATES DEPARTMENT OF AGRICUTTURE
AGRICUTTURAT RESEARCH SERVICE
SOIT AND WATER CONSENVATION RESEARCH BRANCH
in cooperation with the
Minnesota Agriculturcl Experiment Stcrtion
crrd the
St. Anthony Fclls Hydrculic Lcborctory
UNIVERSITY OF MINNESOTA
ST. ANTHONY FALLS HYDRAULIC LABORATORY
LORENZ G. STRAUB. Director
Technical Paper No. 15. Series B
Straight Drop Spillway Stilling Basin by
Charles A. Donnelly and Fred W. Blaisdell
Hydraulic Engineers. USDA. ARS
November. 1954
Study conducted by
..
UNITED STATES DEPARTMENT OF AGRICULTURE
AGRICULTURAL RESEARCH SERVICE
SOIL AND WATER CONSERVATION RESEARCH BRANCH
in cooperation with the
Minnesota Agricultural Experiment Station
and the
St. Anthony Falls Hydraulic Laboratory
4 g g g & a
This paper deseribes the development of the generalized desi-gn
ru.J.es for a nero sti.lling basin .for use lrith the straight drop spillway.
This generallzed. still.ing. basin design'was devetoped because experienee
in the field hacl shown that 'there
was' no 'satisfactory
si;illing basi-n for
the straight drop spillway. Ho'r+ever, liln:ited field eq:erienee indicates
that this ner"r design will adequately protect the dor.n:strear* eharrnel from
scour.
!'fater'fa11ing over the spillway crest falls onto a flat apron. The
nappe i-s broken up by floor blocks, ''rhich also prevent damaging seour of
the dowrstream charurel banks" $cour of the domstreasr .char:nel bed i-s pre-
vented. by _ an end siJ.].. . Flaring r.ringtralls, triangular j-n elevaiicnr Fr€-
vent erosion of ift" a*to fill, For proper operaticn of the stil]ing basin,
the contraction of the fl-ow at the ends of the spillway openi-ng must be
partial-ly suppressed.
The stilline.basin can be'used for. :
on the crest, crest length, height of drop,
rt tTl
t
a rc-i-de l"ange of discharge, head
a-nd dolrrrstrearn tailwater fevel.
3n i:eportant f.endipg is that the stl11ing basin length computed
for the $dni.nun tailwater leve1 required for good perfo::aance may be in-
adequate at hj-gher taiiwater levels* Dangerous scour of the downstreaun
channel may occu.r if the flappe is supported srrfficiently by h:igh tailwater
so that it lands beyond the end of the .stil1ing' basin. A method of cora-
puting the stilling basin length for all tailwater l.evels i-s presented.
The design rules developed as a result of the laboratory test's
were carefully cheeked and verlfied. An exarnple sholrs how these nrles are
applied to the design of a field strueture.
1 T 1
A B S T RAe T
This paper describes the development of the generalized design
ruJ.es f or a new stilling basin . for use with the straight drop spillway .
. s generalized stilling, basin design , was developed because experience
in the fie l d had shmm that 'there ' was ' no 'satisfactc:ry stilling basin for
.., e s t raight drop spillway. However, limited field experience indicates
_ at this new design will c:deq-qately protect the downstream channel from
scour .
v'Jater falling over the spillway crest falls onto a flat apron. The
nappe is broken up by floor blocks, ,ihich a:lsoprevent damaging scour of
the dovmstream channel- banks. Scour of the downstream channel bed is pre
vented by an end sill • . :F'laring Wir::gvm~ls, 'triangular in elevation, pre
vent erosion of the dam filL For proper operation of the stilling basin,
t he contraction of the flow at the ends of the spillway opening must be
par t ially suppressed.
The stilling basin can be used for a wide range of discharge, head
on the crest, crest length, height of drop, and dovmstreamtailwater level.
An ~p'ortant f~ndi?g is that the stilling basin length computed
for the minimum taihrater level required for good performance may be in
adequate at higher tailwater levels. Dangerous scour of the downstream
channel may occur if the nappe is support-ed stuficiently by high tailwater
so that it lands beyond the end of the Btilling basin. A method of com
puting the stilling basin length for all tailwater l evels is presented.
The design rules developed as a result of the laboratory tests
were carefully checked and verified. An example ShOvlS how these r ules are
applied to the design of a field structur e .
iii
"lT T,IrirDr\r-rT irt rrtTnl.T-LI\j1ILLIJJUUIIVI'J . . . . . . . . t . . . t , . + o . . . . :
FirqvI0$s i,i0FJi a a a .
r i n X T r n i i t \ T T qu v l \ l u M v
A b s t r a c t . . . t . ' a t . ' . . . . . t . .List of I l lustrations . . r . . . ' . ' . . ' ' . .r . . .I r i s t o f T a b l e s . . . r . . f . , . . , . . . . .L i s t o f S S t i r b o l s . t I r . r . r . e ' . . . . r e . . t . t .
F r o n t i s p i e c e . . . . . r ' . . . . . .
A P P S . . I A T U S A 3 ] l P R C C I D U ] i E . . ' . ' i . ' . . ' , . . . o . . ,
m:qm DTc-rTlT rtqI!rl" l l l luuir. l l i . t . e . . . . . . a . . t . .
L e n E t h o f B a s i n . . . . . . . . . . . r . . . . ' II { a p p e T r a j e c ' ; o r y . . . . . . . . ' r } r . } . .D i s t a n c e t o F l o o r B l o c k s . ' . r . , . . . . . , . .D i s t a n e e t o E n d S i l l . ; ' r . . , ' ' . . .
T a i l w a t g r n e p t h . . ' . . i e r . . . . ' ' . . . ' IFloor Bloek and End Sill lieight . . .Ffoor Block i5dth and Spaci[g . r . r . ] . . . ) . ' I . . . .S i d e l t a l l H e i g h t . . . . . . . . . r ' . . . . e . . . . a .f i i n g w a 1 l s . . . + . I a . . . , . . . . . . 'A p p r o a c h C h a r r n e l . . . . . . . . .A e r a t i o n U n d e r l { a p p e . } i . . . . . ' i , . . 'C h e c i i T e s t s . . ' . . .
SUI'rlUlftJ. . . . ' . t l . . . . t
EXj{{PLE 0$' APPIJCATI0}'] . . + . . . . . . | . .' . . . . . . r . .
' l f i k] i nry:.rnlrrrIJILJJ-JLJ6IdIJ1IJ/ . . . . . . . . . . . . . . . I | . . '
TJ^ -^r. dSr:'
iii1t
\riviii
I\J
12
1 4n l/ r l
t o
2 7
1 r
L'/
CON TEN T S
Abstract List of Illustrations List of Tables List of S;ymbols Frontispiece
INTRODUCTION .
PREVIOUS HORK
APPARATUS Ai'iJD PROCEDUHE
TEST RESDLTS Length of Basin •
• •
•
Nappe Trajectory Distance to Floor Blocks Distance to End Sill
Tailwater Depth
•
Floor Block and End Sill Height Floor Block vJidth and Spacing Side"t-Jall Height "Hingwalls Approach Channel Aeration Under Nappe • Check Tests
SUlvlHARY
EXA1'IPLE OF APPLICATION • •
Bibliography . . .
iv
•
•
• '. ..
• •
• ..
. .
•
•
• •
Page
iii v v
vi viii
1
2
3
5 5 5
10 12 13 17 19 23 24 24 25 26
27
29
35
! r ! . 9 9 e g ! l g g I g g S , I g g g .Figure
F r o n t i s n i e c e . I i I r . . . 3 . . . c . r . o 1 . . o r . .
1 t e s t A p p a l ' a l u s . . , f * r f . . r . . . . . * 1 .2 Design Chart for De'i:errni::ation of ** , . .: o ' . *
3 The Bed Scour fs leeper than Necessary and the Bank'Ssour Is Excessive Beeasse of k:proper location orAbsence of the Floor Blocks ; . . r . . l r . r . .
l+ Floor Blocks Located 0,8 dc fronr the Point',rlherethe NappeStrikes the Basin Floor and 1.75 dc fromthe End of the Stilling Basin Give l{axj:nura Protectionto the Bed and Banks * | . . . r . . o a .
5 Floor Blocks lo*ated. 0.75 de fron the End of theStiJ.ling Basin Are Ineffeetive; t'he Bed Scour j-sDeeper ihan l.lecessary, ancl the Fank $cour is Exces-sive . . . . . r a r . . . . r . . . . I a
6 Determination of ?ailwater Depth . . . . ) * ., c .
7 effect of Taihraier Ievel on Downstrearn Scour . r ,n ^E Seour Near End of St i l l ing Basin . ' I r ' | . r . I
9 Effect of Proportion of Basin i""Iidth 0ccupied byFloor Blocks on $cour of Fed arrd Banks r . . . .". ,
10 Straight Drop Spil}*ay Stilling Basin . . . . . . .
11 Example of StraightDrop Spilhray Stilling Basin De-signed. for illgh Taj-},rater' . . . . r . . . . .. . c
12 Hr,anpJ-e of StraightDrop Spillway Stilli:rg Basin De-"signed for Nc:raa1 Tailwater . . . . . . . . ' t ..f
a t t
a f *
a l t
Page
viii
11
I 1
1 fL,
JO
22^ O1 0
32
a2
i a *
f r f
* t t
a c l
a 6 c
a ] . ,
+ * . )
rTr^L't ^r d U I E
$o.
I
1I
IIITft.LV
! I E T g T T A E I E g
Floor Block and f ind $i11 Height . . . . r . , . . . . . ' r . 18
F l o o r B l o c k ' ' r r l : - d t h a n d S p a c i n g . . r r ? r ' . r . . r I f , , 2 A
$iderrlall Height ?gsts c c . r . . . . . . . . . ' s * r r. 23
S u i ? m a r y o f C h e c l c T e s t s . . ! . . . . . . . . . . . r . , ' 2 6
LIS T o F ILL U S T RAT ION S -----_ ..... _-----Figure
Frontispiece .. .. .. .. .. • •• • .. .. • • • • .. .. .. • • • • • .. . . . I
2
3
Test Apparatus • • • • • • • .. .. .. .. • .. • • • · .. • ••• Design Chart for Determination of x . . .. . • • • • • • a The Bed Scour Is Deeper than Necessary and the Bank . Scour Is Excessive Because of Improper Location or Absence of the .Floor Blocks ................. . . . ..
4 Floor Blocks Located 0.8 dc from the Point 1rnlere the Nappe Strikes the Basin Floor and 1.75 dc from the End of the Stilling Basin Give Maximum Protection to the Bed and Banks .. .. .. • .. • • • • • • • • • • .. • • •
5 Floor Blocks Located 0.75 dc from the End of the Stilling Basin Are Ineffective; the Bed Scour is Deeper than Necessary, and the Bank Scour is Exces-
6
7 8
9
10
11
12
Table No.
I
II
III
IV
sive • • .. • • • • • • • • .. . . . . • • • • • • • • Determination of Tailwater Depth • .. • • • • •
Effect of Tailwater Level on Downstream Scour · .. • •
• •
• • Scour Near End of Stilling Basin • .. • • .. • • .. .. .. .. Effect of Proportion of Basin Width Occupied by . Floor Blocks on Scour of Bed and Banks ••• •• # . • •
· . .. . • • .. . • •
Straight Drop Spillway Stilling Basin ............ .
Example of Straight Drop Spillway Stilling Basin De-signed for High TailT,vater .. .. • • •• ....... ~ • • ..
Example of Straight Drop Spillway Stilling Basin De- . signed for Nonnal Tailwater ••• •• ............ .
LIS T o F TAB LE S;
Floor Block and End Sill Height • • .. . • • • • • • • • •• Floor Block vJidth and Spacing ·. • .. •
Si deHall Height Tests • • • .. • • • • • • • • • • • • ••• . .. . . . . . . ...
SUffi,'uary of Check Tests ... 0 • • • .. • • • • • 0 • • ....
v
Page
viii
3 9
11
12
13
15
16 16
22
28
32
33
Page
18 20
23 26
! r g r g q l ) Uv l rI I f , l r S
-l(f^
4.
u
' T
!
T ,l)
n
v
ll
x-U
ar
nX
? 1 q
Y"T
Xd
ciisiaace frora tailwater'surfaee to floor of stilliirg basin^ t o
crj-rica1 depth = lf (r;/L)'/E = Q/l) n
acceleratlon due to ;ravi-tY
specific head in'approach to crest = depth plus veloclty head : (3/2) de
crest length = stilling basin rridth
minimruii stilling basin length = *o * 1,
* *"
discharge
erj-tica1 velocity
horizontal distance from crest to point where upper surfaee of free-falling nappe strikes still.ing basin floor
horlzontal distance frorn crest to point at which avel:age of uppersurfaces of free-falling and tangent neppes strikes stilling basinf ' tnnr . = (u + - ) /2r "-F' r\fj]
distance to floor blocks fron point at which average of upper su.r*faces of free-falling ancl tangent nappes strikes stilling basin floor
dl.stance from upstreara face of fLoor blocks to enci. of stilling ba.sin
horizontel d"istance from crest to upper surface of free-failing nappe
horiaontal dist;rnce.fron cfest to Uppe-r surface of suhi:rerged nappe
horizontal distance from e_re6t to point at,whj.eir upper sr.rrface of free-falling nappe plunges .inio tailwater
horizontal distance from crest tc point where upper surface of tangentnaplre strikes stilling basin floor
"y vertical d.istanee fron cyest to stilling basin floor (y is negative)
y* vertical dlstance frpm crest to upper surface of free-falling nappetr (y- is positive abovd the crest and negative below the crest]
Jr, vertical clists.nce from crest to t,arl-tra,ter surface (n is positiveu 1.rhen tire tai}w&ter.surfaeeis above the crestr negativeirhen the tail-
r,rater surfaee is belor'r the crest)
\n
I
d 2
d c
x a
x c x
n
y n
1 1ST o F SYMBOLS
distance from t aihrater ' surface to floor of stilling basin
crit ical depth = 3 (Q/L)2/g = (2/3) H , ' .
acc eleration due to grc:tvity ·
specific head in' approach to crest = depth pius velocity head := (3/2) d c crest length = stilling basiriwidth
minimum stilling' basin length =x t x. + x a D c discharge
critical velocity
horizontal distance fromerest to point where upper surface of freefalling nappestrikes .stilling basin floor
horizontal distance . from crest to point at 'timch average of upper surfaces of free-falling and tangent nappes strikes stilling basin floor ' = (x + x )/2
"F '1'
distance to floor blocks from point at lfhich average of upper surfaces of free-falling and tangent nappes strikes stilling basin floor
<#'
distance from upstream face of floor blocks to end of stilling basin
horizontal distance frOIl} crest to upper sur~ace of free-falling nappe
horizontal distance ,from crest to upper surface of submerged nappe
horizontal distcillc.efrolnGrest to point at.whJch upper surface of freefalling . nappe plunges . into tailwater .
horizontal distance from crest to point where upper sUl"face of tangent nappe strikes stilling basin floor
vertical distance from crest to stilling basin floor (y is negative)
vertical distance fr9)J1Crest to upper surface of free-falling nappe (y is positive above the crest and negative below the crest)
n
vertical distance from crest to tailwater surface (Yt is posit.ive 1·rhen tbe . taihT9.ter . sur! ace ,is above the crest , negative Vlhen the tailHater surface is beloH the crest)
vi
STFAIG}{T !]lfiF $i}II,,]"'i";AY STILLI}{0 BJTSIN -X.
II{fR,O}UCTICl'J
The straight drop spilh.;ay is, just as the name 3mplies, a straigirt
:;erfal1 r.reir. Ti-te water flor'ring over" the spillway fa1ls onto a horizcnt-
a1 apron. ?he energ;in ihe '.+e-te:' is dissipatedby rieans of blacks, si-lls,
anC 'i;aik;ate::. lhe wets:" is discha.rged fron the stilling h,asin int,o the
Cc',.i-nsiream channel in such a inarlner as 'bo prevent deiaaging s€o1:.r,
The straight drop spill i"ay is useC as ar1 erosion control- struc-
+.ure in gu1Iles, as a .::r'ede conircl structure in drainage ditches, as an
irriaa' j-on drop and cireck stnrcture, an.,i. is l spil}"'ry for eertir d.a:s.
A generalized clesign for a s'braight, drop spillr'av stil l ing ba.sin
r+a-s develcpecl" as a result of ihe tesi,s Cescri-bed in this paper. The de-
sign is applicablc to relative heights of fal-l rar;ing fron I.O y/a^ to^ J l -
t> y/a^ and r,o crest len;ths ;reatcr than 1.5 d^. l{ere y is the ver-9 V
tical distence bet'..,'een the crest and the stilling basin floor, asrd d" is
the critical dei:i}: af f1ow. '
: : l '
fhi-s e:ryerimental in'restigation'"+as begun early ::n7951- at ti:e re;
quest ojl the En,qineering Council of the Soil Conserraticir Serrice, U. S.
DeparLnent af Agriculture. :t wa.s corai:leied late tn Ig53. Tire study was
nad.e by the steff of 'Lhe Ag.ricul-tural Research Sers'j-cu-"t* lo"*ted. at the
Si. An'bl:any FalJ-; I{rdraulic T,ab*ratcry, eniversii;y of I'Ij*nesotae }iinneapo-
lis. There the Agricultural Research,$ervice, the iriLnesota Agricultural
E4perinent Station, and the St. Anthony Fells li-v-Cra'u1ic taboratory eoop€r-
ate in .L,he solu'tion cf pro'cIens eoncerning consenration h)'draulics. The
stuclies uhich are being cono.uci;eci by the hSricr,-Itural Research Service at
the St. A:rthon], lalls Hyd:'iutic Laboratory of the Lnivei'sity of l.{ii'rnesota
are eC,rainistered by the l"ie.tcrshed ii'rdrclogy Secticn of tha Soil and t',aier
Conservation -"eseaz'ch Branch. The testi:rg and much of the analysls rras
done h,;r Cha::"les A. Doane11y, iSdraiil ic Engineer, Agricultural I'eseareh
" i t - *+ ^ " , r + . , *a1 : - ] .CSgafCh Se- ; - f * ̂ ^ - r ^ *^ -+ r ; ^ r , - r ^ t ) ^JigI ' l -CUIAUv
n_ aCe repor! l lo . Ll l-)U4-)1.
:-q).4-,""The stuCiesat the Si;. Ani;hony .lalls H]'d:'aul-ic La'boraiory, initiated
by Soil Conservation $ervice - Resee-rch on January 1, 19110, l:ere t:'e-ns-ferred to Agricultural Research Serrrice on Janua"ry 7, L95\.
...
-xSTRAIGHT DROP SPILUJAY STILLING BASIN
IWffiODUCTION
The straight drop spilhmy is, just as the name :Luplies, a straight
o-.-erfall vJeir . The ,,-rater floHing OVel" the spilhmy falls onto a horizont
al apron . The energy in the lpJater is dissipated by means of blocks, sills,
and taihmter . The 'Hater is discharged from the stilling basin into the
do';m stream channel in such a manner as to prevent daJrtaging s.cour.
The straight drop spilhJCW is used as an erosion control struc
ture in gullies, as a grade control structure in drainage ditches, as an
irrigation drop and check structure, and as a spilhJay for earth dams.
A generalized design for a straight drop spilhJay stilling basin
Has developed. as a result of the tests described in this paper. Tl:l..e de
siE;n is applicable to relatiVe heights of fall ranging from 1.0 yld to c
15 y l d and to crest lengths greater than 1.5 d • c
Here y is the ver-c
tical distance betv,een the crest and the stilling basin floor, 2,nd
t he critical depth of .floH.
d c is
This e).rperitnental investigatior1vJasbegun early in 1951 at the re..:.
quest of the Engineering Council of the Soil ' Conser-vatiem Service, U. S.
Depart.ment of Agriculture. It vIas completed late in 1953. The study Has
made by the staff of the Agricultural Research Service~H<- located at the
St. lmthony Falls ItJdraulicLaboratory , University of Hinnesota, l'hnneapo
lis. There the Agricultural Research Service, the Hinnesota Agricultural
ExperiJnent Station, and the St. Anthony Fa:lls Hydraulic Laboratory cooper
ate in the solution of problems concerning conservation hydraulics. The
studies Hhich are being conducted by the Agricultural Research Service at
t he St. Anthony Falls Hydraulic Laboratory of the University of Hinnesota
are administered by the VJatershed Hydrology Section of the Soil and itJater
Conservation Research Branch. The testing and much of the analysis was
done by Charles A. Donnelly, Hydraulic Engineer , Agricultural Research
-l~Agricultural Research Service Report No. hl-504-52 .
,~-l~The studies at the st. Anthony Falls Hydraulic Laboratory, initiated by Soil Conservation Service - Research on January 1,19L~o, 'were transferred to Agricultural Research Ser-vice on JanuaI"J 1, 1954.
STF,AIGIN' NftCP SIJI1,1,I,,.iAY STIILI$G E/r.SITf -,.
Ii']TN.ODUCTION
?he siraight drop spillnayis, ju-st es the name i*rpli-es, a straight
overfall r'reir. ?he weter flowing over the spill',ray falls onto a hor"izont-
a1 e.pron. ?he energrin the ruater :-s <ilssipatedby n:eans of bl-oclcs, silIs,
and tai}-reter. ?he uater is rlischerged f:'o:a the stilJ-ing ba.sin into the
dol.mstyean chennel in such a rlrr.nner as to pr-event d:;raging scour.
The strai3ht drop spil}^ray is asecl as a.rr erosion control sirrrc-
ture in gu11ies, as a ..;r;de control- st:-"icture jn drainage ditches, es an
irr i ;at ion drop and checl: stnrcNure, and es a spi lhlay for earbh dans.
A generalized Elesign for a s*i,raighi drop spilli"ray stilling basin
r+as developed. a= a result of the tests described in this paper. The de-: r - - j - - 1 , r . ' l ^ + ^ - ^ - t ^ r ; - . ^ l - , - - ^ ; * - " - ^ *
- - t
" l -Sign is applicable to relati're heights of fal1 rangr-ng -rroir t.0 y/d* to- J I - -
L5 V/a^ and to crest len3ths greaier than 1.5 d.^, Here y i-s the ver-
; i*sin floor, e;nd. d^ i-s
the critical denth cf flor+.. . :
This s**tfurenial i:rvestigatiorr r'ras begun early in1951 at the re-
quest of the Enginee::i-n.g Council of the SoiI Conservaiicr-r Ser'/ice, U. S.
Departnent of Agriculture. It Vras co;-rpleted laie in 1953. The study was
mad.e by the staff of Nhe Agricultural Fuesearch Sev,ri-s"Js* 1o"*ted at the
St. An-r,hony Falls livdraulic Laboratary, Universityof i{innesota, Hi::neapo-
1is. ?here the Agricultural Research $ervicer. fhe itinnesota Agri-cultural
E:<perinent Station, and the St. Anthorry Falls lF-rdra.ulic l,aboratory cooper-
ate in the solution cf problens coneerning conser"ation h4rdrauLics. The
studies wirich are being eonducted by the hgricult*ral F.esearch $ervice at
the St. .r"'n{,hsn3r r-alls l{ydrri-riic Laboretory of the iJniversity of i-iinnesota
are a"rininis+;ered b)' the r,.,-etcrshed l{;r<irolog' Seciion of the Sail and ].'iater
Conservation H.eseerci:. Braneh. ?ire testing and nuch of the analysis was
done b-' Charl-es A. Donnelly, Sd,raulic Fngi-neer, A3ricultural Xesearch
-x- "Agi'icultural iesearch ,Se:vice ieport iio. L1*50jt-52.-x-)i-, :"'The
studies at the St. Ant,hony Fa11s l{ydr:aulic La}:oratory, initiated.by Soil Conservaiion Service - Research cn January 1, 19h0, nere trans-ferred to Agri-cu1tr:.r'a1 Research Se:-:rice on Je,nuery 1, 195h.
-)~ STPJUGHT DROP SPI1L!lJAY STILLING BASIN
INTRODUCTION
The straight drop spilhmy is, just as the name irnplies, a straight
overfall Heir . The lfater flo1fJing over the spillway falls onto a horizont
al apron . The energ'J in the water is dissipated by means of blocks, sills,
and taihmter. The 1fmter is discharged from the stilling basin into the
dmillstream channel in such a manner as to prevent d&l1aging s.cour.
The straight drop spillHay is used as an erosion control struc
ture in gullies, as a grade control structure in drainage ditches, as an
irrigation drop and check strilCture, and as a spilhmy for earth dmrrs.
A generalized design for a straight drop spillway stilling basin
1fJas developed as a result of the tests described in this paper. The de
sign is applicable to relative heights of fall ranging from 1.0 y/d to c
15 y/d and to crest lengths greater than 1.5 d • Here y is the ver-c c
tical distance behleen the crest and the stilling basin floor, and
the critical depth of flmf.
d c is
This experimental investigation1flasbegun early in 1951 at the re..:.
quest of the Engineering Council of the Soil Conservati<m Ser-vice, U. S.
Department of Agriculture. It vms completed late in 1953. The study was
made by the staff of the Agricultural Research Service-lH~ located at the
St. Anthony Falls Hydl"aulicLaboratory , University of Minnesota, I1inneapo
lis. There the Agricultural Research Service, the Hinnesota Agricultural
Exper~'Tlent Station, and the St. Anthony Falls flydraulic Laboratory cooper
ate in the solution of problems concerning conservation hydraulics. The
studies w11ich are being conducted by the Agricultural T-tesearch Service at
the St. Anthony Falls Hydraulic Laboratory of the University of Hin..'1esota
are administered by the Hatershed Hydrology Section of the Soil and Hater
Conservation Research Branch. The testing and much of the analysis was
done by Charles A. Donnelly, flydraulic Engineer , Agricultural Research
-:~Agricultural Research Service Report No. 41-504 .... 52.
~-l*"The studies at the st . Anthony Falls flydrau1ic Laboratory, initiated by Soil Conservation Service - Research on January 1,1940, 1"lere transferred to Agricultural Research Service on January 1, 1954.
2 -
ljeiwj-ce. This paper Irlas coilpiled by h-Ln and Fred 1'.'{. Blaisdellt F::oject
Supe:.:risor, r+ho is also responsible fc:' the nappe trajectorSr anaiysis'
The iechnical content anC presentation of the paper heve been criticalll'
re1;ier.reC b;'!r. Alrrin G. ,'-nclerson, Assisi;:nt Professor of hydr;ul5-cs, 5t.
:inihon;' Fall-s Hydr:ir}-c l,aboratory, and lir, i'i. I'1. Cu1p, Head, lesign Sec-
*i nn in,,i "rpnri n^' ;t-i rri ci nn Sni 1 Conservation Service. iiditofj-al prepara-U - L U I I , f , l J . * I - l g U I L l t L u L v l u l v r r t v v + 4
tion r.ras with ihe assistance of the Laboratory staff . The thanks of 'r,he
am*,hors go -bo all who have so generously contributed construciive co*:nents.
This repori is broken d.olnrinto a munber of sebtions. Tntroduc-
tory sections describe ;+revious work, the tesi progf&:rl, e.Ild the apparatus
and. procedure used in conducting the tests. The results of the tests are
suriimarized 1n the fo:rn of design rules and equations '
PA,trVIOUS '$I0Ri{
lxcessive scour ai; the outlet of a number of s'i;ralght d.rop spill-
i^ia;Zs located at the i"Jhiting Field itlaval Au:ciliary Air $ration, i"iilton,
Florida, resultecl in a reclu-est for model stuCies of th.is outl-et and for
recoiulenclation of a better outlet design. The i'ihiting Field strtrctures
had been designecl according to the eriteria presented in the.,paper entitl-ed
rtHJ-d.raulic Design of Dron Strrrctures for Gu11y Controlrt l1]". I'todel stud'-
ies eonducted j-n 19bB with a downstreem channel fosned of sanC verified
the excessive sQoi:r observed at lihiting Field l2].
A serj-es of tests was ccnducted in l-950 using the outlet desi-gn
mentioned. in the previous paragraph to see if r"ringrtalls triangular in eie-
vation r"ronld red.u.ce the scow. Triangul-ar r"ringwalls had previously been
found effeciive in controlling bank scour i3, hl. Tirese tests T{ere spon-
sorr.r.t "!r:r itarr"ion Iif of the Sbil Conserva-bion Service. They slrorred that
r,rhile the bank scour r,ras reduced ihrough the u-se of the trrangular wing-
walls, not enough energy r,ras d.issipated. in the outlet to reduce t]:e bed
scour to a iolerab]-e aaount.
lr satisfactory stilling basin incorpora.ting floor bloeks and an
end sill r+as developecl through ieodel studies foruse ai iihiting Field 12]-
Subsequent experience at ifhiting l,-ie1d has shoun the complete absence of
scour in the channel downstrea:n from this stilling basin and. has verified'
the laborator;r stuclies. The instrtctions frorn ihe Engineering Council
rsere to develop generalized. d.esign rules for thls stilling basin'
-t'-i,h_,*b"r" in brackets refer io bibLiography l-isted on Page J$.
2
Scrvice. This paper was co:r;1piled by him and Fred vI. Blaisdell, Proj ect
Supervisor, 1-,ho is also responsible for the nappe trajectory a.."lalysis.
The technical content and presentation of the paper have been critically
reviewed by Dr . Alvin G. Anderson, Assistant Professor of Hydraulics, St.
Anthony Falls Hydr2,ulic l,aboratory, and Er. H. H. Culp, Head, Design Sec
tion, Engineering Division, Soil Conservation Service. Editorial prepara
tion was v-Jith the assistance of the Laboratory staff. The thanks of the
authors go to all 1oJho have so generously contributed const ructive comments.
This report is broken down into a number of sections. Introduc
tory sec tions describe previous 1,{ork, the test p rograLil, and the apparatus
and procedure used in conducting the tests. The results of the tests are
summarized in the form of design rules and equations.
PREVIOUS ~iORK
Excessive scour at the outlet of a number of straight drop spill
ways located at the ~;]hi ting Field Naval Auxiliary Air Station, IYlilton,
Florida, resulted in a request for model studies of this outlet and for
recommendation of a better outlet design . The ~'.}bi ting Field structures
had been designed according to the criteria presented in the paper entitled ~~
tlHydraulic Design of Drop Structures for Gully Controli' [1)". Model stud-
ies conducted in 1948 v-rl th a d01oJl1stream channel fOl'l1led of sand verified
the excessive scour observed at ~'Jhiting Field [2).
A series of tests vlaS conducted in 1950 using the outlet design
mentioned in the previous paragraph to see if Hinglvalls triangular in ele
vat ion 1ilOuld reduce the scour. Triangular wi ngr.rJ'alls had previously been
found effect ive in controlling bank scour [3, 4]. These tests were spon
sored by Hegion III of the Soil Conservation Service . They shov-Ted that
v-lhile the bank scour was reduced through the use of the triangul ar l.nng
walls, not enough ener6J vIaS dissipated in the outlet to reduce the bed
scour to a tolerable amount.
A satisfactory stilling basin incorporating floor blocks and an
end sill 1,laS developed through model studies for use at VJhi ting Field [2].
Subsequent experience at lJhiting Field has shmm the complete absence of
scour in the chan.."lel dOv-Tl1stream from this stilling basin and has verified
the laboratory studies. The instructions from the Engineering Council
were to develop generalized design rules for this stilling basin.
'~t'uItlbers in brackets r efer to bibliography listed on Page 35.
APPARATUS AND PROC,EDIIRE
The test apparatus is shown in Fig. 1 The waterfor the e>peri-
nents r.ras obtained from a constant-Ieve1 tank installed in the Lacoratory
lrain supp\r channel. ldater entered the constant-level tank through a 12-
in. butterfly valve which was hrydraulically operated from the nain floor.
The exit was through a 6;i-n. pipe. The quantity of water was controlled
by a 5-in. gate valve, diseharged i-nto a stlIIlng pool, and passed under
a solid baffle which sewes to quiet and d:istribute the flow before it
goes to the 1.0-ft type H-flume whlch was used for measuring the quantity
of water.
Waterfronr the ll-flurne drops into a stilling pooland passes under
a soli-d baffle which se]:ves to quiet and distribute the fLow in the 6-ft
wide, lO-ft 1ong, and 2-ft deep approach channel. The approach charmel
r+as made of steel- staj-r stringer channels bolted together. For most of
the tests, the approachto the crest was e concrete channel 1eve1 with the
N-R-5 7i:4
Fig. I -TestApporotus
3
APPARATUS AND PROCEDURE
The test apparatus is shown in Fig. 1 The water for the experi
ments was obtained from a constant-level tank installed in the Laboratory
main supply channel. Hater entered the constant-level tank through a 12-
in. butterfly valve which was hydraulically operated from the main floor.
The exit was through a 6-in. pipe. The quantity of water was controlled
by a 6-in. gate valve, discharged into a stilling pool, and passed under
a solid baffle which serves to quiet and distribute the f~ow before it
goes to the 1.O-ft type H-flume which was used for measuring the quantity
of water.
Water from the H-flume drops into a stilling pool and passes under
a solid baffle which serves to quiet and distribute the flow in the 6-ft
wide, 10-ft long, and 2-ft deep approach channel. The approach channel
was made of steel stair stringer channels bolted together. For most of
the tests, the approach to the crest was a concrete channel level with the
Fig. 1 - Test Apparatus
I
4
crest and. equal to the srest lengt'h i-n bottour width" The eoncrete channel
sides had. a 1 an 2 slope, ..The outlet char:nel was 5 ft widen 10 ft longt
and 2.5 ft ddep. The hea&rall between the tllo ebannels was provided r+ith
an opening fsr insertion of itre models" Ae adjustable gate at the do'r*a-
streefl end of the exit charurel contrsls the tail*rater level.
A poi-nt gage r,ras attached to a carrj-age wh-ich ran op rollers along
the top of tire char:nel in sueh a nar:ner that 1eve1s enprhere ire the approach
charxrel ar:d in the test section eould be readily obtaiqed. Tbis gage was
used in setting ihe nodel-s to the eorrect el-evation and in detetrtdnir:tg the
level-s of the rsater surfaee and the sand bed" ?he modeLs 'lrere :nade of p1y-
sood and. white pine, With the use of, }rmber, clu"nges were :aade rnrith very
little efforb. CIrdiaary coacrete sand pasoiag an 8-mesb screen was used
for the strean bed d.or,nrstrean from the spillway. fbe eroeisn of the sand.
bed nas used as a $ea$ure of the effieieney of the outlet.
In eaeb experS*rent, a stiIlfurg basia was i-astalled and the strearn
bed was filled, sith sand to an elevation above the top of the end si11.
Ttre bank slope was approximaiely I on 2, ?he stream bed was flooded so
that the initial rr.rsh of iraterLhrough the stiLl-ing basin roou"ld not erode
the strean bed exeessively" fhe gate valve tn thp supply l!ne' tras then
opened to give the desired. &ischarge, and. the tailtraiez' Level was ad.justed
to give the carrect depth. A flot* photograph was takes dr:ri*g itre test.
After the water had rr:n through thE nodel for tsio hoursr the valve was
elosed and the water allosed to di!'ain* fhe water 3eve1 in the outlet lras
measured at irlteryals during the dralnage proeess by measrs of the point'
gage" Zero elevation was as*r,red to be the elevation of the top of, *?re
end. sj.11" tr'ihite wocl yar"a tras placed on the water 1j:re at l-in, isrtervaSs
to define the eontours" The eodSqred bed was photographed t's raeord the
scour"
Ihe data obtained fusing each test consj.sted of the stn:cture di-
xxensiaas, flsw da*a, netes, end photographs. The photographs provided the
principal mear:s of recording and analyaing the perforraance of the slme*
trJ.re" Since only oae featnre of the sii3li$g basirr was changed for each
testo the phatographs provid.ed a record. of the eff*c* of eaeh change and.
serued to define the opti-fi$xt d.inensionr"
4
crest and equal to the crest length in bottom width" The concrete channel
sides had a 1 on 2 slope . ..The outlet channel was 5 ft wide, 10 ft long ,
and 2.5 ft deep. The headwall between the t wo channels was provided lvith
an opening for insertion of the models. 1m adjustable gate at the down
stream end of the exit channel controls t he tailwater level.
A point gage was attached to a carriage which ran on rollers along
the top of the channel in such a manner that l evels anywhere in the approach
channel and in the test section could be readily obtained. This gage was
used in setting the models to the correct elevation and in determining the
levels of the water surface and the sand bed. The models were made of ply
wood and white pine . l-li th the use of lumber ,changes were made with very
little effort. Ordinary concrete sand passing an 8-mesh screen was used
for the stream bed downstream from the spillway. The erosion of the sand
bed was used as a measure of the efficiency of the outlet.
In each experiment, a stilling basin was installed and the stream
bed was filled vIith sand to an elevation above the top of the end sill.
The bank slope was approximately I on 2. The stream bed was flooded so
that the initial rush of water through the stilling basin would not erode
the stream bed excessively. The gate valve in t l1.e supply line. vTaS then
opened to give the desired discharge, and the tail~ater level was adjusted
to give the correct depth. A flow photograph was taken during the test.
After the water had run through the model for t wo hours, the valve was
closed and the water allowed to dfain. The water level in the outlet was
measured at intervals during the drainage process by means of the point
gage. Zero elevation was assumed to be the elevation of the top of the
end silL Whi te wool yarn was placed on the water line at l-in. intervals
to define the contours . The contbured bed was photographed to record the
scour.
The data obtained during each test consisted of the structur e di
mensions, flov1 data, notes, and photographs. The phot ographs provided the
principal means of recording and analyzing the performance of the st ruc
ture. Since only one feature of the s t illlllg basin was changed for each
test, the photographs provided a record of t he eff ect of each change and
served to def ine t he optimum dimensi ons.
TEST HESI]ITS
The vesults of the tesis rnade to deterciline the di:irensions of the
strai-ghtdrop sprllway si;ilIing basinwill be pnesented separe'ue1.v- for each
elenent comprising the basin. Tire o::Cer cf' presen'r,e"tj-on is not the order
in t+i:ich the tests r,lere condueted. In fact, it lqas neeessary to siu$r solre
elei;:ents several tjmes because a cha:r"{e in one elel,rent woulC, affect the
perfo:taa-nce of other elernentsr ffid tire best result coulcl only be obtained.
aftei" ea"ch elenent had i-ts optjmurn djmensions. ,
'^-rth of Basi-nr c T T L
ft i.ras recognized before the tests ',+ere begun thet the point at
rrhich the nappe hit the stilling basin floor nould provide one of the di-
nensions f*r ti:e de-b.eminatj.on of the basjn l-ength. Other C:r,rensians d.e-
ten::ining the basjn length e-re the distance from the nappe to the f'1cor
blocks and. the distance fronr the flocr blocks to the end of the basin.
Ea-ch of ihese di:aensions wil-l .l:e
discussed. in turn,
Nappe lraJectory
a
?he equaiion first used rlurjrg these studies to givg t?:.e trajec-
tory of the r-r;':irel surfaee of the free-fc.l1ing nappe is
"+,]t,a-
H^ | / a t a P
Ur {O - U . J -U )
zx( _ _ ) +
ITl t
;::ez-e yn i-s the vertical disi;ance, x* is tJre horj-zontal distence fromI I
t:e crest to the upper surface of the napper and H is the total head..
f . i is equat ion r , ' is der ived fron data presented b,- D: ' . A" T. Ippen [5] for--:-e free overfell, si:rce '-}: s,r'a'i..ht drcp spil-1 i,;e;r is assu:ieclto l"rave the
a;prcach che.nnel level r'-ith 'i;he spi,J-lwa;r erest.
Thrs equation pro.red satisfactcr;:.' '::rti1 tests T.lere ;..ui'L 1.r:-th the--€:-l--'i:,ier 1evel close to tjre spi1h"'e.y crest, lror t]:ese tesis the nappei'd -ci ial]- freel;r Lrut l.ras sup*,rorted by the high tai}i:ite::" ?he result'*=s i:r::i ice na,:pe hit Lhe sirean ted aioi"jl:rstr+ernof the stillinl: basin and.
.' 5
TEST RESULTS
The results of the tests made to determine the dimensions of the
s traight drop spillway stilling basin will be presented separatel y fo r each
element comprising the basin. The orde r of presentation is not the order
i n which the tests "rere conduct ed. In f2.ct, it iv-as necessary to study some
elements s everal times because a change in one element would affect the
perforraance of other elements, and the best result could only be obtained
after each element had its optimum dimensions.
Length of Basin
It was recognized before the tests iv-ere begun that the point at
vJhich the nappe hit the stilling basin floor would provide one of the di
mensions for the determinatlon of the basi,,- l ength . Other dimensions de
termining the basin length are the distance from the nappe to the floor
blocks and the distance from the floor "910cks to the end of the basin.
Each of these dimensions will be discussed in turn.
Nappe Trajectory
The equation firs t used during these studies to giVE? the trajec
t ory of t he upper s urface of the f ree-fa lling nappe is
~ ·::ere
y n
H = 0.46 - 0.105
is t he vertical dis tance, x n
is the horizontal distance from
~ :.e crest to the upper surface of the nappe, and H is the total head 0
:':Lis equation 1ms derived from data presented by Dr. A. T. Ippen [5] for
~::e f ree ove r Iall, since the s traight drop s pilhmy is assuI!led to have t he
-J roach channel level Hith the spil11vay crest.
This equation proved satisfactory ul1til t e sts Here run u-rith the
";.ai ~·-c..Le r l evel close to the spilhray crest. For these tests the nappe
" :lot fall f r eely but i'las supported by the high tailuat er . The result
t: E..t the na~:,pe hit the stream bed dO'l-ffistream of t he sti lling basin and
b
sconred a deep hoLe there, The fact that greaier $oo1rr was obtainecl r'rith
a higher tailwater 1evel had a;r important effect on the stilling basin de-
sign. Although this diseovery is conirar'' to the widely held' opinion that
higher tai-h.rater w'i1l car:se less $e011r to occur, it is an entirely logical
finding. The r+aier in the free-falli-ng nappe is assumed 'bo heve a con*
stant horizontal velocit;' and a vertical- velocity accelerating under the
effect of gravity. }-fter the free-falling nappe plunges into the tail--
gater, gravity is no longer effective and the zubmerged- nappe rrill con-
tinue in the direction the free-fal1ing nappe was tlaveling when it entered
the tailwater. Near ihe crest the upper surface cf the free-fa1lirtg nappe
trajeciary has a relatively fla!=slope, and il tne tailt"rater ]evel is af--
so close to the crest, the subraerged. nappe w'i11 cont|mre cn this flat
slope. The result is, of course, ihat the submerged nappe trajectory is
rorell downstreen of the free'falling nappe trajectory uhen the tailwater
l-evel- as ru-gn.
One qualification to the statement regard,ing the plunging nappe
should. be made- i,Ihen the tailwater level ls considerably above the crest
of the spillway, the nappe does not plunge through the iailwater but 'rfloatsrt
on or close to the surface of the tailwater. For ihis conditionr the nappe
does not attack the bed downstrean from the stilling basin''" Duri:rg the
tests it rsas noticed. that the rrsurfaee nappert occulred' r"rhen the d.epth of
the tailwater above the spillway crest leve1 e.xceeded two-thirds the crj-ti-
ca1 depth approximately. Therefore, it i-s eoncluded that the effect of
high tailwater levels on the positi-on of the nappe need not be considered
in the determination of the stilling basin lengti: when the tailwater level
exceeds the spillway-lcrest elevation'p1us tr^ro-thirds the criticd- depNh,
but the effect of Sailwater on the nappe t:'ajeciory must be considered for
tai-lwater elevatisns lower tharr the spillway crest elevation plus tr'ro-1;hirds
the critical d"epth. T]1 otherword.s, the ma-t'i-mi:m tailrraier level that wi1l
affect the stilling basin length 5-s that leve1 uhich is ttro-i,hirds the
criiical. depth gbcve the spilh+ay crest level'
After discovering that the taitwai,er lerrel in-fluenced the nappe
trajectory, -bests trere made .consideri-ng that the nappe is free-f a| ii:g; io
the tailr+ater level anC coni,inues on a iangent be}'onC that point- These
tests resultecl j-n consid.erably tr-onger basins w*en ihe tai-},rater r+as high.
In fact, the expei.jments sborsed that the basins '*rere longer than Ir-ecessary
6
scoured a deep hole there. The fact t hat greater scour was obtained 'I,lith
a higher t ailwater level had an important effect on the stilling basin de
sign. Although this discovery is contrary to the 'Iridely held opinion t hat
higher taili·mter vlill caus e less scour to oc cur, it is an entirely logical
finding. The water in the free-falling nappe is assumed to have a con
stant horizontal velocity and a vertical velocit y accelerating under the
effect of gravity . After the free-falling nappe plunges into the tail;;,.
vmter, gravity is no longer effective and the SUbmerged nappe 'Hill con
tinue in the direction the fr'ee-falling nappe was travel~ng when it entered
t he tailvmter. Near the crest t he upper surface of the free-falling nappe
trajectory has a relatively f lat. slop$, .Sllldif the tailwater level is 3~
so close to the crest, the submerged nappe will continue on this flat
slope. The result is, of course, that the submerged nappe traject ory is
,\-1811 downstream of 'the free""falling nappe trajectory when the tailwater
level is high.
One quali f ication t o the statement regarding the plunging nappe
should be made. Hhen the tailwater level is considerably above the crest
of the spillway, the nappe does not plunge through the tailwater but lIfloats tl
on or close to the surface of the taihrater . For thi s condition, the nappe
does not attack t he bed dOvmstream f rom the stilling basin •. ~ During t he
tests it vlas noticed t hat the tlsurface nappe lt occur red when the depth of
t he tailwater above t he spilhray crest level exceeded two-thirds the cri ti
cal depth approximatel y . Therefore, it is concluded t hat the effect of
high tailwater levels on the position of t he nappe need not be considered
in the detenninatiQn of the stilling basin length when the tail~.,rater level
exceeds the spillway :" crest elevation 'plus two-thirds the critical depth ,
but the effect of ~tailwater on the naplle trajec tory must be considered for 1_ . '.
tailwater elevations lower than the spilhray crest elevation plus t ,vo-thirds
the critical depth. In other wordS, the maxitlllUTI taih.,rater l evel that wil l
affec t the stilling basin length . is t hat level uhich is two- thirds the
critical depth ?-bove the spilhmy crest level.
After discovering that the tailwat er l evel influenced t he nappe
trajectory, t ests were made ,consi dering that the nappe is f ree-falling to
the t ailwater level and cont inues on a tangent beyond that pOi~lt. These
t ests r esulted in considerably longer basins ifhen the tail~.,rater vIas high .
In fac t, the experiment s showed t hat the basins were longer than necessary
T
sc they were shos"tened successivel;r utrltt th*t were so short that their
perfor',nance becar;re poorr .As a result cf ihese iests, the *ptiraunr trajec-
tory cf ihe 'r:pper nappe sr.rrface for use in determi:ring one of the elements
*aki-ng up ihe basin length ''*as foend to be mid,*ay between the free-fal1ingcnd f ho c r . i ' - a r . ^od t f a j ee tO f i eS .s i j v v e v f 4 v e .
?his mean trajectory "r+a-s used for all subsequent tests and was
for:nd i;o give entirely satisfactory results, It 1s proposecl only for use
i:r de'r,err:rining the length of the straight d.rop spill;"ray stilling 'basi:r
and
should not be used ilor cther purposes until it i.s confir:aed for such usen
?he eqr.ration of the upper surface of the free-fallilg nappe pro-
posed. for use is
This equei,ion is a reerrangement and a subsiitution of
the general equaiion for free-felling nappes presented
T+ ^-.^'r.:^^ +^ ]Lg free overfal-l only.J V c l i P f J U J L U ! i - !
v- o,ho6 * /:.r*5 - f+.:ae f'%
0.l+06 + ,B,l:gS - J+.368 :\ rl / d .
i
n
ri
f r \
3de/2 for H in
[ 6 ] .by Blaisde1*l
At lhe point r"'here the upper surface of the free-falling nappe
strikes the stil]ing basin f1oor, Ea,. (1) becone" '
( 2 )
where x,, is -r,he haviaantal distance frorn the crest to the upper surface
of the free-fa1ling nappe at the elevatien of -r,he stilling basi:n flaor,
The eqriationfor the upper "u"f*"" of the submerged napps irajec-tory abave the tai}.,ra-ter leve1 is the same as that for the free-fa1ling
nappe. The poi:rt at which the upper nappe plunges into the 'uailueter is
0.1+06 + I e \
I'
F = -
j!.
U4 = 3
*-here x, is the1-.
the surface of ihe
harizontal distan-ee
upper nappe plunges
frorn the erest to the point at which
into ihe tailnater and y+ is theU
7
so they were shortened successively unt:Ll they were so short that their
performance became poor • . As a result of these tests, the optimum trajec
tory of the upper nappe surface for use in deierminingone of the elements
making up the basin length li as f ound to be midway between the free-falling
and the submerged trajectories.
This mean trajectory was used for all subsequent tests and was
found to give entirely satisfactory results. It is proposed only for use
in determining the length of the straight drop spilhray stilf ing basL'1 and
should not be used for other purposes until it is confirmed for such use.
The equation of the upper surface of the free-falling nappe pro ..
posed for use is
x n
= - - 40386 y n
(1)
This equation is a rearrangement and a substitution of 3dc/2 for H in
t he gene ral equat ion for free-falling nappes presented by Blaisdell [6].
It applies to the free overfall onlye
At the point where the upper surface. of the free-falling nappe .. strikes the stilling basin f loor, Eq. (1) becomes
(2)
where is the horizontal distance from the crest to the upper surface
of the free-falling nappe at the elevation of the stilling basin floor.
The equation for the upper surface of the submerged nappe trajec
tory above the tail'dater level is the same as that for the free-falling
nappe. The point at which the upper nappe plunges into the taihrater is
(3)
\-lhere is the horizontal distance from the crest to the point at which
t ne surface of the upper nappe plunges into the tailwater and Yt is the
B
vertical distance from the crest to the ta-ilwaier surface. It is necessary
to keep the signs correct, renembering -i;hat yt is positive above crest
elevation and negative below, fhis is il-lustratedinthe definition sltetch
of Fig. 2, The equation of the trajectory of the upper nappe surface below
tailwater leve1 1s
a.69r + 0.228 (x"/a")z - tvota")
0.185 + 0.l+56 (xrla")
nhere *rr" j.s the horj-aontal distance from the erest to ihe upper surface
of the submerged nappe. Fquation (l+) lras obtained. by considering that the
portion of the nappe trajectory above the tailr^rater 1evel has the saae
equation as does the free nappe trajectory, trhile below the tailwater level
the nappe trajectory has a slope equal to
a (yrld")= - 0 . 1 8 5 - a , \ 5 6
T
Ll.
xns i l , 1
. / 1 1 \o. \xt lcc/
Equation (5) ean be obtained
At the point where
jectory strjkes the stil-1ing
by rearranging and
the upper surface of
basin fIoor, Eq. ( l+)
differentiating Eq. (3).
the subnrerged nappe tra-
becomes
t \ t
\ o /xm
l_
.1
a
Values of *" have been computed for a wide
results are presen'i;eo. graphically in Fig. 2.
0.69r + a.228 (*r/a")z - ( :r /d")
0.185 + a,b56 (xr/a*)
The clistanee from the -;erest at which the average of the irpper
surfaces of the free and. submerged nappes strikes the floor *" is used
to deteruTine part of the stilling basin length. The eque.tj-on for t. is
= k * * T (r)
range of cqnditions. lhese
8
vertical distance from the crest to the tClihrater surface. It is necessary
to keep the signs correct, remembering that y t is posi ti ve above crest
elevation and negative below. This is illustrated in the definition sketch
of Fig . 2. The equation of the trajectory of the upper nappe surface below
tailwater level is
x ns
d c
2 0.691 + 0.228 (xt/d) - (y /d ) c n c (4)
't~here xns is the horizontal distance from the crest to the upper surface
of the submerged nappe. Equation (4) Ivas obtained by considering that the
portion of the nappe trajectory above the tailwater level has the same
equation as does the free nappe trajectory, vJh,ile below the tail'tfater level
the nappe trajectory has a slope equal to
d (Yt/dc)
d (xt/dc )
Xt
0.185 - 0.456 -d c
(5)
Equation (5) can be obtained by rearranGing and differentiating Eq. (3).
At the point where t he upper surface of the submerged nappe tra
jectory strikes the stilling basin floor, Eq. (4) becomes
0.691 2 + 0.228 (xt/d) - (Y/d ) c c (6)
The distance from the ~;crest at vlhich the average of the upper
surfaces of the free and submerged nappes strikes the floor x is used a
to determine part of the stilling basin length. The equation for x is a
x =----a 2
Values of x have been computed for a wide range of conditions. These a
results are presented graphically in Fig . 2.
x.,/dc2 3 4 5 6 7 8 9 1 O
I
o
I
2
3
4
4 sgc
6
7
I
9
t o
YtG+o.7
+o.65
+o.6
+o.55
+O.5
+o.4
+o.3
+o.2
+o . l
o
Fig. 2 - Design Chort for Determinoi ion of x^
Lower noppe(No toi lwoter)
Toilwoter level
A-Tongent or point I,\ of submergence I
N'*x!:1,*oi"a trojectoryFree noppetrojeclory
o 1
4 6 7 8 9 10
Yt de
9
2 +0.7
3 Lower nappe (No toi 1 water)
6
7
+0.65
+0.6
+0.5
+0.4
8 ~angent at point
..L Mean of submergence de trajectory ~ ~ -+~~r+-~t----''Irl-~d-~~d-~-'" +0.3
~ \" Submerged nappe
9
Free nappe , \ traje ctory -t-;'~l-tr---t'~Hr+~+-~--"IIrl-"In trajectory --\ :\ +0.2
~ "~Xa/d:----;
r--+-+-~~rl-~-~~~-P~~~~
Fig. 2 - Design Chart for Detenni nation of x a
10
" htrhen y/dc, vr/d"r or Tt/d* exeeeds 0"728r tire valae ur:.der
ihe rad.ical 5:: Xqs" (f), ie), end (3) necan:es negative and the racis i:f
the equation aye i:aaginary, I{owever, si-nee the stilliag basj:r i-ength is
not affected b;r ihe tailwaier levels which exceed bro--Lhirds the criticai
d.epth approximately, tVrlA*> 0"6?r approxj:aaielylr ihis li:,:itaii-on is
not Smportaat here. &eferring *o Fig. ?, it is suggested that the cnrve
for v./a = a.7 be r:,sed rghen y,ld exceeds +A,7. ?h-1s rule was used"L ' c ' r ' ' cduring the labovatory studies with entj-rely satisfactory resr:1ts,
Distance to Floor Bl*cks
Sufficisnt distanee is requ:ired betneen the point at rrhish the
rrpper nappe strikes the basin floor and the flcsr blocks tc pertri:it the
stream io besome approximately para13e1 to the f1*ar l:efore it reaches
the b1-ocks* The dete:xrir:aiion of ihe *pti-num d:imension proved to be large-
ly a sratter of the judgroent af the sbseffer. It was deslred to make
this diri,ension as sma11 as possible. ifowever, if the floor bl*cks are tos
close to the nappe, a l:-igh boil is ihrorE"s. cff of the blocks, lu'her: ihe
distance between the r:pper nappe and the fl-oor blocks
0"5 d^, they proved to be largely ineffeciive, This
? was less tha*
shorm by ihe
se?eve bar:k ercsion in F'ig. 3a where the floor blecks are lacated ai the
point r'rhere the upper nappe strikes the stilllng basi:r floor; that is,
where *b = 0. The scour in Fig. 3a is as severe as that in Fi-g, 3b where
no floor blocks are used. l.Ihen *b = 0.5 d" the boil caused by the fSoor
blocks r'ras higher than was eonsidered desirable. i',then % r+as ineveased
to O.Bd"r the appearanee of the water sarfaee was satisfactory, A$
shown in Fig, [, the bed sconr was decreased and the bl-soks ga're sufiicient
protecii-on ie the bar:irs so they stood at' thcir angle of repose, The d:i-s-
tance q = 0.S d^ Eas used. for all subscquen* tests sith resalts thath F
were complete}-y satisfectary,
?1:e early tests to detersrine % were rsade using d pair of
longitudinal si1ls in the stilli*g basiR. Later it rsas diseovered that
longitudinal sills are r:nne*essary if the floor bloeks are proper'3-y p:"opar-
tioned and spaced" i'Io fuviher siudy'aras ltade'bs redeierTiline %. Hcvever,
the tests made with 5 * *.8 d* *irsued this d"istance *c give sailsfa*'bary
stil1i-ng basin perf cr:rrranc e,
10
~men y/dc ' y~dc' or Yt/dc exceeds 0.728, the value under
the radical in Eqs. (1), (2), and (3) becomes negative and the roots of
the equation are imaginary. However, since the stilling basin length is
not affected by the tailwater levels which exceed two-thirds the critical
depth approximately, (y t/ d c > 0.67, approximately), this limitation is
not important here. Referring to Fig. 2, it is suggested that the curve
for Yt/dc = 0 .7 be used when Yt/dc exceeds +0.7. This rule was used
during the laboratory studies with entirely satisfactory results.
Distance to Floor Blocks
Sufficient distance is required behveen the point at which the
upper nappe strikes the basin floor and the floor blocks to penni t the
stream to become approximately parallel to the floor before it reaches
the blocks. The determination of the optimum dimension proved to be large
ly a matter of the judgment of the observer. It was desired to make
this dimension as small as possible. However, if the floor blocks are too
close to the nappe, a high boil is throvm off of the blocks. Hhen the
distance between the upper nappe and the floor blocks ~ was less than
0.5 d, they proved to be largely ineffective. This is shovm by the c
severe bank erosion in Fig. 3a vlhere the floor blQcks are located at the
point where the upper nappe strikes the stilling basin floor; that is,
where ~ = O. The scour in Fi g . 3a is as severe as that in Fig. 3b 1fhere
no floor blocks are used. "men ~ = 0.5 dc
the boil caused by t he floor
blocks viaS higher than was considered desirable. vihen ~ i.Jas increased
to 0.8d, the appearance of the 'tvater surface was satisfactory. As c
shovm in Fig. 4, the bed scour was decreased and the blocks gave sufficient
protection to the banks so they stood at their angle of repose. The dis
tance ~ = 0.8 dc
was used for all subsequent tests with results that
were completely satisfactory.
The early tests to determine xb uere ma.de using ;Ef pair of
longitudinal sills in the stilling basin. Later i twas discovered that
longi tudinal sills are urmecessa.ry if the floor blocks are properly propor
tioned and spaced. No further study was made to redetermine YD ' However,
the tests made with Yo = 0 . 8 dc
showed this distance to give satisfactory
stilling basin performance.
1 1
theFloor Blocks l,ocated at, the Point ivhere
lJappe Strikes the Bas-,rt Floor
b. No Floor Blocks
Fig. 3 - The Bed Scour ls Deeper thon Necessory ond the Bonk Scour lsExcessive Becouse of lmproper Locotion or Absence of the Floor Blocks
a. Floor Blocks Located at the Point ,,,here the upper Nappe Strikes the Basin Floor
b. No Floor Blocks
Fig. 3 - The Bed Scour Is Deeper than Necessary and the Bank Scour Is Excessive Because of Improper location or Absence of the Floor Blocks
11
,
t aI L
Fig. 4 - Floor Blocks Locoted 0.8 d" from the Point Where the NoppeSti ikes the Bosin Floor ond |.75 d^'from the End of the 5t i l l ing BosinGive Moximum Protection to the Bdd cnd Bonks
The recomrnended distanee from the point at r+hich the average of
the upper surfaces of the free-fa1ling and submerged nappes strikes the
stilling basjn floor to the upstr€am face of the fLoor blocks is
x . - 0 . 8 dD C
( B )
Distance to End Sil1
If the distance between the floor blocks and the end siIL is
too short, neither the blocks nor the end si1I are fu1ly effective. ?his
is evidenced both by excessj-ve scour of the channel bed and strong eddj-es
rvhi-eh erode the banks and the dam filI.
The ninimirn distance between the floor blocks and the end sil]
x thatprevents this excessive scourwas found to be L.75 d . Di-stancesc ' C
greater than 1.75 dc had little beneficial effect on the scour pattetr.
Values of x, as great as 2.7t d were tested. Figure I shows that thec - e
floor blocks are located too close to the end sil1 when x" = 0.75 d"'
I,Jlren x * !.75 d , as jn Fig. l+, the floor blocks are fu\y effective.c c
12
Fig. 4 - Floor Blocks Located 0.8 de from the Point Where the Nappe Strikes the Basin Floor and 1.75 de from the End of the Stilling Basin Give Max imum Protection to the Bed and Banks
The recommended distance from the point at which the average of
the upper surfaces of the free-falling and submerged nappes strikes the
stilling basin floor to the upstream face of the floor blocks is
(8)
Distance to End Sill
If the distance between the floor blocks and the end sill is
too short, neither the blocks nor the end sill are fully effective. This
is evidenced both by excessive scour of the channel bed and strong eddies
which erode the banks and the dam fill.
The minimum distance between the floor blocks and the end sill
x that prevents this excessive scour l-;as found to be 1.75 d. Distances c c
greater than 1.75 d had little beneficial effect on the scour pattern. c
Values of x as great as 2.75 d were tested. Figure 5 shows that the c c
floor blocks are located too close to the end sill when x .. 0.75 d • c c
~·Jhen x = 1.75 d, as in Fig. 4, the floor blocks are fully effective. c c
Fig . 5 - F loor B locks Locoted 0 .75 dc f rom rhe End o f rhe St i l l i ng Bos inAre lneffective; the Bed Scour ls DeEper thon Necessoryr ond thl BonkScour ls Excessive
Here agai-n the judgment of an exlerienced observer is essenti-al
to the deterndnation of the nin-inu'r value of x^ that gives the rnost
satisfactory performance.
It is recommended, as a result of these tests, that the rrinimun
dlstance between the upstream face of the floor blocks and the exlt of the
still ing basin x. be
1 n f 't " l ) d
val-ues of *" greater than r.75 dc may be used if , for sorae reason, thebasj-n must be lengthened. The lengi;hs *u and
% should not be variedappreci-ably fron the values given i-n Eqs. (?) ana (B).
Tailwater Depth
A sufficj-ent depth of tailwater is required so that the waterleaving the stilling basin has no opportun-ity to plunge and scour a hole
in the strean bed; the water surface (tailwater level) in the downstream
1 o \: r )
Fig. 5 - Floor Blocks Located 0 .75 de from the End of the Stilling Basin Are Ineffective; the Bed Scour Is Deeper than Necessary, and the Bank Scour Is Excessive
13
Here again the judgment of an ex:.-='erienced observer is essential
to the determination of the rninir,wn value of x that gives the most c
satisfactory performance.
It is recommended, as a result of these tests, that the minimum
di stance between the upstream face of the floor blocks and the exit of the
stilling basin x be c
x :> 1. 75 d c c
(9)
Values of x greater than 1. 75 d may be used if, for some reason, the c c
basin must be l engthened. The lengths xa and ~ should not be varied
appreciably from the values given in Eqs. (7) and (8) .
Tailwater Depth
A sufficient depth of tailwater is required so that the water
leaving the stilling basin has no opportunity to plunge and scour a hole
i n the stream bed; the water surface (tailwater level) in the downstream
Ii+
channel siiould be at approxi*iately the same level as the lrater surface in
the sti1-ling basin, This requ:|res the detersrination of a m:inj*ruro reqr:r-ired.
taillrater depih for the stilling basin.
The niai:au:n pe:nissrble depth cf the tailwater above the sfiiS:ing
basin floor de was found to be 2.T5 de, The tai},rater depih over the
end" sill is L.75 dc, since the end. s'il1 is g,h d" iiigh. The resulting
veloci-ty a.t the exii of the stilling basin is
^ ^ t= J . l l 1
r.rr., fnr tr:r"imr.q rlalge5 Of H And the corresponding valaes of d",
3 i + 5 6 f t
t-I Oal
Y o*c
T;IL . I 2
. L l Z
t 1 -
u
1!
a,67
c.
J . l 4
a , v v
4 ' ) o
t . o {
2 r L 7
? ? ?
r ' ^ a
l+.AO
r, LR
I T
f n cr v s
It is apparent 'Lhat the adopted rainj-*r'um taifs{ater depth results in veloc-
ities at the stilling basin exit ihat are, in most cases, gveater than
can be tolerated by the ordinary mate-r'ials comp:'iring natural dor"rnstrear,'r
channels. Therefore, ii: is assrmied that e:ry ati;enpt to furLher decrease
dZ lsould be of no practical value since argr decrease in dZ *"+o;.:,1d cau.se
higher exit veloci--uies, Even r,rith tlie present velociiies, $osre widening
of the dcrqnstream channel near the stilling basin e6r:. be expecied, This
is tolerated because! it does not endanger the outle* or the dare fi11, srrd
further increases j-n ihe minimr:::i tailisater reqr:-treneni l-rill urrnecessarily
increase the cost cl ihe oi:.tlet.
The resalts of the tests to deterraine the nrinj:nurn aceeptable
tailr^later level are presented in Fig" 6. The tests -r'Iere conducied as
noted in the sectian deseribing rrApparatus and Procedurerr using tailwater
leveis varying frorn an excessivel], high to an excessively 1ow level. /rt
the conelusion of the tesis to deterraine the tail"r'=ater depth, the phcta-
graphs of the bed contours Tirere studied and gfven a. rati-ng of good, falr,
or poor as each indjvidual case r'rarranteci. T;pical photographs ar* showr in
Fig, 7. In Fig. 7a the tai}aa"ter le.rel a*a$ excessil-e1;'high (Ct = A.Lil d.).
14
chaIl.l1el should be at approximately the Si3me level as the v,rater surface in
the stilling basin. This requires the determination of a minmtull required
tailwater depth for the stilling basin.
The minimum permissible depth of the tailwater above the stilling
basin floor
end sill is
d2 was found to be 2.15 dc '
1.75 d, since the end sill is c
The tailwater depth over the
0.4 d hiah. The resulting c 0
velocity at the exit of the stilling basin is
v
or, for various values of
H =
d = c
v
1
0.67
2.65
2
1.33
3.74
M 1. 75
= 3.24 d 1/2 c
H and the corresponding values of
3
2.00
4.58
4
2.67
5.29
3.33
5.91
d , c
6 ft
4.00 ft
6.48 fps
It is
ities
apparent that the adopted minmtull tailwater depth results in veloc
at the stilling basin exit that are, in most cases, greater than
can be tolerated by the ordinary materials comprising natural dOvmstream . channels. Therefore, it is assumed that any att empt to further decrease
d2
would be of no pr actical value since any decrease i n d2
would cause
higher exit velocities. Even "Ji th t he pr esent veloel. ties, some ~,ridening
of the d01IDstrearn channel near the stilling basin can be expected. This
is tolerated because it does not endanger the outlet or the dam fill, and
further increases in the minmum tailwater requirement l;ull unnecessarily
increase the cost of the outlet.
The resul ts of the tests to detennine the minirnum acceptable
taihrater level are presented in Fig. 6. The t ests ~vere conducted as
noted in the section describing IIApparatus and Procedure" using tailwater
levels varying from an excessively high to an excessively low level. At
the conclusion of the tests to determine the tailwater depth, the photo
graphs of the bed contours were studied and given a rating of good, fair,
or poor as each individual case vmrranted. T;ypical photographs are sho"t,m in
Fig. 7. In Fig . 7a thetailwater level was excessively h:igl (d2 = 2.40 dc)'
r 5
2 .40
2 .3 0
2 .20
9 t , nO 6
2 .O0
lr.o t?.o r5.o r4.o l5.o 16.0
Fig. 6 - Determinotion of Toi lwoter Depih
Both the banks and the bed look good; eonsequent\y this scour patterrr was
given a rating of trgood.tr In Fig. ?b the tailwater depthwas thatadopted
for design purposes (dZ - 2.15 dc). Herealso the scourpattern was given
a rati:ng of trgood.n In Fig. 7c the tailwater depth was a 1ittle l-ow(d^ - 2.O0 d ). The banks are eroded more than is felt desirable and- z c '
the bed scour is greater than is shor,na in Figs. Ja and 7b. This scour
pattern wasgiven arating of trfairrrt sinceit isnot very bad, but it does
leave sonethingto be desired. The tailwater 1eveI for F*g. Za was exces-
sive\y Iow (d2 . 1.p0 d")r the scour of the banks ean be seen to be
excessive, and the bed is deepened considerably. This scour pattern was
given a rating of npoor.rl
The results of the analysis of the photographs, when plotted in
Fig. 5 aga5nst the relative height of the drop, show that the nrinjmr:n
desirable depth of the tailwater U, j-s 2.I5 dc and that UZ/d" is
independent of the relative height of drop. Although there is the possi-
bility that some scour patterns would be rrgoodrr when de is less than
2.I5 d"t tailwater depths lower than 2.15 dc would.ordinarily give on\yrfairtr or rrpoorrr scour patterns ard it is unr,rise to decrease the desiga
tail-water depth below the recorunended value
d2 - 2.15 dc (ro1
Ad.ditional verification of the fact that Ur/U" should be a
constant is presented bv Nazir Ahmad [7]. Mr. Ahmad found that R./q2/3
15
2.40 I I u
0 PERFORMANCE • Check test, Good 0 o Good 2.30 o Fair
00 0 A Poor
2.20 0
0 0
0 p 0 0 0 0
0 0
'" 0
!:J. 0 .6.0
0
~ de 2. 10
0 () 0 '" 0 2.00
'" 08 0 0
1.90 000
0 0 '" 0
rr", "'''' '" '" '" .
'" '" '" '" 1.80 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0
y/dc
Fig. 6 - Detenninotion of Toilwoter Depth
Both the banks and the bed look good; consequently this scour pattern was
given a rating of IIgood." In Fig. 7b the tailwater depthwas that adopted
for design purposes (d2
• 2.1.5 de). Here also the scour pattern was given
a rating of "good." In Fig. 7e the tailwater depth was a little low
(d2
- 2.00 de). The banks are eroded more than is felt desirable and
the bed scour is greater than i s shown in Figs. 7a and 7b. This scour
pattern was given a rating of "fair," since it is not very bad, but it does
leave something to be desired. The tailwater level for FJ g. 7d was exces
sively low (d2
- 1.90 dc)' the scour of the banks can be seen to be
excessive, and the bed is deepened considerably. This scour pattern was
given a rating of "poor."
The results of the analysis of the photographs, when plotted in
Fig. 6 against the relative height of the drop, show that the minimum
desirable depth of the tailwater d2
is 2.1.5 de and that d2/d
e is
independent of the relative height of drop_ Although there is the possi
bility that some scour patterns would be "good" when d2
is less than
2.1.5 d, taihrater depths lower than 2.1.5 d would ordinarily give only e c
"fair" or "poorll scour patterns and it is unwise to decrease the design
tailw&ter depth below the recommended value
Addi tional verification of the fact that d /d 2 c
( 10)
should be a
constant is presented by Nazir Ahmad [7]. Mr. Ahmad found that R/q2/3
I O
a. trGoodn Scour PattemIligh tailwater (a2 ' 2.110 d")' Banks and
bed are good.
c. trFairrr scour Patteral
lailwater s1i-ght1y low (d2 = 2'0O dc)'
Banks scoured a little and a slightincrease in bed scour.
b. trGoodil Scour Pattersr
Fqig.n tailwater (d2 = 2.15 dc). Banks andbed show l-1ttl-e scour.
d. rrPoorlr Scour Pattern
Tailwater excessively low (d2 = 1'90 d'g).
Scour of both banks and bed is excessive.
Fig. 7 - Effect of Toi lwoter Level on Downstreqm Scour
F ig . 8 - Scour neor End o f S t i l l i ng Bos in
16
a. "Good" Scour Pattern High tailwater (d2· 2.40 dc ). Banks and bed are good.
c. "Fair" Scour Pattern Taihrater slightly low ( d2 c 2.00 dc ). Banks scoured a little and a slight increase in bed scour.
b. "Good" Scour Pattern Design tailwater (d2· 2.15 dc )' Banks and bed show little scour.
d. "Poor" Scour Pattern Tailwater excessively low (d2· 1.90 dc ). Scour of both banks and bed is excessive.
Fig . 7 - Effect of Tai Iwater Level on Downstream Scour
Fig. 8 - Scour near End of Stilling Basin
is a ccnst;nt, where A is t?:e dei:th from ii:e water surface to ihe bottom
of il:e $cour hcle (see Fig. E) and q is 'i,he discharge per unit width of
the siilling basin. Since
e = vcdc = G% ac = gT/zu*t/,
elru
shere o is assr::ncc.
R = d 2 * o d " = t 2 . L 5 * o ) d "
to be a constant, (see Fig. 8),
p
\:t
= - - +--e/ J -1
c
d 2 * o d " d ' + o d " d Z
r ̂ L/z^ s/2,,2/3 _r/i^\ 6 6 * c J 6 * c
?lri.s alge=*raic manipulati-on incJ.ice.tes t}:at R/qZl3 and do/d^ are varia-z ' cbles rrlt.i ch di-ffer in absolute aagni-tude only b;' the application of cerbain
constan'ts and fu:";l'iec' verifies tlle finchng that d,/d. is a constant,
The cheek tests plotteci in Fig. 6 showed tf,lt a tailwater depth
of 2.15 a^ gave eniirely satisfactory scour pat:-.errrs.
Floor Block *:rd En{_Sill Height
The heighis of ihe floor bloeks and the end sill greatly 1nflu-
ence the perf*r:rance of the sti-l-}ing basin and help to deter:nine ihe amount
of scour in the downstreem channel. it e'as found that the floor blocks
-or5naril;' influenced tlre arouni of bank erosi-on r.rhile the primary- effect
of end sill- heiglht r'ras on the depth of bed scour,
The tests nade to det+:Ttine the floor block and end si1l heights
are sumile.:'ized in Table I. .$-ilter ca.refully considering these data, the
opti:m:.m floo:. blcck height uas tel:en as C,E d,- and the end sill height
o .h dc .
T]:ree thi-ngs were looked for in cornparing the data of Tabl.e T:
(i) fiie ;,-aJri;iiur? aeni;h oj scou:: should. not be excessive and should. be ire1l
^ 1 . J
A a . L > T u- = = COnStant
t / z t l zn- / / * " / J
17
is a const2nt, 1-There R is the depth from the "Jater surface to the bottom
of the scour hole (see Fi g . 8) and q is the discharge per unit width of
t he s t illing basin. Since
q = v d = r::::.lgd d = ;:;1/2 d 3/2 c c V6Uc C 0 C
and
R = d2
+0 d = (2.15 + a)d c c
-here a is assl.lliled to be a consta..'1t (see Fig. 8),
R
2/3 q ( 1/2d 3/2)2/3 g c
= a 2.15 + a
+ ---- = --------1/3 1/3 g , g
constant
This algebraic manipulation indicates that R/q2/3 and d2/dc
are varia
bl e s 1'Thich differ in absolute magnitude only by the application of certain
cons t ants and further verifies the fi ndi ng that d2/dc
is a constant.
The check tests plott ed in Fi g . 6 sho-tied that <\ taihvater depth
0 _ 2.15 d gave entirely satisf ac t ory scour patt erns. c
Floor Block and End Sill Height
The heights of the floor blocks and the end sill greatly influ
ence the performance of the stilling basin and help to determine the amount
of scour in the dOl.,Tnstream channel. It Has found that the floor blocks
_ rimarily iJ:l~luenced the 81uount of bank erosion i-Jhile the pr:L-nary effect
of end sill height ,-Tas on the depth of bed scour.
The tests made to determine the floor block and end sill heights
are summarized in Table I. After carefully conSidering these data, the
optimum floor block height Has taken as
0.4 d • c
0.8 d c and the end sill height
Three things were looked for in comparing the data of Table I:
( _ ) The ;-naxlurum depth of scour should not be excessive and should be well
1 B
Table I - FL00R BLOCK AND EI\IDSIIT I{EIGHT
' i lepl"h oi Soorr
( inehas )
Test T,ong. Si11No. Helght'"
:__^ (42
u . ) o c
o . )75o.562o.552o.6000 .600
0.5000.lr500 . o z t
99 0 .625100 0.800101^ "
I U '
10 j ' - t a.5?5
1o)r')* 0.625109 a.625106 0.137107 o.)J37108 0 .137
. t loor t j lock Lnd Jf l l
Heiqht* Heleht*
MaxlnunDlstancefrom End
Depth of BasinNext to Next tolYlngrail End 5111
-2+ -2-1+ -l +-0 .5 . _o .8^ /- v . ) a . )_o.t _0.5_0.t _o.5^ /- r i . ) 4 , ) -
4 .5 - 1 . 0{ . ) - U . - l
-1 .3 -1 .1
( inches)
,36z . o o
2.662.66z . o o
2.55z .oo
z . c o
z . o o
L. ooL. ooLr. ooI .oo! . 00L 'ooL. ooL.ooL 'ooL.OOI .oolr. ooL.00h.00L. oolr.co
L . ooL.oolr, colr. CC-t)r. oo
L. oo3 . 3 3j . t l) . ) 13 . i 3l . l ?
BankEro sion
8L
86a t
88R A
90
93
a A
97
109110111l�16117
o.6?5o.625o,375r .25oo.625
0.?50o.375^ (A)
o.562o.750o.750o.3750. t62u .5oz0.6000.6000.500
0, l+50o . 6 2 5o.6250. 800o.625o,625a , 6 2 5o . 6 ? 5o , 5 2 '0 .1170. h i70 . 1 1 7o.5250. L3?v . ) l )
1.25a1 . 2 5 o
o ,5oo0 .6000 . 8 0 0o. 8oo0 .600
o .? too.375o. J15o,379o.375o .3?5o .375a.37ia.3750. L00
0 .3000 .1000 .3000. 3000 .313
o ,6250. Lcoo . 3 1 2v ' j t >
a . 3 7 5c. 312o . 3 7 to,3r20 .137A.)r37o.25a
a,250o.625a, i75o . 3 7 50. 1000,lr000.5o0c .100ii . lco
-2+-1+-1+{ . o
- 1 . 0
- l . o
- t . J- 1 r L !
- ! . U
- l r u
- 1 .3-1 .0_0 .7-.'t .0- t . c
- t . o- t . 0-1 . . o-I.2-7.2
-1.2-0 .6- t . o- r . c
--1.c
-0. l r- 1 . 0- 2 . O
-t .0
-r.2
- 1 . C
- 1 . 1-0. q:- 0 . 7
-0.8
-0 .7
-1 .O-1 .O
- t , 1- t J . o
- 0 .7
-1 .0
- 2 . 0- J . o
- 2 . C
-1.2
- i . t
-0. ?
-o .8
-7.2
-0 .7*0 .5-1 .0-0 .5o .0
-0.1r
- t . o
GoodGooCGoodGoodGood
CoodGoodFairPoor.Poof
FairFairFairGooCFair
PoorPocrPoor
Coo.lPoor
Lr5
Jt
5L0)))3320
5506lr2)h
PoorPoorGoodGoodGooC
GoodPoorGoodPoorGood
GoodGoodGoodGoodGooC
118 A .62512lr 0. 500r25 c,5ooL26 0.800\27 0 .8CCr2e 0.600
l n L e r n s o i ec
i l ) :Two row5 cf blocl ts
00Llr2
55
t0o)6
away from the downstrean end of the outlet; (2) the scour a-1ong the wing-
wa11s and at the end of the basin should be a rninj.num; and (3) tne Uant
erosj.on should have a ttgoodtr rating, a rrfairrr or rrpoorrr rating i-ndicating
that ed.dies had washed away an excessive anount of bank material. A study
of Table I shows that Tests No. 87, BB, 89, 100, 116, and 127 best nreet
these criteria. The
tests were:
Test No.
relative floor bl-ock and end si1l heights for these
ftelative floor block
BT BB 89
height o.562 o.75o a.75a
100 116 L27
o.Boo L.25a o.Boo
0.1+00 O.625 0.1100Relative end sill height o.375 O.375 O.375
18
Table I - FLOOR BLOCK AND END SILL HEIGHT
IJepth of Sr:our ( i nches)
Maxi mum Di s t ance
Test Long. Sill Floor Block End Sill d from End Next to Next to Bank c No . Height" Height* Hei!lht* ( i nches) ,Depth of Basin Wingwall End Sill Er osion
84 0.750 0.750 2. 66 -2+ 4 - 2+ -2 Poor 85 0. 375 0· 375 2.66 -1+ 5 -1+ - ) + Poor 86 0. 562 0· 375 2.66 - 1+ 2 -0. 5 -0. 8 Good 87 0 . 562 0. 562 0. 375 2. 66 -0.6 3 -0 . 5 -0.5 Good 88 0. 562 0. 750 0. )75 2. 66 -0.6 ) - 0. 5 ...{l . 6 Good
89 0 .75 0.750 0· 375 2.66 -1.C 5 -0 . 5 - 0.6 Good 90 00375 0· 375 0· 375 2 .66 -1.C 4 - 0 .5 -O . ~, Poor 91 0. 562 0 .562 0. )75 2.66 -1.0 0 -0 . 5 - 1.0 Good 92 0. 562 0. 562 0· 375 2. 66 ..(J. 3 3 -o.S ..(J . 3 Poor 9) 0.600 0 .600 0. 400 4.00 - 1. 8 5 -1. ) -1. 3 Good
90 0 .600 0.600 0. )00 0. 00 -1.3 ) -1. 0 -1.2 Good 95 0. 500 0. 500 0.)00 0 . 00 -1.l ) - 1. 2 -l. h Good 96 0 ·500 0. 500 0. )00 L. OO - 1.u 3 - 1.2 - 1.u Good 97 0. 450 0. u50 0· 300 4.00 - ] .L 2 - ).2 - 1.1: Good 98 0.625 0. 625 0. )13 4.00 - 1. 1: 0 - 1.C - J.L Gooc
99 0.625 0.625 0.625 4. 00 - 1.3 5 - 1.1 ..(J . e Good 100 0.800 0 .800 0. 4Co 4.00 - 1.C 5 - 0. 5 -c.5 Good 101'''''' 0 .625 0. 'll2 L.oo -0 . 7 0 -0 .7 -0.7 Good 102** 0.625 0.-)75 4.00 - LO 6 - 0 .1l ' -0 .6 Good 103 "-1' 0 .625 0.625 0 · 375 4. 00 -1.0 4 ..(J . B ...{l . R Good 104':1-* 0 .625 0. 625 0· 312 L. OO -1.0 2 - 0.7 -0. 8 Good 105 0.625 0 .625 0.375 4.00 - ).0 3 - 0.8 -0 .8 Good 106 0.437 0.L37 0· 312 4 .00 - 1.0 0 -0. 7 -0 . 8 Fai r 107 0. 437 0. 0'17 0. 037 4.00 - 1.2 S - 1.0 - Cl . P Poor 108 0. 437 0. 437 0. 037 4.00 -).2 5 -1.0 -O. P. Poor
109 0.625 0. 625 0. 250 0.00 -1.2 0 - 1.1 - 1.2 Fair 110 0. 625 0.437 0 .250 L.oo -0.6 0 -0.6 - 0. 6 Fair 111 0· 375 0. )75 0.2, 0 4. 00 -1.0 4 -0 .7 - 0. 7 Fair 116 1.250 1.250 0.625 0. 00 - 1,. 0 0 -0. 5 -0 . '0 Good 117 0. 625 1.250 0. 175 0. 00 - 1.2 - 1.0 -1.0 Fair
118 0. 625 1. 250 0· 375 h. oo - 2.0 5 - 2.0 - 0. 5 Poor 12L 0. 500 0 .500 0.)00 ) . )3 - 3·0 5 -3 ·0 0.0 Poer 125 0.600 0.600 O.uOO ) .33 -0. 4 -0 -O . L -o. h Poor 126 o.BOO 0 .800 0· 500 3· 3'1 - 0 .1 C -O . L, - 0.1: !!air 127 O. ACO O. eoo c . Loo 3. 13 - 1. 0 5 -0.5 -O . S Good 128 0. 600 0.600 -: · 300 3.J l - 2. 0 6 - 2.C - 1.0 Poor
In terns of d c ';:- :~ Two r ows of blocks
away from the downstream end of the outlet; (2) the scour along t he wing
,valls and at the end of the 'iJasin should be a minimum; and (J) the bank
erosion should have a "good" rating, a "fair" or "poor" rating indicating
that eddies had washed away an excessive amount of bank material. A study
of Table I shows that Tests No. 87, 88, 89, 100, 116, and 127 best meet
these criteria. The relative floor block and end sill heights for these
tests were:
Test No. 87 88 89 100 116 127
Relati ve floor block height 0.562 0.750 0.750 0.800 1. 250 0.800
Relative end sill height 0.375 0.375 0.375 0.400 0.625 0.400
1 A
l,Jith the exception of Test No. EJ, all floor blocks were twice as high as
the end sill, Both higher and lo"reer ratios of floor block height to end.
sil1 height produced either a greater depth of scour nerb to the end sil1
and r,ringwalls, or poorer ba"nk erosion, or both. Alsoo irith the exception
of Tests No. BT and 115, all end sill-s were approxfurately 6,l+ d" high
and all floor blocks were 0.8 dc high. fhe lesser height was selected
because the tailuater depth was greater for these tests than was later de-
ter:rlined to be the best min-imum depth. tihen the tailwater depth was re-
duced, there was a greater opportunity for the strean to scour the bed. in
plunging over the high end sill than in passing over the lower end sill.
Although longitudinal sills were employed during most of the
tests summarized in Table T, subsequeni tests r+'ithout longitudinal si11s
and with floor blocks and end si1l heights of 0.8 dc and g.b de.r r€-
spectively, showed that these heights were eompletely satisfactory.
As a result of the tests made to deternine
:reights, it is recommended ihat:
the height of the floor blocks be 0.8
the height of the end. si11 be 0.1+ d^
the block and sill
n
Floor Block '[.trj-dth and Spacing
The actual width and spacing of thE floor bloeks, as well as the
:roportion of tbe stilling basin,ridth occupied by the bloeks, have been
found to have an importarrt effeet on the perforn:anee i-n previous sti3.1ing
basin studles. fhe straight drop spil*lway stil1.ing basinwas no exceptioni
If the floor blocks are too wide, they do not break up the stream into
mall enough segments to di-ssipate the high-veloeity fI-ow in a short dis-
tance. If the bloeks occupy too nruch of the stilling basin width, their
cor,rposi-te action becomes more like a solid sill than like individual blosks.
Fina11y, if the blocks oceupy an insufficient proportion of the basin width
they become j-neffective. There is, therefore, an optimura spacing and pro-
::ortion of the basin width occupied by the blocks that must be dete:nrined.
The primary effect of varying the floor block w:dth and spaci-ng is on the
anount of bank erosion obtai-ned.
?he tests made to deterniine the block width and spaclr€ are sum-
narj-zed in Table 11. The same things were looked for in Table II when
19
Hith the exception of Test No. 87, all floor blocks were twice as high as
the end sill. Both higher and lower ratios of floor block height to end
sill height produced either a greater depth of scour next to the end sill
and wingwalls, or poorer bank erosion, or both. Also, with the exception
of Tests No. 87 and 116, all end sills were approx::iJnately 0.4 d high c and all floor blocks were 0.8 d high. The lesser height was selected
c because the tailwater depth was greater for these tests than was later de-
termined to be the best minimum depth. itJhen the tailwater depth was re
duced, there was a greater opportunity for the stream to scour the bed in
plunging over the high end sill than in passing over the lower end sill.
Al though longitudinal sills were employed during most of the
tests summarized in Table I, subsequent tests without longitudinal sills
and vn th floor blocks and end sill heights of 0.8 d and 0.4 d, re-c c s pectively, showed that these heights were completely satisfactory.
As a result of the tests made to determine the block and sill
:te i ghts, it is recommended that:
the height of the floor blocks be 0.8 d c
the height of the end sill be 0.4 d c
Floor Bl ock "lhdth and Spacing •
The actual 'It.Jidth and spacing of the floor blocks, as well as the
proportion of the stilling basin width occupied by the blocks, have been
~ound to have an important effect on the performance in previous stilling
basin studies. The straight drop spillway stilling basin was no exception.
If the floor blocks are too wide, they do not break up the stream into
small enough segments to dissipate the high-velocity flo'ltJ in a short dis
tance. If the blocks occupy too much of the stilling basin width, their
composite action becomes more like a solid sill than like individual blocks.
Finally, if the blocks occupy an insufficient proportion of the basin width
they become ineffective. There is, therefore, an opt::iJnum spacing and pro
portion of the basin width occupied by the blocks that must be determined.
The pr::iJnary effect of varying the floor block width and spacing is on the
amount of bank erosion obtained.
The tests made to determine the block width and spacing are sum
arized in Table II. The same things were looked for in Table II when
2 0
comparing the effect of the floor block width and spacing as were looked
for in Table I when comparing the effect of the floor block and end s111
height. A study of.Table II shows that the block width has no detectable
effect on the bed or bank scour. However, j-t will be shown in the section
on ttsidewall heighttt 'that wid,e blocks cause a tr:igh boil in the basin and
thus requi-re tr-igher sidewalls. This indieates that thene is a limit to
the lridth of the i-ndlvidual bl-ocks that nrust be taken into account r+hen
designing stilling basins.
Table II - Ft00R BLOCK hTDTH AI\D SPACING
Basi,r Wldth0ccupled
Block bv Blocks longryicth* (ier cent) silts
o.z t 50 .0 2o .25 L1 .7 2o.25 111.7 20 . 2 t 5 0 . 0 0o .25 50 .0 2o .?5 5o .o L0 . 3 7 5 5 0 . 0 00 .15 50 .0 0o .5o 5o .o oo . ! t 60 .0 o0.3o lro.0 0o .L5 5o .0 0o .5L 60 .0 oo .5o 55 .o o0.110 5O.0 0o . Lo 5o .o 00.!0 53.J o
Depth of Scour
----L!"sbgs)Marin'rn Next to At End of Bank
Depth lflgell Basln ErosionTestNo ,
1881891 0 n
( tnc ie" )
lr.col+. OOt+.OOlr.OO
L.ool+. OOL.ooL. oolr.oo1r.00L.oo5 . t J
3 . 3 3J . t t2.672,67h.00
^ _a . J v
2 . 3 02 . 3 0
2 . jO2 . ) O2 . 3 02 . J O
a . wZ . J U
z . J v4 . L )
z . L >
z . L t
2 .002 .30
_x-2.50< . > v2 . 5 o
2 . 5 0
2 . 5 0
u ( a
2 . 2 0
2 . 2 02 , 2 0
z . z )
-1.5- L . )
- r . )_r.5
_.t- . )
- r . )
_ L . )
_ L . ,
- t . )
-r.7t - 1 . )
_2. l r- L . )
-o.8
GoodPoorPoorFair
FairFairGood0ood
GoodGoodPoorGood
GoodGoodGoodGoodOood
1q)' l s 1
19Ut9i
196198
201
z v ata1
zoi'*2C,5206
-1.2^ a
-o.8- 1 . ? 4 .8-1 .2 -O .8
-1 .5 { . 8- \ . J l t t 7-0 .1 -o . l- \ . j - L . t
- 1 .3 4 .8-1.3 -O.8-1 .8 4 .8-1.5 -o.8
-o.8 -7..2- L . 1 - L . a
-1.0 :L.2-o.3 4.8{ . ) I . t . t
*--In terlF ol o^
#Blocks "r" O. l t d" long; al l otherblock lengths are eoual to thetrr idth
Although the I,r'idth of individual blocks is not criticalr it is
essential that a sufficient nrunber of floor bloeks be used to break up the
nappe into
turbulence.
small strea.ms. These smal1 streans then decay into isotropic
The d.istance required for this decay to talce plaee depends
to a large erbent on the size of the streams into which the nappe is bro-
ken by the floor blocks. Beeause of these consideratj-ons, it is recom-
mended that the floor blocks be o.h dc wide. A variation of 0.15 dc
from tlr-ls ljrnit is per:n:issible in order to fit the blocks i-nto the stilling
basin and avoid, od.d. d.j-:rnensions. However, it is stressed that the recom-
mended floor block width is O.h d. and that this di:nension should be
held as closely as is practically possJ-b1e.
20
comparing the effect of the floor block ,iLdth and spacing as were looked
for in Table I when comparing the effect of the floor block and end sill
height. A study of, Table II shows that the block width has no detectable
effect on the bed or bank scour. However, it will be shown in the section
on "sidewall height" 'that wide blocks cause a high boil in the basin and
thus require higher sidewalls • This indiaates that the:re is a limit to
the width of the individual blocks that must be taken into account 1vhen
designing stilling basins.
Table II - FLOOR BLOCK ~{[DTH AND SPACING
Basi:! Width Depth of Scour Occupied ( inches)
Test de * * Block by Blocks Long Maxi:num Next to At End of Bank
~ Width* No . (inches) .JL (per cent) Sil~ ~!:tL Win~g Basin Erosion 188 4.00 2.30 2.50 0.25 50 .0 2 -1.5 -1.2 -0. 8 Good 189 4.00 2· 30 2·50 0.2 5 41. 7 2 - 1.5 -1. 2 -0.8 Poor 190 4 . 00 2.30 2.50 0.2$ 41.7 2 -1. 5 -1. 2 -0.8 Poor 191 4.00 2. 30 2· 50 0.2 5 50.0 0 -1.5 -1. 2 -0.8 Fair 192 4. 00 2.30 2. 50 0.2 5 50 .0 2 -2.0 -1.6 -0.8 Fair 193 4.00 2·30 2·50 0.25 50.0 4 -1. 5 - 1.3 -0.3 Fair 194 4.00 2·30 2.50 0.375 50.0 0 -0. 5 -0. 3 -0· 3 Good 195 4 . 00 2.30 2.50 0 .75 50 .0 0 -1. 5 -1. 3 -1. 3 Good 196 4 . 00 2.30 2.50 0.50 50 .0 0 -1. 5 -1.3 -O. B Good 198 4.00 2. 30 2.$0 O.~S 60.0 0 -1.3 -1.3 -0. 8 Good 199 4. 00 2. 30 2·50 0.30 40 .0 0 -2.0 -1.8 -0. 8 Poor 201 3.33 2.15 2.20 0 . ~5 50.0 0 -1. 5 - 1. 5 -0. 8 Good 202 3.33 2.15 2.20 0. 54 60.0 0 -1.7 -0.8 -1.2 Good 203 3.33 2.15 2.20 0.50 55 ·0 0 • - 1.5 - 1.2 -1. 2 Good 204** 2.67 2.00 2.25 o.~o 50 . 0 0 -2 . 4 -1.0 -1.2 Good 205 2.67 2.00 2.25 0.40 50 .0 0 -1.3 -0 .8 -0. 8 Good 206 4.00 2.30 1. 75 0.40 53.3 0 -0. 8 -0.5 -0.3 Good
*In terms of d c
**Blocks are 0.75 d long; c all other block l eng t hs are eoual to their width
Although the width of individual blocks is not critical, it is
essential that a suff icient number of floor blocks be used to break up the
nappe into small streams . These small streams then decay into isotropic
turbulence. The distance required for this decay to take place depends
to a large extent on the s i ze of the streruns into which the nappe is bro
ken by the floor blocks. Because of these considerations, it is recom-
mended that the floor blocks be 0.4 d wide. c A variation of 0.15 d c from this limit is permissible in order to fit the blocks into the stilling
basin and avoid odd dimensions. However, it is stressed that the recom-
mended floor block width is 0.4 d c and that this dimension should be
held as closely as is practically possible.
2L
The floor bloeks for the tests were ordlnarily square in p1an.
However, for Test $c. 20L (see Table II), the floor blocks were 0.1+ dc
wide by 0.7, d" 1ong, and the ssour depths are somewhat greater than
those for coapanion Test No. 205 where the floor blocks were g.h ds wid.e
by 0.L dc 1ong. The miaimu:* perarissible distance betr*een the floor
blocks and the basin erlt is quite short and thj-s entire. distance is re-
quired for energy dissipati-on. If sone of this space is occupied by ex-
tra long floor blocks, it will not be available for energy dissipation,
and adCi-tional $cour in the downstream char:ne1 will result. It is there-
fore recommend.ed that the floor bloeks be square in plan with the dimen:-
sions indj-cated in the preced:i::g paragraph.
Study of ?ab1e fT al1so shows that the proportion of the basin
ridth occupied by the floor bloeks should be between 50 and 60 per cent of
the stilllng basin r^ridth. This is also shoi.rn in Fig. 9r where the con-
tours of the scour are al:nost the same 1n Fig, 9b as they are in Fig. pe.
For these photographs the portion of the basin !flidth occupied by the blocks
is 50 and 60 per cent, respeetively. In Fig. !a, where the proportion is
l+0 per ceni, the maximrm depth of seour is greater and the bank erosion
is much more seYere. '
' The tests show that longitu*tnal sills are nej-ther si-gn:ificantly
benefi-ci-al nor har,nful- as regards the hydraulic perforxrance of the still-
ing basin. The longitudinal si1ls may be used to strengthen the stiDi-r:g
basin floor j-f ihis proves desirable, If longitudinal si1ls are used,
they should. be located to pass through a floor b1ock. Their height should.
be deternined by structural requirements.
Summarizing: ?he width, spacing, and length of the floor blocks
shoul-d be approxi-:nately 0.h dc with an extrerne variation of + 0.15 d"i
it is not necessarythat the floor blockT'fiidth and spaeing be exactly equal,
but the blocks should oeeupy between 50 and 50 per cent of the stilling
basin width; a half spaee should be located next to the basin sidewall;
and longitudinal sil1s passing througb the floor bloeks may be used for
strrrctural pu.rposes rs-ithout detrjmental hydraulic effects.
21
The floor blocks for the tests were ordinarily square in plan.
However, for Test No. 204 (see Table II), the floor blocks were 0.4 d c
wide by 0.75 d long , and the scour depths are somewhat greater than c
t hose for companion Test No. 205 where the floor blocks were 0.4 dc
wide
by 0.4 d long. The minimum pennissible distance between the floor c
blocks and the basin exit is quite short and this entire distance is re-
quired for energy dissipation. If some of this space is occupied by ex
tra long floor blocks, it will not be available for energy disSipation,
and additional scour in the dOiVllstream channel will result. It is there-
fo r e recommended that the floor blocks be square in plan with the dimen~
s ions indicated in the preceding paragraph.
Study of Table II also shows that the proportion of the basin
widt h occupied by the floor blocks should be between 50 and 60 per cent of
the s t illing basin width. This is also shown in Fig. 9, where the con
t ours of the scour are almost the same in Fig. 9b as they are in Fig. 9c.
or these photographs the portion of the basin width occupied by the blocks
s 50 and 60 per cent, respectively. In Fig. 9a, where the proportion is
o per cent, the maximum depth of scour is greater and the bank erosion
s much more severe.
The tests show that longitudinal sills are neither significantly
eneficial nor hannful as regards the hydraulic perfonnance of the still
ing basin. The longitudinal sills may be used to strengthen the stilling
asin floor if this proves desirable. If longitudinal sills are used,
t .. ey should be located to pass through a floor block. Their height should
be detennined by structural requirements.
Surrnnarizing: The width, spacing, and length of the floor blocks
s houl d be approximately 0.4 d with an extreme variation of + 0.15 d " c - c it i s not necessary that the floor block width and spacing be exactly equal,
but the blocks should occupy between 50 and 60 per cent of the stilling
basin width; a half space should be located next to the basin sidewall;
and longitudinal sills passing through the floor blocks may be used for
structural purposes without detrimental hydraulic effects.
22
a. Blocl<s Occupy lro per Cent of BasinI,.fid.th. Test No. 199. Bank erosionis severe and bed scour is excessive.
b. Blocks CccuPYI"\'idth. Test i'lo.erosion are good.
5O ler Cent of Basin196. .Bank and bed
n Rl nnlcs Crenrrr-'.. 60 Per Cent of Basinv .
.".lidth. Test I' io. 198. Bank and bederosion are good.
Fig. 9 - Effect of Proporfion of Bosin Width Occupied by Floor Blocks on Scour of Bed ond Bonks
22
b. B1ocks .Occupy 50 Per Cent of Basin Hidth. Test No. 196. ·Bank and bed erosion are good.
a. Blocks Occupy 40 Per Cent of Basin ('-Tidth. Test No. 199. Bank erosion is severe 2nd bed scour is excessive.
'.
c. Blocks Occupy 60 Per Cent of Basin \·Jidth. Test No . 198. Bank and bed erosion are good.
Fig . 9 - Effect of Proportion of Basin Width Occupied by Floor Blocks on Scour of Bed and Banks
Sidewall }{eight
:ln additional height of sider'ra11 is requt red above the noninal'i;aill+ater 1eve1 to prevent overtoppi-ng of the sid.er,ralls as a result of
natural !trarr,er surface fluctuations, turbulence urith:in the stilling basin
eausecl by the floor blocks, and. boils and. stand.ing lraves resulting from
the floor blocks and end si1l,
?he resulis of the tests to deternrine the height
and standing r'raves are given in Table III. Inspection of the
of the boils
table reveals
Table IIT - SIIISTIALL HEIG$T ?ESTS
Basin Dirirensions Are ?hose Reeommend.ed in Tf:-is Paper
CheckTest No.
1 J^ la t l
)a
/ o + \\ I t / /
n l , nn
n ?nn
v e l r v
0.200
t^ / ^1 . > u3 .33l+.00( n n) ' v v
^ above stilling
Blocks
( t ) V
z . o o2 , 7 2L . I )
basin floor
si11
2.1+0a . 4 v
2,322,l+0
-\."In terms of d
th.at tire height of the boil or stanCirrg wave at the end si1l is 2.h0 dc
above the stilling basin floor, Since ihe tai}.rater depth d.- is c t(' s
the height of the boil at the end of the basin t"
";;;;" -:r";"
tt"-t"ti-, v
sater surface. I{owever, the highesi boil is caused by the floor blocks.
The inaximum boiJ. height at this location l-s sharnrn in Table fII to be
2.75 de or 0.60 dc above the tailwater leveJ*.
It is recoruaend.ed, as a result of the tests sur,unarized here,
that the top of the sid.ewalls be located in a rain-i-:in:ra distance of 0.85 dc
above the i;ailwater level-. This wifl- give a freeboard. above the :naxjmuro
obserued boil height of A.25 dc. It is believed that this is the n-lni:ilun
freeboard that should. be pernr:itted.. Even r+ith this freeboard, spra;, and
qrlash r,rill probably overtop the si-deual.ls occasi-onally"
23
Sidewall Height
An additional height of sidevrall is required above the nominal
tailuater level to prevent overtopping of the sidewalls as a result of
natural vrater surface fluctuations, turbulence 1ili thin the stilling basin
caused by the floor blocks, and boils and standing waves resulting from
t he f loor blocks and end sill.
The results of the tests to determine the height ' of the boils
ru'1d s tanding vraves are given in Table III. Inspection of the table reveals
Table III - SID1'HALL B""EIGHT TESTS
Basin Dimensions Are Those Recommended in This Paper
d Height of Check c
~~-At Floor
Test No . (ft) L Blocks
23 0.400 2.50 2.50 24 0.300 3.33 2.66 29 0.250 4.00 2.72 30 0.200 5.00 2.75
" "'In terms of d above stilling basin floor
c
~;:.
Boil" At End Sill
2.40 2.40 2.32 2.40
..
~~at t he height of the boil or stancl.ing wave at the end sill is 2.40 d c above t he stilling basin floor. Since the tailrv-ater depth d
2 is · 2.15 d ,
c the height of the boil at the end of the basin is 0.25 d c
above the tail-
ater surface. However, the highest boil is caused by the floor blocks.
- e maximUm boil height at this location is shown in Table III to be
2 . 75 d or 0.60 d above the taihrfJ.ter level. c c
It is recommended, as a result of the tests summarized here,
at t he top of the sidewalls be located in a mirlli.llum distance of 0.85 d . c
a oove the tailwater level. This will give a freeboard above the ma7..imum
o served boil height of 0.25 d • It is believed that this is the minimum c ~reeboard that should be permitted. Even with this freeboard, spray and
spl ash will probably overtop the sidewalls occasionallyo
2]l
llilswalls&
lJingr"ralls located at an angle of h5o r,rith the stilling basin
cenierline and having a top slope of 1 on 1 were used "bhroughcut the
stz'aight drop spil}^ray stilling basin test prograll l,lo special wingl,e11
tests r.rere made because the results of tests orr the box inlet drop sp111-
r+ay outlct t8j and on the SAF stilling basj-n [3J iraa previously indicated
*La* +Ln r . r i rm-r^ ]1 fonn used. here uould be sat is factory.L / I i d t / U l t g i T I f l S w d A f f W f l l L u o g q l I g I q s l v u r u u v e s v !
The tests on the straight drop spillway stilling basi:r showed
these r..'ingl,ra11s to be eornpletel;. sat-lsfac'i;or1r. Tlre *raterial in back of
the l*ingwalI did not erode ai all but rested. at its nati:ral angle of re-
poser The scour at ihe end of the wingr.rall raas not greater t.han antiei-*
pated.from previous tests. These concJ.r:sions assune, of coursee a properly
propsriioned stil-ling basin,
Jt is reconuaended that the wingr,ral-ls be losated ai an angle cf
l+5" witn !,he stilling basin centerljne and that the iop slope bp 1 on 1.
If it is desirable io use ather r.rilgwall positions or top slcpesr it is
sugg*sted. thai; reference'r-:e reade to publications [l+] or [B] for the prob-
able effect of such ehanges.
Approagh Channel
The shape of the approach channel Ha.s fourdto affect the stiIl-
ing basin perfonnance, It is important, therefore, that certain rainj:nr:m
cond.i'lions be met vith re1:ard to the si:a"pe of ihe apprcach char",r:.el' These
conclitions ar'€ not unduly restrietive.
In all insiances the bed of the approach chairnel 'was 1eve1 trith
the crest of the straight drop spillr.+ay. This eli:rinated the cant::action
of the rxrder surface of the nappeo Devlation from this IeveI approach
channel ca:r be eapected to afiect the posiiion ai r,{hish the nappe strjkes
the stilling basln floor and., as a result, the lengih of the stilli::g
Dasl_n.
F=r sone i,esis th': ap,p::cach channel tras very wide, ihe appraach
cfia:rnel flcor'.ia-s horizontal, and no d.i}ceS rrrere used; that is, i}:e head-
r+all- exte::sion -.+e.s carrierl across the fu1l wid.th of the approach che,nnel.
For ihis approach charurell the contraction at the ends of the spi3*lr.ray
24
Wingwalls
Wingvmlls located at an angle of 450 lfl th the stilling basin
centerline and having a top slope of 1 on 1 were used throughout the
straight drop spillway stilling basin test program. No special wingHall
tests I"Jere made because the results of tests on the box inlet drop s pill
tvay outlet [8J and on the SAF stilling basin [JJ had previously indicated
that the Hingtvall form used here '.!Quld be satisfactory.
The tests on the straight drop spill,vay stilling basin showed
t hese wingrN"alls to be completel y satisfactory. The material in back of
the v;ingwall did not erode at all but rested at its natural angle of re
pose. The scour at the end of the Hinv'mll was not greater than antici
pated from previous tests. These concl usions aSS111'1le, of course, a properly
proportioned stilling basin.
It i s recommended that the wingwal1s be located at an angle of
450 with the stilling basin centerline and that the t op slope be 1 on l.
If it is del?irable to use other vdngwall positions 9r top slopes, it is
suggested that reference be made to publications [4] or [8J for the prob
able effect of such changes.
.. Approach Channel
The shape of the approach channel was foundto affect the still
ing basin performance. It is important, therefore, that certain minimum
conditions be met 'iJith regard to the shape of the approach channel. These
conditions are not unduly restrictive.
In all instances the bed of t he approach channel was level vlith
the crest of the straight drop spillway. This el~ninated the contraction
of the under surface of the nappe. Deviation from this level approach
channel can be expected to a ffect the position at w"hich the nappe strikes
the stilling basin floor and, as a result, the length of the stilling
basin.
For some tests the approach channel was very wIde , the approach
channel floor uas horizontal, and no dikes vlere used; that is, the head
wall extension 1,yeW carried across the full width of the approach ch,mnel.
For this approach channel, t he contraction at the ends of the spilhmy
25
.otch was so great that the ends of the nappe landed well away from the
sii|ling basin sider,ral1s. Thus, the fu11 w"idth of the stilling basin was
not used to dissipate the energy in the nappe, and the higher velociiies
eoncentrated. at the center of the outlet caused additional scour in the
ccrrnstrean channel.
Correction of this poor flow d"istribution in the stilling basin
arci d.ownstrearn ehannel is quite si:np1e. It is accomplished by properly
sbaping the approach charuIel. to reduce the contraction at the ends of the
spil-lway. If the toe of the dike is located at the end of the notchr the
iike slope along the headvall extensi-on i-s I on 2 or steeperr the top
r:-::h cf the dike is located downstream frora the headwall, and the upstrean
si:;e cf i;he dike is 3 on 1 or flatter; the contraction *ri1l be suppressed
#j:ciently to resr:lt in acceptable stilling basin perfon*ance. lloweve:.,
:., is felt tha-t ordinarily the dike top w:dth e'd11, for reasons of econo-
x3r, 'ce
located upstrea:n of ihe headwall. fhls should give, in effectr an
agprcach channel with 1 on 2 side slopes and a botto*i width equal io the
=c".ch !.idth. This fi:.rther suppresses the contraction at ihe ends of the
s;:liway opening and results in even better stilling basin perfcrmance.
S-s latter approach charure1 shape approximates the condition of a ditch
=i-eg a bottom width equal to ihe notch length. ?he suppression of the
e.s. contractions fcr the ditch approach cha.r:nel shape will insure sat'is-
iac-rcry stilling basj-n p€rfcrmance.
&te other app:'oactr cha:rne1 caution must be mentioned. ?he bed
a:rd banks just upstree$ from ihe spillway crest r*j-11 be scoared if they
are not protected by riprap or paving. Tentativelyo it is suggested that-.ais protectlsn be exier:ded upstream a distance eqrlal to twiee the depth
:f 'uhe spillway noich. ?he heaviest stone should be loeated close to the
:rctch with particularly heavy stone in the vicin:ity of the ends sf the
roteh.
Aerglion gqder Ngppe
the a;ir removed from beneath the nappe by the plunging water
=rst be replaeed in order to prevent, low pressures whieh rright cause flue-
tuati-on of trhe nappe and extra loads on the simcture. Foriu::ate1-y, ihe
recommended approaeh charrneJ. fo:m pe:*rits suffieiest contractisn at the
25
"otch Has so great that the ends of the nappe landed well away from the
stilling basin sidewalls. Thus, the full width of the stilling basin was
not used to dissipate the energy in the nappe, and the higher velocities
concentrated at the center of the outlet caused additional scour in the
do"mstream channel.
Correction of this poor flow distribution in the stilling basin
a.:! d downstream channel is qui te simple. I t is accompli'sbed by properly
shaping the approach channel to reduce the contraction at the ends of the
spillway. If the toe of the dike is located at the end of the notch, the
e slope along the headwall extension is 1 on 2 ' or steeper, the top
of the dike is located downstream from the headwall, and the upstream
f the dike is 3 on l or flatter; the contraction will be suppressed
_:':'c" entlyto result in acceptable stilling basin performance. However,
':'s felt t hat ordinarily the dike top width will, for reasons of econo
e located upstream of the headwall. This should give, in effect, an
.proach channel with 1 on 2 side slopes and a bottom width equal to the
h width. This further suppresses the contraction at the ends of the
way opening and results in even better stilling basin performance.
-=is l atter approach channel shape approximates the condition of a ditch
U4~ng a bottom width equal to the notch length. The suppression of the .. " contractions for the ditch approach channel shape will insure satis
!actory stilling basin performance.
One other approach channel caution must be mentioned. The bed
and banks just upstream from the spillway crest will be scoured if they
are not protected by riprap or paving. Tentatively, it is suggested that
"s protection be extended upstream a distance equal to twice the depth
of the spillway notch. The heaviest stone should be located close to the
otch vn th particularly heavy stone in the vicini ty of the ends of the
no t ch .
Aeration Under Nappe
The air removed from beneath the nappe by the plunging w~ter
rrust be replaced in order to prevent low pressures which might cause fluc
tuation of the nappe and extra loads on the structure. Fortunately, t he
recommended approach channel form permits sufficient contraction at the
?o
ends of the weir notch so that air has access to the underside of the nappe.
Therefore, no special provision for aeration is necessar3r. In factr the
use of offsets or widening of the stilling basi-n to provide aeration is
not recomnended. since it adversely affects the stilling basin performance.
If bu'i:tresses are used to support the headwaIl, access of aj-r to
the space between the buttresses may be cut off. In this case it is nec-
essary to provide aeration passages through the buttr€ss€s. G. H. Hickox
has shown how the sj-ze of these aj-r passages can be deternrined [9].
Check Tests
A series of check tests was planned and earried out after the
d.esign rules for the stilling basin had been established. The purpose of
these tests was to check the overall performance of the stilling basin
under the complete range of eond:itions for which it is useful.
The check tests and the results obtained from them are sunma-
rized in Table IV. In every case, the stilLing basin perfonned satj-sfac-
torily and accord.ing to expeetat5-ons. In other words, the check tests
verified the adequacy of ttre design nrIes.
Table IV - SII,lltriARY 0F Ci{ECK TESTS
Scour*( feet )
92ne1qn! o r 5o1r
Al Floor At EndBlocks S i11
Chec kTest No.
*c- 6
;t v . )
I o . L r9 0 . 3
10 0 .111 0 .212 0 .1
1 1 0 . 3l L o .25a5 o .?) ,6 0.1517 0 .1
18 o. l rT9 O .L20 O. l r21 0.1+22 0.1|
?3 o . !z \ o . 329 o .25l0 0 .20
Bankll""-&!
Very GoodGoodGoodOoodGood
Very GoodVery Good
GoodVery OoodVery GoodVery GoodVery Cood
GoodGoodGoodGood0ood
GoodGoodGood
z.to 2 ' )ro? .56 2 .L02 . 7 2 2 . 3 22 . 7 5 2 . \ O
v
10.003 .00) . 1 )
5 .00
10.oo
t , 572 .00t ( d
3 '335.00
2 . 5 02,5o2.50
) . ) )L.oo5.00
* iyt
- 8 .?5
- 2 . O O+ 0 . 3 8- 3 . ? 5- , , 7 5- L ) . 4 >
+ 0 .083- o.o25_ o. t5- 1 ' ) o- 1J.75
+ 0 .50+ 0 .60+ 0 . 7 0
0 ,00_ o , l 5- u . J >
i l a
- 1.31r_ 2 . 8 1
MaxinmDistancefron End NexL to Next to
Depth of Basin lliingrall E"g_9fU
o.1o 0 . ! 0 .01 0 .050.1o 1 .2 0 .01 i o .0Lo.1o 1.0 0.0L 0.0ho.23 l .L o ,a5 0 .12O.1O 1 .2_ 0 . O3. . .__ 0 .0Lo.1L 1 .3 o .o2J : : o .o8o. ro 0 .6 o .o2* o .o?
o,1o l- .0 o.olr o.olr0 .13 1 .3 O.O? 0 .O7o.12 0 .5 0 .02 0 .07o.1o o .7 o .o2** o .ozo .og o .5 o .o3** o .o5
o.l l 1.? O.10_*.* 0.12o . o t 0 . 3 0 . 0 5 ^ - - 0 . 0 2o.o5 0.8 o.o5:rnr o.o20.15 r. lr o ' 12 o.080.08 1 .3 0 .05 o .o8
0,09 r .2 0 .06 0 .06o.o? 0.6 0.06 o,o50.15 0 .6 0 .00 0 .07
oBelor top of end sil l
" ^ I n t e m s o f d "
**"Abotu top of end sil l
ends of the weir notch so that air has access to the underside of the nappe.
Therefore , no special provision for aeration is necessary. In fact, the
use of offsets or widening of the stilling basin to provide aeration is
not reconunended since it adversely affects the stilling basin performance.
If but tresses are used to support the headwall, access of air to
t he space between the buttresses may be cut off. In this case it is nec
essary to provide aeration passages through the buttresses. G. H. Hickox
has shown how the size of these air passages can be determined [9 ].
Check Tests
A series of check tests was planned and carried out after the
design rules for the stilling basin had been established. The purpose of
these tests was to check the overall performance of the stilling basin
under the complete range of conditions for which it is useful.
The check tests and the results obtained from them are summa
rized in Table IV. In every case, the stilling basin performed satisfac
torily and according to expectations. In other words, the check tests
verified the adequacy of
Check d Test No . *'l:-
-.£ .:L...--6 0.1 10.00 7 0.$ 3. 00 8 O.L 3. 7$ 9 0 . 3 $ . 00
10 0.3 $ . 00 11 0 . 2 7.$0 12 0 . 1 10.00
13 0 · 3 1.67 lL 0.25 2. 00 15 0 .2 2. 50 16 0.15 ) . )) 17 0 .1 5 .00
18 0.4 2.$0 19 o . L 2. 50 20 d . !.. 2 . 50 21 0 . 4 2. 50 22 0 .4 2 . 50
2) 0 . 4 2 . 50 24 0 . ) 3· )) 29 0.25 L.OO )0 0.20 5 .00
*Below top of end sill
<>->In terms of d C
*,>l:'Above top of end sill
Table
*;~-
:L - 8 .2$ - 1.25 - 2.00 .. 0·38 - 3. 2$ - $ . 7$ -13. 2$
.. 0.083 - 0 .02$ - 0.75 - 1. $8 - L. 75
.. 0 . $0
.. 0 . 60
.. 0. 70 0.00
- 0 .75
- 0 · 35 - 1.18 - 1.84 - 2. 8L
the
IV
design rules.
- SUHI1ARY OF CHECK TESTS
Scour " (feet )
Maximum Distance f r om End Next to Next to
Dept h of Bas in Wingwal! End Sill - .-0 . 10 o . !.. o . OL 0 .0$ 0 .10 1. 2 o .OL o .oL 0 .10 1. 0 o .OL O.Oll 0.2 3 l.L 0.1$ 0.12 0 .10 1.2 0 .03 , o . OL o. l L I. ) 0.02',;-:1-* 0 .08 0. 10 0 . 8 0.02*** 0 .07
0 .10 1.0 O.OL O. OL 0 .1) 1. ) 0 .07 0.07 0.12 0 . 6 0 . 02 0 .07
*"":t-i} 0 .10 0 .7 0.02 0 .07 0 .05 0 . 5 0 . 03*'''* 0 .05
O.lL 1. 2 0 . 10 0.12 0 .0$ 0.8 0.05*"* 0 .02 0 .05 0 . 8 0.05';-:>-:> 0 .02 0 .15 1.4 0 . 12 0 .08 0 .08 1.3 0.0$ 0 .08
0 .09 1. 2 0. 06 0 .06 0.07 0 .6 0 . 06 0.05 0. 16 0 .6 0 .00 0 .07
Bank Eros ~~
Very Good Good Good Good Good
Very Good Very Good
Good Very Good Very Good Very Good Very Good
Good Good Good Good Good
Good Good Good
Height of 80il':>-> At Floor At End Blocks Stll ---
2.50 2 . Lo 2 .66 2.!.JO 2 . 72 2 . 32 2. 75 2 . !.JO
z7
sffis4anr
?he results of the tests and the rrrles for the design of tbe
straight drop spillway stilli::g basiJr are sursrnarized belas* Heference
should also be rnad.e to Fig. 10"
1* fhe minimum length of the stilling basj-n Ib i"s
% = * * * % i * * * * * + 2 . 5 5 d e
?he disianee-frora the headwall to the point where the sur-fcoa nf *ho rrnnay nappe strikes the stilli-ng basin floor x
4̂
is given by Eq. (?)" ?his equation is solved graphicallf irl
F ig* 2*
The distanee frorrr the point at shieh the swfaee of tbe r:pper
nappe strikes the stilling basin floor to the upstream faee
of the floor blocks \ is
: q = 0 * B dn a
€* The distance between the upstrear* face of ihe flcor bloeks
and the end of the stillinE basin x is .c
x :: : I"75 d. e c
2* ?he floor blocks are proportioned as follows:
3a The height of the floor blscks is
o*8 d-v
b. the uidth and spacing of the floor blocks shou.ld be approxi_-
nately
0-l+ dc
but avariation of :0"15 dc from this Uroiiis pet"ur:issible*
?he floor blocks should be square in p1an,
The fl-oar bloeks sbsuld occu.py between !0 and 60 per cent of
the stilli-:rg basin width.
g a
( B )
(s )
C *
d r
27
SUMMARY
The results of the tests and the rules for the design of the
straight drop spillway stilling basin are summarized below. Reference
should also be made to Fig. lO p
1. The minimum length of the stilling basin ~ is
T~ = x + x + x = x + 2 ~55 d ~ a b · C a c
a.. The distance - from the headwall to the point where the sur
face of the upper nappe strikes the stilling basin floor xa
is given by Eq. (7) ~ This equation is solved graphical~ in
Fig. 2.
b. The distance from the point at which the surface of the upper
nappe strikes the stilling basin floor to the upstream face
of the floor blocks ~ is
o ~8 d c
(8)
c" The distance between the upstream face of the floor blocks
and the end of t he stilling basin x is <#'
C
x 2::. 1.75 d c c
2& The floor blocks are proportioned as follows:
a~ The height of the floor blocks is
0 .. 8 d c
b. The width and spacing of the floor blocks should be approxi
mately
0~4 d c
but avariation of + 0015 d from this limit is permissible. - c
c. The floor blocks should be square in plan~
d. The floor blocks should occupy between 50 and 60 per cent of
the stilling basin width.
28
Section of Center Line
Fig. l0 - Stroight Drop Spil lwoy Sri l l ing Bosin
trFloor Blocks -E "
Longitudinol Si l l (Opt ionot)7 E
trtrtrtrtr
28
'//AV" "I'..c<I';·
L
.. Upper Nappe
. :. ..
.' .. .. •• '.' .' :~ •. I--------......l~-_I
•. t-----" .. ..-.------ La
Section at Center Line
o Floor Blocks-'i] ...
Longitudinal Sill (Optional) 0
Plan
o o o o o o
Fig. 10 - Straight Drop Spillway Stilling Basin
Slope I to I
~ -1-
End Sill
2g
3 o ?he Sieigkt B'f the s.ad $il.l- LF
0J+ d6
h' Iongitud$-na} g{ll.effitr tm uqpd fstr stn:ciural pr:rFases* Th*y are
neither bene,f,lci-al nor henafu3 irydraulicalJy. tf used, *h*y shor:-ld
pass through, not betueen, the floor bl-ocks*
5 " fhe *j-d.ewall FreigJ*t abenre the tail+rater 1eye3 should be
g"SF de
6. ?he w3-:rgwalla shoets i:e loeated ai an angle of h5e with the si:t*
B" ?he approach *hensle--� ohouldr
ao Be Ievel r+ith the crest of the spi-Ilway*
9 " i"io spe*ial pr*viel.on f,*r asrati*a cf the space beneaih *he ::appe
is requl-red.af the approach charurelis shaped &s recsisiTrended. here*
fiXAN$PMA BbJ,J
:-*PPLIfiATTS}i
. Ap ex*npleis serked.orrt'here t"s shawhow t'l:e mles given i-n thispaper are apFlied te the deseg:i of a s*i}lirre basia for a straight drap
spi11wa6r* ?l:e seleeted examgrle j-s nst neeessarily tppical but is *hosen+^ 1--+*- ^-'+ +La applic*ti*n of the d*sign ru1es"v u u a l t E i V U V v ! l , C
The spilftray deslgn ctir5raeity iE taken to be 33$ efs. The straightdrop spilk*ayis i-r: a d.iieh with a ]"1+"00*ftbottopl r*id.th* Ti:e n*rma1 *epth
of flatr i* t!:e ditch ie h,00 fto ??re tetal hsa* H ab*ve the spilliaay
1et cerrterllsre esd
7 " The riin-lrnum heieht
the stillJ.ng baein
ehsuld have a tep slcpe of 1 on
cf the tailuater surface above
de I's
dA * P*XS d*
I r
the flsor sf
t au/
b o Harre the tog of nhe dike ar ihe tce of ihe eide s1+pe inter-
seet:-the.:. approeeh ctrannel f1o*r at the ends ef 'Lire spill*ray
notch; the approaph ehzurnel at the headwall should have a
b*ttcp trldth *qu.aL tq 'lhatr *f the spillway e*tch,
Ee protected cy riprap or paving for a riistance upstream frorn
ihe headeell eqrel tp trm tj$,ss the r:*teh *epth*
29
31' The height 0,1 th~ ~nd sill ~s
4. Longi tudinal $i116' IM\Y l;)e 'Us.~d fo;r structural purposes", They are
neither be:n~!:j.~ial nor harmful ~dra.ulically Ii' If used, they should
pass through, not be,tween, the floor blocks.
:5,. The side.vall heigllt above the tail<water level should be
6. The wing'V-lalls shov,ld be located at an angle of 450 l .. ith the out:...
let centerline and should. have a top slope of 1 on L
7.. The minimum height of' the taih;ater surface above the floor of
the stilling basU\' d2
i$
( 10)
8" The approach cllm;mel should:
a" Be level ,ifith the cre,j3t of the spillway ..
bQ Have the toe of the dike or the toe of the l.iide slope inter
seckthe~ approach channel floor at the ends of t he spillway
notch; the a:pproa~h channel at the headwall should have a
.bottom tddth equal tq that- of the spillway notch.
c ,,' Be protec.ted by ri"prap ox" paving for a distaflce upstream from
the headw91l equal to two t:iIrles the notch depth.
9. No special provision for aeration of the space beneath the nappe
is required if the appro.aeh channel is shaped as recommended here" . ,
EIAM:rlZ OF APPLICATION
Ap. eXBlYlple is worked·o:ut here to show how the rules given in this
paper are applied to the design . of a stilling basin for a straight drop
spillway,. The selected e~ple is not necessarily typical but is chosen
to bring out the application of the design r'ules"
The spillwaydesi~ capacity is taken to be 330 cfs. The straight
drop spilhray is in a ditch wit~ a 14.00<-ft bottom width., The normal depth
of f low in the di teh is 4 ~OO ft.. The total head H above the spillway
? n
crest is assuned to be l+.00 ft, the velocity head being negleeted in this
caser^ for a crest lengtir I of 12.50 ft. ?he d.rop in the ditch gra.de
'"+hichmust be controlled is 6.C0 ft. The nor:aal depthof flowin the do"rn-
streern d-itch is J+.00 ft, but under flooC conditions backr.iaterfrom a siream
mey raise the taib+atey so that its 1*ve1 is 1.10 ft above the spillway
crest '
?he drop from the spil}+ay crest to the basin floor y must
firsi be detec?rined. .4. lanowledge of the tailwatqr Cepth is necessary to
nake this determinatioF. The critical depltr is taken as do = ( 2/S) x
L.00 = 2.67 fL" Therequired tailwater depthis 2.15 dc above the st111-
ing i:asi-n floor or dZ = 2'I5 x 2.67 * 5.73 tt' I{or:nal tai}water leve1
is 2.00 ft below the spillwey crest so the still-ing basin flcor must be
placed. -2.00 - 5.73 = -7.73 ft relative to (letoi.r) the spillway crest
level, Therefore: X = -7.73 ft {use -7.75 tL). The floor of tl:e still-
ing basin is, therefore, I.75 tt below'the grade tr-ine of the downstream
cha-nne1.
The basin length t, wil1be determinednerb. The basin length
coraputations are carried out in iabular fo::n for both norr*al and flood
tail-rse-ter levels.
Dimension Tailwater
\t
v / dc
Yt/ o.
x /d"a ; c
i-
^ O: i = UrO Cl
h Av v
Distanee to floor bloclcs- a J . / \
x = J . / ) d ( r i l r - n r - m u m /r F
Easin leneth L. (r,rin:murn)- i J
4II t /
ft
.F+
.F+
ft
].T
ft
$orna1
- { . { >
-?.g l
-2 .00
- U t l 2
3 .810.132.73
t2.26 (72.25)
b.67 (l.l.75)
76.93 (r?,OO)
Floodn q r J
- 1 . 1 2
-2 .91
+1.50
+A,56
17.60
2,73
t9.73 (a9.75)| / n I I o / \
4 . o { \ 4 . ( 2 )
2b.bo { zh.5o)
.\|^The velocity head is assrunedto er'aount to 0.1$ ft, and veloci-ty head.
recovery ai; t-,ne headl.rall where the velociQr 1" u*to reduees the heedr^ral1ireehnard h-r f,hig anount.
30
crest is assumed to be 4.00 ft , t he velocity head being neglected in t his
case,-::- for a crest length L of 12.50 ft. The drop in the ditch gr ade
l-Jhich must be controlled is 6 .00 ft. The norm.al depth of flow in the dmm
s t r e am di tch is 4.00 ft, but under flo od condi tions bachmt er from a stream
may raise t he t a i hrater so that its l evel is 1.50 ft above t he spillway
crest.
The drop from t he spillway crest to t he basin f loor y must
f irst be determined. A knOivl edge of the t ai l watEilr dept h i s necessary to
make this determination. The critical depth is taken as d = (2/3) x , c 4.00 = 2.67 ft. The required tailwater depth is 2.15 d above the still-
c i ng basin floor or d2 = 2.15 x 2.67 = 5.73 ft. Normal tailwater l eve l
is 2.00 f t below the spillway crest so the s t illing bas in f l oor must be
pl aced - 2.00 - 5.73 = -7.73 ft relative to ( be l Oiv ) t he s pillway cres t
level. There f ore , y = -7.73 ft ( use -7.75 ft). The f loor of t he s t ill
i ng basin is, therefore, 1.75 f t below t he gr ade line of t he do"rns t ream
channel.
The basin length ~ will be determined next. The basin length
comput ati ons are carried out in tabular form for both normal and flood
t ailiiate r l evels.
Dimension Tailwater
Y
y/d c
Yt
Yt/dc x /0. a c x a ]~ = 0.8 dc Di stance to f l oor bl ocks
x == 1.75 d (minimum) c c
Bas in length ~ (minimum)
ft
ft
ft
ft
ft
ft
ft
Normal Flood
-7.75 -2.91
-2.00
-0.75
3.8 10.13
2.13
12.26 (12.25)
4.67 (4.75)
16 .93 (17.00)
-7.75 -2.91
+1.50
+0.56
6.6
17.60
2.13
19 .73 (19.75)
4.67 (h. 75)
24.40 (24 .50)
-::-The velocity head is assmned to amount t o 0 .15 ft, and vel ocity head recovery at t he headHall VJ"here the ve l ocity is zero reduces the headwall freeboard by this amount.
31
the principal con'Lro1ling dj*rensions have been rounded of,f and-"-:e ror:nded valu-es are given in parentheses. It r+ill be notieed that the
:asin length is much longer for the high tailwater than for ncrmal tail-'d?'.?T. The longer length naturally detecrej-nes the required length of
:as:n. The basin dimensions are shor'rn in Fig, 11. The slope of ihe dam
:-l' has been assurired to be 1on 2 and has been dashed in ta shorq its l-o-
:a--i cn. It r^ri11 be noticed that the high tail+later requires a basin soiile-
r:.a*" ionger than is necessary to retain the fill. iiinjmum basin lengths
a:: used and the cli-ke has been shifted dcwnstreas until its dor"rasiree$ toe
---::sects the wing.wall at the ele"ration of the end sil1.
If there had been onl;r n6s;ral ta:-lsaier depth j-n lhe clcr.rnstrea&
::-a:::el, the basin dimensions c*uld have been those shor"m in Fig. 1?" For'-,::s taj-lnater condition the co:aputed basin length is so shcrt t]:at it does
nc-. :etain the fiIl. It is therefore necessarlr to lengihen the basin even'-:.:::-h the dike has been shlfted upstrea:E as far as possible. To do this,
i.-.e -" ciistance between the floor bl ocks and the end si11 is increased
l::-, ',he rnininumconpaiedvalue of h.75 tt to a required 6.25 tt. In this
:is: li.e fil l governs the basin length rather tl:an the hydraulic design
:: . : -- t : :a.
The r*ini:rum sider.:a11 height abcve the taril+rater leve1 is 0.85
i, = 1.35 x 2.67 = 2.27 (use 2.25) t t . This deternines ' r ,he height of theg:::xafl- at the encl of the basin and the leneth of 'Lhe wins,+a1l.
The end si1l height is 0.L d. = 0.h x
The hei3ht of the flcor b] ocks j-s
::se 2 .25) tt .
? .67 = 1"07 iuse 1.0 i l ) f i ,
0 . 8 d ^ = 0 . 8 x 2 . 6 ? = 2 , L 3
The floor blcek lridth and spacing should be appro:rinately 0.h
l. lr x 2.67 = 1.07 ft, anC they should occupJ,'betl"ree* 0.50 x l-,2,5 =
f t and 0.60 x l ,2 .5 - ? .50 f t ,
To fit the floor blacks into ii:e basin r'ridth and k*ep i.rrthin
-,:.ese l-i:;rj-taticns rer:"ui-res a mrmber of trials and'considerable juggling.
i.:;ever, if seven bloeks 3.a-1/2 zn. (0.95 ft) +ride (tne finisheri.ridth of a
. : ; '12 plank) arc used, the I ' r ic i th occupJ-cd by t ,he blocks is 6 f t 3-I /z
:::ches. ff the edge of the fi-rst blcck is located b-:4r :n. frcra the
'.,-a:}r the remain:ing blocks are spaced 10 in" apart.
31
The principal controlling dimensions have been rounded off and
t .e rounded values are given in parentheses. It will be noticed that the
basin length is much longer for the high tailwater than for normal tail
vater . The longer length naturally determines the required length of
basin . The basin dimensions are shovm in Fig. 11. The slope of the dam
has been assumed to be 1 on 2 and has been dashed in to show its 10-
a ion . It will be noticed that the high t ailwater requires a basin some
'!la l onger than is necessary to retain the fill. l1inimum basin lengths
--e used and the dike has been shifted dOvmstream until its downstream toe
- tersects the wingwall at the elevation of the end sill.
If there had been only normal tailwater depth in the dOvmstream
--= ......... el , the basin dimensions could have been those sho,m in Fig . 12. For
s t aihrater condition the computed basin length is so short that it does
retain the fill. It is therefore necessary to lengthen the basin even
the dike has been shifted upstream as far as possible. To do this,
e x distance betw-een the floor blocks and the end sill is increased c
~he minimum computed value of 4.75 ft to a required 6.25 ft. In this
ase e fill governs the basin length rather t han the hydraulic design
=i:..eria .
The minimum sidel-/all height above the t ailwata.r level is 0.85
= 0 . 85 x 2.67 = 2.27 (use 2.25) ft. This determines the height of the c _:de all at the end of the basin and the l ength of the win~iall.
c
The end sill height is 0.4 d = 0.4 x 2.67 = 1.07 (use 1.00 ) ft. c
The height of the floor blocks i s
e 2 . 25) ft.
0.8 d = 0.8 x 2.67 = 2.13 c
. 25
The floor block width and spacing should be approximately 0.4
0 .4 x 2. 67 = 1.07 ft, and they s hould occupy between 0.50 x 12.5 =
f t and 0 .60 x 12.5 = 7.50 ft.
To fit the floor blocks into the basin width and keep vri thin
.e se limitations requires a number of trials and . considerable juggling .
- ever, if seven blocks 11-1/2 in. (0. 96 ft) wide (the finished width of a
2 by 12 plank) are used, the width occupied by the blocks is 6 ft 8-1/2
:.nches. If the edge of the f irst block is located 4-3/4 in. from the
-all , the remaining blocks are spaced 10 in. apart.
) 1
o l- < r l_ T l
i ----l-
L,.ro'
II
9.25'
Section on Center Line
l !l ' t r
tz.5' 7 Elocks ot l l .5'*[
Fig. I I - Exomple of Stroight Drop 5pi l lwoy Srl l l ing Bosin Designed for High Toi lwoter
32
1 3tol
. , 7.75'
'; ,' ': '" ''':·;·0····,: :.°:··· ;.·. ·.· · '·.·0·; .':. · , . 1>" ' • .. ;' ,
17:60' ------~
" J1.50' .....
1-- - --- --- 24.50' - - -------i::i. _____ J
I I I I
I I LJ
12.5'
Section on Center Line
4.751j
o ". 0
7 Blocks ot 1 1.5'~
10,,_0
6 Spaces ot o 475,,-0
Fig, 11 - Example of Straight Drop Spillway Stilling Basin Designed for High Tailwater
9.25'
\ a
I
ro.r3r --+2.r2r
r8.50'
Secfion on Cenler Line
tr7 Btcks or rrs'*f] a
ta .J
' 6 ao*"t o1 19"-U
Fig. l2 - Exomple of Srroight Drop Spil lwoy Sti l l ing Bosin Deslgned for Normol Toi lwoter
3 to I
I
14.0'
3 to I
7.75'
r :,~--- 10.13' ---'12.12'
12.5'
18.50' ------I~
Section on Center Line
7 Blocks ot 11.5'-(] ..
6 Spaces 01 'O·~D o o
4.75"_0
Fig. 12 - Example of Straight Drop Spillway Stilling Basin Designed for Normal Tailwater
33
3l+
The approaeh ehannel is assrtfied to have a th.0-ft bottom $idth
and l- on 3 sido slopes. Sinee the notch is only 12--l.12 ft 1ong, there
will have to be sone narrorfiing of the ditch boticm near the spillway in
order to have the side slopes intersect the crest at the ends of the noteh.
In add.ition, it is recommended that the side slopes at the headnall be
1 on 2. Therefore, a short dike w11l be used lrith an 8.0-ft top width, a
1 on 2 end sloper ed a 1 o* J upstreanr slope, fhis use of the dike ica11
r"rill also serve to reduce the required. length af the headwall extensioa.
The dj-ke is i*etaIled. as shoi,rrl'in Figs. IL and 12', fhe approach chan:rel:
close to the spillway is aJ-so riprapped to protect it frsm seourr
This eompletes the hydraulic design of the straight .drop spil1-
way stilling basin.
34
The approach channel is assumed to have a 14.o-ft bottom width
and 1 on 3 side slopes. Since the notch is only 12-1/2 ft long, there
will have to be some narrowing of the ditch bottom near the spillway in
order to have the side slopes intersect the crest at the ends of the notch.
In addition, it is re~oIllIll.ended that the side slopes at the headwall be
1 on 2. Therefore, a short dike will be used with an 8.0-ft top width, a
1 on 2 end slope, and a 1 on 3 upstream slope. This use of the dike wall
v.rilJ, also ser,ve to redu?e the required length of the headwall extension.
The dike is ir,istal1ed as shown " in ·Figs. 11 and 12'. The approach channel
close to the spillway is also riprapped to protect it from scour.
This completes the hydraulic design of the straight drop spill
way stilling basin.
- .. , '
" {L r
D T . l 1 T T N / l E A D I I ] /! f ! ! J U U I L N f I I I
r - 1[J-J i'Iorris, B, T. and Johnsono D. C. ttllydraulic Design of Drop Strue-
tures for Gully Control"rr Transactions of the ArnericanSociety of Civil _Engineers, V
tZl Blaisdell, Fred td. a:rd. Donnel1y, Charles A. {yclraulic l{odel Studiesfor trilhiting Field $aval- Ai:' Statis boratory Project Repor!I{o, 2J, January, 1950. !O pages.
t: ] Blaisde1l, Fred. T,{. ttDevelopment and l{ydraulic }esign, $t" AnthonyFa11s Stilling Basin.rr Transactions of -i;he A.*erican Soci-ety of 9rvi1 Engineers,
tl+] BlaisdelJ-, Fred 'bJ"
and Dorrnelly, Charles A, Itydraulic lgsign of theBqx fnlet Drop_Spillr+ay. U. S, Departr:ent ol Ag:ic.r:.1ture,
--Soil eonser"atioE-Ferwice, SCS-?P-105, July L951. !3 pages.
t5J Rowe, I{*nier. Engi-neerilg Hydraulics. Ner* York: John trIiley 8r Soasornc . , f f i rg5o.
f,6l B1aisdel1, Fred.'*.i* trEquaiion of ihe Free-Fa11ing fappe.tr Froceed-l*g,p_ of tle American Society of Civ-j-I Engineers, VtT;-m,ffi
tZ] Ahmad., llazir. rrl{eehanisn of Erosion Below I$draulie T4lsy}4sorr Pro-eeedi:rgs of ihe Fiinnesota International isdraulics Coni6-tion, University of i'iinneso-i,a, St, Anthony Fa,11s lSdraali-cffiratory: FF. 133-1L3. Augusi o 1953.
t8] Donnell;., Charles A. Design af an Out1et for Box Inlet Drop Spi1l-wp4. U. S. Departneat of Agrieulture, Soil Conservatio:rffiice, SCS-TP-63, t'iover:rber, 1gh7 " j1 pages*
lgJ lliekox, G. I{. rtAerationof Spillways"tt Trq,qsaeti-ons"of }}? Sraeric?+Society of Civil Engi:reers, Vo1, 109, pp. 537-566. 19hh"
35
BIB 1 lOG RAP H Y
[ lJ Horris, B. T. and Johnson, D. C. !!Hydraulic Design of Drop Struc-tures for Gully Control 0 n Transactions of the American Society of Civil Engineers , Vol. 108, pp. 887~940. 1943.
[2 J Blaisdell, Fred \i . and Donnelly, Charles A. Hydraulic Hodel Studies for liJhi ting Fiel d Naval Air Station. University of Hinne-:sota, St. AYithony Falls Hydraulic Laboratory Project Report No. 23, Janua~J , 1950. 50 pages.
(J ] Blaisdell, Fred W. IlDevelopment and Hydraulic Design, St. Anthony Falls Stilling Basin. 1I Transactions of the American Society of Civil Engineers, Vol. 113, pp. 483-520. 1948.
4] Blaisdell, Fred W. and Donnelly, Charles A. &Jdraulic Design of the Box Inlet Drop Spilhvay . U. S. Department of Agriculture,
__ Soil Conservation Service, SCS-TP-I06, July 1951. 53 pages.
5] Rouse, Hunter. Engineering Hydraulics. Ne~v York: John vviley 8£ Sons, Inc., pp. 530-531, Fig . 12, 1950.
6] Blaisdell, Fred iJJ . flEquation of the Free-Falling IT appe. II Proceedings of the American Society of Civil Engineers, Vol. 80, Separate No. 482, 'pp. 1-16. August, 1954 •
. 7) Ahmad, Nazir. "Iv1echanism of Erosion Below Hydraulic \,Jorks. n Proceedings of the Hinnesota Int ernational Hydraulics Convent ion, Univers i ty of Hi nnesota, St. Anthony Falls Hydraulic LaboratoFJ, pp. 133-143. August, 1953.
8 Donnelly, Charles A. Design of an Outlet for Box Inlet Drop Spillway. U. S. Department of Agriculture, Soil Conservation :service, SCS-TP-63, November, 1947. 31 pages.
9) Hickox, G. H. "Aeration of Spillways ,II Transactions of the Arllerican Society of Civil Engineers, Vol. 109 , pp . 537-566. 19440
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