hydraulic --------- ----- model studies
TRANSCRIPT
! ~j 'I
HYDRAULIC MODEL STUDIES --------- ----- -------
FOR
PART V • • • • Studies of Open-Channel Junctions
Project Report No. 24
Prepared by
Charles E. Bowers
January, 1950
Conducted by SOIL CONSERVATION SERVICE - RESEARCH
United States Department of Agriculture in cooperation with
Minnesota Agricultural Experiment Station and the .
St. Anthony Falls Hydraulic Laboratory
The Naval Auxiliary Air Stati.on, Whiting Field, i.s located near
Milton, Florida. The surface of the plateau on which the airfield is
located is about 1]0 feet above the surrounding terrain. Prior to the
work described here the runoff from the paved runways and the surface
area has been carried down the sides of the plateau in unpaved ditches.
Although numerous structures have been used to control the grade of the
ditches, severe scour of the bed and banks has occurred because the
sandy-clay soil is readily erodible. The maintenance problem has become
so acute that it was decided to design an entirely new system to convey
the water down the sides of the plateau. Parts of the proposed drainage
system involved new and untried methods of handling the flow, and these
designs were developed by means of hydraulic models. other structures
involved designs on which it was felt that model tests were expedient.
The model. studies are reported in five parts. Each part covers
one general type of structure. Parts I to IV, covering studies on a
straight drop spillway, a cantUevered ditch outlet, pipe-ditch transi·
tion structures, and a detention·-type box-inlet drop spillway, are pre
sented in Project Report No. 23. Part V, covering the channel junction
studies, is presented in Project Report No. 24. The model studies were
authorized by Mr. Lewis A. Jones, Chief, Division of Drainage and Water
Control, Soil Conservation Service - Research, on September 20, 1948.
Dr. M. L. Nichols is chief of Research for the Soil Conservation Service.
Each specific model study was requested by Mr. Arthur F. Moratz, Head,
District Operations Design and Construction Section, who was responsible
for the structural design under the direction of Mr. Edwin Freyburger,
Regional Engineer, Upper Mississippi Region, Soil Conservation Service.
The tests reported in Parts I to IV were performed by Mr. Charles A.
Donnelly, Hydrau1ic Engineer on the Soil Conservation Service staff, as
Project Leader, while the tests reported in Part V were performed by
Mr. C. E. Bowers, Research Fellow on the st. Anthony Falls Hydraulic
Laboratory staff, as Project Leader. All model studies were conducted
under the supervision of Mr. Fred W. Blaisdell, Project Supervisor of the
Soil Conservation Service research work on soil conservation structures
11
at the St. Anthony Falls Hydraulic Laboratory. All research conducted
by the Soil Conservation Service at this Laboratory is i.n cooperation
with the Minnesota Agricultural Experiment Station and the St. Anthony
Falls Hydraulic Laboratory.
Acknowledgment should be made here of the fine cooperation exhibited
by all members of the Laboratory staff concerned with these studies.
Wi thout this cooperation it would not have been possible to complete the
large volume of di.fficul t work wi thin the short time available.
iii
CON TEN T S _._------
Page
Preface • • • • ii List of Illustrations • • • • • • • v Frontispiece • • • • • • vii
PART V. STUDIES OF OPEN-CHANNEL JUNCTIONS • • • • • 1
Introduction • • • • • • • • 1 General • • • • • • • .. • 1 Apparatus • • • • 2
Model Tests • • • • 5 Structure C-5 • • • • 5
General • • • • 5 Design 1 (Initial Proposal) • 6 Design 2 (Verti.cal Sidewalls) 9 Design 3 (Transverse Weir) • • • • 9 Design 4 (Undershot) • 16 Design 5 (Counterdisturbance) • 16 Design 6 (Piers) • • • 19 Recommendations · • • • 24 Other Designs • • • • • • • • 24
Structure c-4 · • • 27 General Terrace Outlets • • 33 Structure P-8 • 37
Design 1 (Initial Proposal) • 38 Desi.gn 2 (Increasing Froude Number) • 38 Design 3 (Submerged Piers) • • • • 39
Structure P-7 • • • • • • • • 44 Pressure-Momentum Relationships • • • • 50
General • • • • • 50 Structure c-5 • • • • 55 Structure P-8 • • • • • • 58 Structure P-7 • • • • 60
Comments • • • 61
iv
Figure
1
2
3
4 5 6
7 8
9
10
U
12
13
14 15
16
17
18
19
20
21
22
23 24
25
Sketch of Experimental Arrangement • • • • •
• • • General View of Test Apparatus .• •• Structure c···5, Design 1 - Initial Design • • • Structure c-·5, Design 1 .- Maximum Discharge Structure c-5, Design 1 - Modified Discharges Structure c-5, Design 2 - Vertical Sidewalls Structure c···5, Design 2 .- Maximum Discharge
· . . . • •
• • • •
• • • Structure c-5, Design 3 - Proposed Design •• •••• Structure c-5, Modified Design 3 for General Model Tests • Structure c-5, Design .3 - Comparative Effect of
Lateral Elevation . . • . . • • • • . . . . . • • Structure c-5, Design 3 - Effect of Narrow Lateral Structure c-5, Design 5 - Counterdisturbance ••••
•
• • Structure C-5, Design 5-· Effect of Counterdisturbance •• Structure c·-5,
Structure c-5,
Design 6 -' Pi.er Design . . . . . . . . . . Design 6 - Pier Design • . . · . . · . . .
Structure c-5, Design 6 - Pier Design . . . . . . . Structure c-5, Design 6 -' Depth of Flow at Design
Discharge ...•.•••.••••.....•.•• Structure c-5, Design 6 - Velocity Di.stribution i.n the Main Channel . • . . • . . . • • . . . • • • • • • Structure c-4, Design 1 - Proposed Design · . . . . . Structure c-·4, Design 1 - Maximum Discharge Conditions Structure c-4, Design 2 _. Pier Design • Structure c-4, Design 2 -' Depth of Flow • · .
• • • •
· . Terrace Outlet - General Design • • • • • • • • • • Terrace Outlet - General Design • • • Structure P-8 -. Comparison of Three Designs
• •
· . · .
• •
· . · .
•
Page
.3
4 7 8
10
11
12
13 13
15
17
18
20
21
22
23
2.5
26
29
.30
31 32 35 36
40 26 Structure P-8, Design 3 - Recommended Desi.gn •• •••• 41 27 Structure p-8, Design 3 - Depth of Flow • • • • • • • •• 42 28 Structure p-8, Design 3 .- Speci.al Di.scharge Conditions •• 4.3 29 Structure P-7 - Proposed Design • • • • • • • • • • • •• 46 30 Structure P-7 - Maximum Discharge Condi.tions • • • • • • 47
v
Figure
31
32
33
34 3.5 36
structure P-7 - Water Surface Profiles and Sidewall Hei.ghts .. ............• . • •
structure p-·7
Structure P-7
Structure P-7
Structure C-·.5
- Intermediate Discharges • • •
- Special Discharge Conditions
- Depth of Flow at Junction • •
- Pressure·-·Momentum Curves •
•
•
•
Structure c--.5 - Pressure-Momentum Relati.onshi.ps for Vari.ous Inlet Main Discharges • • • • • • • • • •
vi
•
• •
. . .
Page
48 49 .51
.52
.57
.59
iff n .. ;it
!H ;·r Hi
m n~ Hi
~. 1-'.
At Structure P-7 Froude numbers are low so that flows in both channels pass through the hydraul tC jump and Join at subcritical velocities.
Flow at Junction of Two Channels
J
PAR T V -. - - ,-
STUDIES OF OPEN-CHANNEL JUNCTIONS* ------- ---- ------- ---------
INTRODUCTION
General-
The Naval Amdl.i.ary Air Station, I'Ihi ting Field, is to have a storm
water dtsposal system tn which the existing pipes and terraces under
and in the vicinity of the runways and building area will discharge
into paved trapezoidal open channels. Many of the channels join other
channels as they pass down the sides of the plateau on which the air-·
field is located. The grades of the main channels and of many of the
lateral channels are such that water flows at supercritical velocities
or at velocities greater than that of a gravity wave (V > vgd). The
difficulties anticipated in joi,ning two streams of water, one or more
of which is flowi,ng at supercriti,cal velocities, led to the request for
model studies of several of the channel junctions.
The primary objectives in the present study include (1) the de
velopment of junction desi,gns for specified operating conditions which
would result i.n reasonably smooth flow downstream of the junction and
(2) the determination of the necessary wall heights in the vicinity of
the junction. Economi.c and structural considerations involved in the
junction designs were consi.dered in the final selection.
Dependent upon the junction design, the discharges, velocities,
and related phenomena of the flow i.n the vicinity of the junction, a
hydraulic jump may form in one or both of the inlet channels. This may
necessitate a large i,ncrease in the height of the sidewalls in the
vtcinityof the junction. On the other hand, if the flow passes through
the junction at velocities greater than the critical, standtng waves
may form whi.ch have a height greatly in excess of a normal freeboard
and whi.ch continue to osci.llate back and forth across the channel for
a considerable distance downstream from the junction before being damped
llSoil Conservation Service Report No. MN-R-3-41.
2
by frictional forces. These standing waves necessitate higher sidewalls
not only in the vicinity of the junction but for a considerable dis
tance downstream. As available information on junctions of this type
is almost nonexistent, it was necessary to resort to model studies in
order to determine the flow condi.tions and the minimum sidewall heights.
Two general types of junctions were studied. One type consists
of the junction of two large channels in which the lateral and inlet
main have comparable discharges. The other type, called terrace out-
lets, consists of a junction between a main channel and a terrace channel
having a relatively small discharge.
The maximum discharge ranges from 380 to 960 cfs in the main chan
nels and from 25 to 70 cfs in the terrace channels. The maximum velocity
of flow encountered is approximately 30 fps.
Apparatus
The general test setup used in the model studies is illustrated
in Figures 1 and 2. It consists of a trapezoidal channel section ap
proximately 25 feet long representing the main channel, and an 8-foot
trapezoidal section representing the lateral, plus the supporting struc
tures and the water supply system. The apparatus was designed to permi.t
variation in the slope, location, and elevation of the component chan-
nels. Water was supplied to the setup from the main laboratory supply
channel through 4--inch flexible pipes. The pipes discharged into special
headboxes which in turn discharged into the test channels. The depth
of flow at the exit of the headbox was regulated by a nozzle and a
surface lip.
The main channel had a bottom width of 7.2 inches and a side slope
of l~ on 1.. With the exception of the junction section, the same chan
nel was used for all studies; thus, it was necessary to vary the scale
ratio from 6.65 to 11..63 to simulate the various prototype channels.
The lateral and junction sections were changed for each study.
The channel sections were constructed of ei ther aluminum or painted
plywood. Experiments indicated that slope computations based on an
OR.-FICES LOCATED IN VERTICAL PIPES
HEAD BO)( i
\
JUNCTION SElmON i , B'. jLENGTH ~~
"~ . ~ . \ AS INL: MAIN/~A t} I
LATERAL
(LOCATION, ELEVATION,I SLOPE a APPROACH I ANGLE ALI. VARIABLE I
HEAD BOX
PLAN ylEW
BAFFLES DEPTH CONTROL
13'
-OUTLE't MAIN
~141 I S" I I ! us I . 1.5 1
I ~7.2"-1 i ...
SECTION A-A (ENLARGED I
- --SUPPORT /VARIABLE SLOPE, ELE-\ \VATION AND LOCATION I
MN - R-3-201
", '" ~ _'''_'0 ., ,.,.,,~.
""',0'
--< "'NO ,//////////// /" u'///I////,
SECTION ON CENTER LINE OF MAIN CHANNEL
Figure I. Sketch of Experimental Arrangement
'/
\.>I
The main channel IS at the right; the lateral, making an angle of 85° with the main channel, enters from
the left. In the background IS the piping system which supplies water to the model.
" , o ... ,,~.,,". -''''"''0,". "" CO"""","" •• ""._ ..... ". ," ,.,,, .. ,,., •• ,,. '" u" ...... _.", •. ,.,., ,,,,,.~ •• , """ .. ," '" ,. """'" '." ••• ""., ,,, ..... ' •• u .. "" ''', .... ,"."".
Figure 2. General View of Test Apparatus l="
n value of 0.009 in Manning's formula resulted in uniform flow in the
channels.
Froude's law was used to relate flow conditions in the model and
prototype.
MODEL TESTS
Model tests were made of only four specific channel junctions
which will be used at Whiting Field. In addition, tests were made on
a typical terrace junction structure. The selecti.on of the junctions
to be studied was made by the Region 3 Engi.neering Division of the Soil
Conservation Service. An attempt was made to study those junctions
posing the most di.fficult design problems since the time available for
maki.ng the studi.es limited the number of junctions that could be tested.
The model tests are described in the chronological order of their per·
formance.
Structure c-5
Initial tests were made on Structure C-5. Here the Owens Court
Terrace Channel, which flows at subcritical Velocities, joins C Ditch,
which flows at supercritical velocities. Since this was the first
:junction tested, five different junction designs were subjected to
exploratory tests before attempting to develop a final design. A sixth
design was not tested due to lack of time. Each of these designs i.s
discussed below.
General
The design condi ti.ons for structure G-5 were supplied by the Region
3 Engineering Division and are listed in Table I in prototype dimen
sions. As mentioned earlier, the main channel has the same width (7
feet) both above and below the junction. The lateral, with a bottom
width of 20 feet, i.ntersects the main channel at an angle of 85 degrees,
with permissible variation i.n angle of plus 5 or minus 10 degrees. It
was stipulated that the lateral could intersect the main channel at an
elevation up to 2 feet above that of the main channel; ground configura·
tions at the site necessitated this limitation.
6
TABLE I
DESIGN CRITERIA FOR. STRUCTURE c-5
Inlet Lateral Outlet
Main Main -----
Di.scharge (cfs) 0-414 0-181 0.·-595 Bottom Width (ft) 7.0 20.0 7.0 Side Slope 1.5:1 3:1 1.5:1
Slope 0.044 0.0095 0.056 Normal Depth (ft)'~' 1. 75 1.53 2.00
Normal Velocity (fps) * 24.4 4.82 29.8
* Froude Number 10.6 0.47 13.8 0.01.5,1,*' 0.035 **. Manni.ng's n 0.015
-----*Based on design discharge.
*"Addi tional tests were run on the final design for n = 0.01.3.
On the basis of computed flow conditions in the main channel, nor
malveloci ty was greater than the critical both upstream and downstream
from the juncti.on for the design discharges. An n value of 0.015 was
used in Manning's formula for computi.ng flow conditions in the main
channel, wh:i.ch was paved. An n value of 0.0.35 was used fOT the un
paved lateral. Flow in the lateral was at less than critical veloci.ty.
The scale ratio for all studies of Structure c-5 was 11.63.
:g~ign !.._ (Initi.al Proposal)
Fi.gure .3 illustrates an initial proposal for the design of Struc
ture c-5, first of a series of five which were tested. It cons:i.sts
of a simple :i.ntersection of two trapezoidal channels with the bottom
of the lateral 2 feet above that of the main.
The performance, as indicated by model tests, was very unsatis
factory. Large waves were created at the juncti.on which continued to
osci.llate back and forth across the channel downstream from the junc
tion. The maximum height of the waves was 6 feet or approximately
three ti.mes the normal depth of the stream. Figure 4 i.llustrates thi.s
I --r--r::-3TVOS "' 0
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The condition shown above is equivalent to discharge of ~1~ and 181 cfs In the Inlet main and lateral respectively. The -vertical spacing of the longitudinal lines IS equivalent to 2 feet.
Figure~. Structure C-~, Design I - Maximum Discharge u ~ ..... " ...... , A""'"'''' S." ~"H"" ................. ,. ... "'''.'''' .. ,. '" .......... ''''"'''''' ... " ...... "' ..... -, •••• A".", •• " ........... h ••••••••. " ................... .
CD
9
condition for the maxiElUm or desi.gn discharge, The disturbance at the
juncti.on might be described as a shock wave caused by the high-velocity
flow i.n the inlet mai.n striking the relatively slow flow issuing from
the lateraL The wave front extended diagonally across the main channeL
Wi th the desibn discharge of 414 cis in the i.nlet main, a decrease
i.n the lateral flow frod 181 to 90 cfs resulted in a wave height of
approximately 5 feet at the junction,
With a maximuIn discharge of 121 ds in the lateral, a decrease i.n
the inlet main :lischarge fron 414 to 207 cfs resulted in the formation
of a h;,draulic jUlnp at the npstream edge of the junction (Figure 5b),
Downstream of the juncti on the floVT was considerably better than when
a jump did not form,
At the conclusion of the r;receding tests, several modifications
of Design 1 were tes ted in which the lateral flow was confined to a
narrower channel and turned so that it entered the main at angles of
30 to 45 degrees. iIo appreciable improvement of flow conditions was
noted. it was concluded that a serious disturbance would still exist
if the lateral flow were turned to enter ablOst parallel to the main
flow unless the lateral flow were accelerated to a velocit~ comparable
to that of the 1'1ain channel
Design 2 (Ver~ical Sidewall~l
In an attempt to suppress the waves formed at the junction, ver-'
tical sidewalls were added as sh01m in Fi.gures 6 ane 7. While there
was no change in the wave height at the junction, flow conditions dowll-'
stream were considerably i,mproved provided the walls extended at least
60 to eo feet dmmstream from the center of the j1mction.
Design 3. (Transver seNeir)
A third design was proposed in wri.ch the lateral would approach
the main channel at a high elevation, be supported over the main chan-
nel, and the floV{ turned through 90 degrees before discharging over a
weir onto the water surface in the nain channel. Figure S illustra tes
the general pri.nciple. FiGure 9 shows a nodification of the above
t·· ;ii i!i ':it. ~i, Hi ii,
m ;H
m
(a) This represents conditions correspond,n9 to prototype flows of ~1~ cfs
in the inlet main and 90 cfs in the lateral.
(b) This represents conditions correspond,n9 to prototype flows of 207 cfs
In the inlet main and 181 cfs in the lat·eral.
Figure 5. Structure C-5. Design I Modified Discharges
..,
~ ,,' k:Lj"'''' I I.· ... ~ .
L ... i • I~
SECTION A-A
1--15' .rA 68' -j i
I I I I 1 11 I 4VERTIGAL SIDEWALLS i i it. I
·T\ ! ! I II
1
1. MAIIt .-~ ·-:I~·· :j .. -t-. -.. - 4 i -;' • ~ ... !!! . : ' - I ,
r l I I T j , t I i
I / I I I l I ! / I! I I I ' I -J I I
HI I /i if I ,I! I II ""/ ! I 48', I ! 1---:/-' -J. I / I 22' I I ; . • } .
. . I I I I . ; P"~ "'SIDE SLOPE" 3.1
. I I ,
MN-R-3-203
Figure 6. Structure C-S, Design 2 - Vertical Sidewalls "; t"", ... " ,' .... "".,,._ , •. , ''''''''''''''''''_.''''''. ,. " .... " "' .". '" "'"""'0 ""'"""" ,,, .. '!"'''' "",t,o. '"' >" ... " .. ,", ' •• '-,'''''.< I "".' "', ~".,,, "', .. ", ... , .. , ..
I-' I-'
...,
."._---- ~
The above design IS similar to Design 1 except for addition of vertical sidewalls at the Junction.
u • 0 • .," ...... , _0"'''''''' ,., c ............ "",, ..... ",. ,. < •••••• " ••• ". " ........... ~.""".'"' .... ,,~."' ".<", ••• ... •• •• t •••• '0'" .... ' •• '" ",0'0"". """''''' •• 1 .. , •••••••
Figure 7. Structure C-5, Design 2 - Maximum Discharge
I-' IV
r WEIR
Figure 8. Structure Proposed Design C'5, Design 3 ..
".,: .
Figure 9.
R "3""204 M N-'
'"~-- LATERAL FLOW
,\
'.', .
Modified Design Structure C··5.
"~"o._ ... [1 '_"'_"'~ .•. .-
,:, t~odel Tests 3 for General
13
proposal that was set up to facilitate model studies on the effect of
elevation and velocity of the lateral flow. With this setup it was I
possible to raise or lower the flow from the lateral with respect to
the main stream wi.th a minimum of diffi.cul ty. Also, by slight modifi-·
cations to the headbox it was possible to vary the horizontal velocity
of the top or lateral stream from the same velocity as that of the main
stream down to a value considerably less. It was assumed that a mini-..
mum disturbance would result if the two streams had the same velocity.
It should be noted that thi.s arrangement was not i.ntended to simulate
the weir of Fi.gure 8 nor to serve as the basis of a prototype design,
but merely to furnish qualitative information on the effect of changi.ng
some of the variables.
With design discharges in both channels the velocity of the lateral
was varied from the same veloci. ty as that in the main channel down to
one-half of tha t amount. No appreciable difference was noted in the
downst.ream flow due to thi.s variation, wi.th the exception of an increase
in the amount of spray at the junction for the lower velocity in the
lateral.
The vertical spacing between the bottom of the lateral and the
bottom of the main was varied from 2.65 feet to 4.6 feet (normal depth
of flow in the i.nlet mai.n was 1.75 feet). Slight surface waves (Fi.gure
10) developed with the latter spacing, but they were not considered
objectionable. Waves were created in the downstream channel with a
maximum flow in the top (lateral) channel and low flows in the i.nlet
main, but their magnitude was only slightly i.n excess of the normal
depth for a maximum discharge in both channels.
Wi th a vertical spaci.ng of 2.65 feet between the channels, it was
found that an occasional surge could cause the water surface of the
inlet main to strike the underside of the lateral channel. The result,
in some instances, was the formation of a hydraulic jump upstream from
the lateral which overtopped the relatively high sidewalls of the model
channel.. A jump also might form if debris lodged on the upstream side
of the lateral. Thus, the tests emphasize the desirabi.li ty of providing
adequate clearance betvreen the surface of the main channel and any
strncture spanning the channel..
Illustrated IS a test setup f9r a design in which the lateral now enters the main channel from the top after being turned through 90., In the top Views the vertical spacing between the bottom of the lateral and the
bottom of the main corresponds to 2.65 feet, while in the bottom views it corresponds to ~.6 feet.
Figure 10. Structure C-5, Desi!ln 3 - Comparative Effect of Lateral Elevation ~ 5 0 .......... o. _., ... "" •. ~." c ...... " ••• ~" .. <O-" ...... . M <0 ••• >".,_ '"'''' .. , ....... ,.""""., ••• " ...... ".1.,. ,., '" ......... "'" .. r ....... " ••••••• ,. U"'''''' ............ .
---- ~
.... VI
16
Figure 11 illustrates the flow condition downstream from the junc
tion when the top or lateral flow is appreci.ably narrower than the sur···
face width of the main channel. The discharges, vertical spacing of
channels, and related conditions are identical 'IIi'i th those of Figure 10,
except for the small pieces at the sides of the lateral which cause a
horizontal contraction of the lateral flow. It may be noted that with
the contracted lateral flow, large waves develop d01'mstream from the
jlllction, i.11ustrating the desirability of spreading the top flow uni
formly over the bottom flow.
While the above tests indicated that it was feasible to add the
lateral flow from the top, the tests of this design were discontinued
because the design was considered i.mpractical due to prototype ground
configura tions. Addi tional tests were conducted later in connection
wi th the terrace outlets where the ground configuration vms more favor· ..
able to this type of design.
Design 4 (Undershot)
Another proposal, referred to as Design 4, was similar to Design
3, except that the lateral flow entered the main channel from the bot·
tom. Although this design appeared feasible, no tests were conducted
because of time li.mitations on the study and the development of other
designs involving a simpler and more economical construction.
Design 5 (Counterdisturbance).
Fi.gure 12 illustrates a fifth design based on the creation of a
disturbance counter to that created b;l' the lateral. An angular wall
whi.ch diverted part of the flow across the channel was placed upstream
from the junction. The diverted flow was reflected off a vertical wall
and counteracted the disturbance caused by the lateral. The flow con
ditions with a maximum discharge in both channels are shown in Figure
13. The method was quite successful, provided the ratio of the mai.n
and lateral discharges was not varied too widely.
·'''"~,,,,<~._,""m~",,_,-.7,,~,,,,,,,,". ,J' I,e ; k ;i AJ ~ Q J. :" ;;, P.awHk ,& .. X ,3ft.; -'. ".2 k, ,2" t . .)t,E .. Qik, JL,. ;3Jt. ,_:_",_,~,J 44$) J,J,i,tAt.,..L . At. t ,\ .. J,.r)R\~.fl1:~~,'H.+:tllLl';nU)::MU,;.,qc!llM¥4 -, - - -':-,,:'---: "-"-'-:::'1
Small sidepieces have been placed on the top or lateral channel to contract the flow. The resultant waves in the main channel emphasize the desirability of distri
buting the top flow across the complete width of the main channel.
Figure II. structure C-5. Design 3 - Effect of Marrow Lateral u • 0 ••• " .... , .r •• " •• " ...... _, ........ , .......... -....... . .. ~ ......................... ,. At"''''·'·' •••• , ...... ~,." ••••• ... ~ ....... , ••• '" ~., ................. U".''''' •• 1 ....... ~ ••
~
! , .. "" ~ i ,...! Nt !! . I
j...3'+-7·-+3~ SECTION A-A
L,~TERAL
'I ~ '"-t i t t : ! !
I • PRISM ~iNE I l--10 ,--...1.---15' • I
SECTION B-B
1"-'1:;, , 35' .1 , , 1 • ! I Ii..... I,! ,
I · • ' '0' , I ' I. 26 'I' '--.. -~ . I " [I ! I .
! iii 1
1 I VERTI~:L WALL i t '" • It. _ t
',j i. -- -, 'I
I • .' r-- i.,.e'\ '. --~ , "4 ~ ~I ~~AIN - I' ...... \0. " ,
... --""" v. , . '--=-- ;. , t I, r I ,
i ~~.~ ~ 1; ~ i.
" ,-- / , I i I ' I I I, , I
I .---; i i 'l~i' I L I \ / I i :c ! I I ej f i ... I I i , I I -J, I, Il LCOUNTERDISTURBANCE ! ~-I-..20' ,f I
A , ! ____ --...; / I • . ,
. ---1..---.. MN -R-3-205
Figure 12. Structure C-5, Design 5 - Counterdisturbance , .. ,., ..... " "" ,0 ,." '" """ "
'",., .. '," " .. "-... """ ,-, ', .. "".,., ",,"" "'~""", ~'"" .. ,"
I-' co
-"'" ......
19
:Qesi~ (Pi~2
Design 6, illustrated in FiQlre 14, is recommended for the proto
type Juncti.on C-,5. It is s:L'lJilar to Design 1 with the addition of a
vertical wall opposi te the lateral and two lone;i tudinal submerged piers
downstream from the lateral.
The vertical wall prevents excessive lateral expansion of the flow
at the junction, v{C!i.le the longi tudi.nal submerged piers assist in damp
ing the transverse waves generated by the jlmction of the two flows.
Figures 15 and 16 show several flow conditions.
Variations in the positi.on, length, height, and nwnber of pi.ers
were studied experimentally. It was fo\md that relatively short piers
could be used for a specified combination of discharges i.n the joining
channels, but for other discharges it was necessary to move the piers.
This apparently resulted from a variation in the longi tudi,nal position
of the cross waves with variations in depth and veloci.ty of the flow.
Long piers were necessary to cover the anticipated range of operating
conditions. It was also fOlmd that an optimwn height of pier existed
for specifi.ed discharges; an average value was selected that is ade
quate for the antici.pated range of operating conditions.
On the basis of visual observations of the flow, it was concluded
that for some operating conditions the flow passed through the junction
at supercri ti.ca1 velocity, while for others a hydraulic jwnp was formed.
The formation of a jwnp was dependent upon the discharges of the main
and lateral channels. For example, wi.th a discharge of 181 cfs i,n the
lateral, a jwnp was formed in the main channel for all in1et'-mai,n di.s
charges less than approxi.mately 260 cfs. For inlet-mai,n discharges in
excess of 260 cfs, a diagonal wave Vias formed which di.d not exhibit
the appearance of a true jwnp. Using an analysis based on pressure-'
nonentlun relationships, it was possible to predict the approximate
range of conditions in "hich a jump would form. This is discussed in
the latter part of this report uncier the heading, "Pressure-IJomentum
Relationshi.ps." FiGures lSb and 16a illustrate the flow with a trans
verse wave, while Fi§;'ure 16c illustrates a condition which produces a
hydraulic jump.
(a) Downst ream
view
(b)' Side View with
Maximum Discharge in both
channe1s
(e) upsteam View with
Max i mum Discharge
in both
channels
The diagonal Lucile wall in the foreground of the lop photogr'aph er'eated
disturbance counter to that caused by the lateral"
Figure 13. structure C-5, Design 5 - Effect of Counterdisturbance u , o ••• ,,~.'" .J ., ... "", So ,"" ",";, ," 00" ..... ," ••• '" y """." ""<"_'.'" roo" '" >t ... ,,,", '" >,.,,",,,,, L.".""",
20
21
SECTION D--O
''''~l:' ~o:~~_ .. _ ........ _ ........ ....... , .........• ~~~N?A~&i~~fl1.'IPIOf S'~45' F!LL~S ~AY'~ \~~.:' ~-:·-·:'-·:·:··:3·3;..:· .~:::::.:~..~.:~i=.~.: .. ~ 5~~=~:·~"":::1 ADDEO FOR STRENGTH'\' '1}RAD. ON DETAIL. OF P fER
LEAD EDGE - C A '1 'J._"., .~ l f' t·· .. 1!}1 E;"'j ~ , . .. .. - ~ i,
A l.".I~~.:~~' ~ .. ~~' ... Z~.. . _ .. _~~,.. '\' .+ ... ' - .' 'j . '
-'=:]"':~""~'~!:~~""" '~. 4. --:----.,,-- -- t --\
"-" ................. j f· CJ
{"j , ~oL . -. -·~J·-l- .. \-F
",,,_ \fi.AI'L~IEW.
/ /// »)//?)>'/ / s'// ?, ) - "-" .- .... --., ._ ,.::, / ,.;7/77/////:;./;0'70'//77, / " -...... L Jr . . '-" S~044- __ _ _ //// / /1 ) 7'';7;- ~/""';7
A l. l 0 I MEN 5 ION SIN FEE r , ... - , .... S~.05i'I--.. ',;
EXCEPT AS SHOWN SECTION ON CENTER UNE .. :a ua: __ ~_
Thi:-o dESiqr
figure !it, Structure C-5, Design 6 ,. Pier Des!,]" , . ( .. " , " " " ." "-,, ,. --'
. ".'"",' ,,>,,., .. , "'" ~ .. , ", '. ',-''- ,-
1 I
22
(a) Side View - No Flow The I"\eavy 1 i nes rep resent the recommended
sidewall heights.
(b) Side View with Maximum Discharge
in Both Channels
(C) upstream View with Maximum d-ischarge
in Both Channels
T~e lo~er two photographs; llustrate the m~ximum discharge cond:tions :n wh'ch C~ = ~lij cfs and Q2 = 181 cfs,
Fig'ure 15. Structure C-5, Design 6 - Pier Design
, . , '" ~ "" "
The two top photographs illustrate flows equal to 414 and 90 cfs in the inlet main and lateral respectively. There IS a diagonal wave front. In the lower two photographs a Jump is formed just upstream of the junction.
The discharges are equivalent to 207 cfs in the inlet main and 181 ofs In the lateral.
Figure 16. Structure C-5,Design 6 - Pier Design u • 00 •• "" •• ' .' "'''''''.'' • ••• , < •••• " ..... ~.,." •• ~ •••• '" .. 000 •• ,.1,._ •.•• I ......... ' •• t'"'''"''' .... " ... "' ~'." •• ••• 0' ..... , ••••••. " ..... , •• ". , ... ,.,.". U'"'''''' " ....... ,.
~" """"-"-"'''--'''''~'~-~
N W
24
For those conditions in which a jump formed, the position of the
jump was dependent upon the discharge of the joining channels. The
flow accelerated dO"l'l11stream from the juncti.on, passing through the
critical stage within a short distance. Under these conditions the
dO"l'l11stream surface was relatively free of surges and waves.
When the flow conditions were such that a diagonal wave formed
rather than a jump, the downstream surface was somewhat rough, as is
illustrated in Figure 17, but it was considered acceptable.
Figure 18 illustrates the velocity distributi.on in the main channel.
As noted earlier, the flow in the lateral channel was tranquil.
Due to its elevation above the mai.n channel, the flow passed through
cri.tical as it entered the main charmel; in thi.s respect the junction
was the equivalent of a drop-.off for the lateral. This prevented the
surges and waves of the junction from traveli.ng up the lateral. A
minimum vertical spacing of the channel bottom of 2 feet 5 inches is
necessary to insure the above conditions.
The recommended wall heights i.n the vici.nity of the junction and
related desi.gn data are shown in Figure 14.
Recommendations
On the basis of visual observations and photographic records, it
was concluded that Desi.gn 6 was the most satisfactory of the designs
tested; the performance of the junction over the anticipated operating
range of discharges and the economic and structural features of the
prototype unit were considered i.n this selection.
Other Designs
In addi.tion to the six designs of Structure c·-5 previously dis-·
cussed, it would be possible to include several other proposals. One
of these designs which received some consideration would employ a radius
curve i.n the lateral to turn the lateral floVI parallel to the main
channel. However, if the lateral flow joinec; the main flow along one
side of the main channel, a shock wave or a hydraulic jump would be
created which would still require the use of walls and piers similar
to Design 6.
! !
iF ~q
;~~ ~::
Hi r i-
fH ~!~
H! ~E
IH
MN-R-3-207
7 'I ! I' I Ii! I I i-NOTES - : i J ! i J THE POINTS REPRESENT THE Ii
I "',! I AVERAGE WATER SURFACE. I
I I I " " I I THERE WAS CONSIDERABLE SURG- I 6 ' ING AND VARIATION IN THE WATER I
1\ i! ;', MAXIMUM HEIGHT OF SURFACE AT THE JUNCTION .
.I I, I V'SURGES ON WALL DUE TO THE SLOPING SIDES (DOWN- .
I I 'I \ I STREAM OF JUNCTIONi THE SURFACE L j ' i AT THE SIDES MAY NOT BE THE SAME
5 , '" ,AS AT THE PRISM LINE.
I I I, ~-,\ 11 LATERAL ENTERS MAIN CHANNEL I i .1 I , " ON RIGHT. SIDE LOOKING DOWNSTREAM
1;/ \1 0',- I •
1-4 lL i: ;1 "',,', i Q'NLET'414CFS QLAT."BICFS.J
~ I \ I': I \~MEAN DEPTH l'" I I I , , ,
, \. " .
I '" "
z i
I 3 -I- I a. , wI· c
~~- , -',
2 ~--~--r-~~~~~~~---1---1--~---1--~--~--~--~--~--~---;
• !
FLOW--j I I o CENTER LINE ! • LEFT PRISM LINE (LOOKING DOWNSTREAM I o RIGHT PRISM LINE I ALTERNATE PRESSURE
L MOMENTUM STAGE a 7.2 FT
I o 1..-1 _-"----'-_-'----'-
- 50 - 40 - 30 - 20 - 10
I I
I T I
o 10 20 30 40 50 60 DISTANCE FROM JUNCTION IN FEET
1 i
!
1 70 80 90 100 110
Figure 17. Structure C-S, Design 6 - Depth of Fiow at DeSign Discharge
120
~
I\) \Jl
------------_ ... __ % ... _V".'.N"'.W_'""'2"O"~,,"","-'Witp:""""e'w"m":'<t"f,{f.!'iWrtowrUi/iPiW,i&jl,?;£t.{,lr,\.'i.\i§$~~j.t'i'i"~;1-_1;,,£-,'i}~'i'F;~'~~;L(:~;tX::; '~-::~'~,:;;'~~::' -~',~f.:,:::;/~":_::",,t:~:;,'(';C.
2,51 I! I x STATION +105' CENTER LINE I i WATER SURFACE ! ~ STATION +105' LEFT PRISM LINE I '\ =="P , ,
" STATION +105' RIGHT PRISM LINE i i
• STATION - 23' CENTER LINE I i • STATION -23' LEFT PRISM LINE I I I
2.0 I 0 STATION -23' RIGHT PRISM LINE f I t
I (LQOKING DOWNSTREAM) i \ I' I I I I QINLET'" 414 C FS , i ! i
I °LAT, =ISlcFS I i WATE~ACE I- 1.51 I I l::l .... i
~ ,.. ~ . , I I ! I
f
t r ~
I I ; i
~ ,,0\ I I A 11! ! t I ~ I DOWNSTREAM I .... FROM JUNCTION U , I ~ I (d,;,,2,33FT) I ~ , t - t 'i" Q5 It, ,.. . I·· I
I "/ I \ I I . .. I I
I 'I I /'./ UPSTREAM FROMI' ,t' JUNCTION I
II • ! ~~; _J1i-, (d=I.63 FT) o i i .
o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 v - FPS
MN-R-3-20B
Figure 18. Structure C-5. Design 6 - Velocity Distribution in the Main Channel
".: ' :::.:,~::.: .;' .::'~;.:;,::;, :~!:;:,:::;~:~·X:·:: ;~~::";:~~;:.::~:~; S<
., 27
A seccnd proposal vhi eh received sone consi.der-a tion VIas baser1 on
the creation of a h;'dr8uUc ;jl;m, in the nai.n charmel for all di.scharges;
the lateral woulri enter the main channe.L jUGt dovmstream froT. the jlJmp
where the :flow ",as tr anqniL Si 11s or other neans woulc'. be used to
force the formation of a ju:np. As the alter:late pressnre-momentUL1
staGe of t,he inlet ,'"ain was 6. i3 feet for a disci arge of 414 cfs, hi.gher
sidewalls V'Ol)J d be req'Jirerl than I.or the reconnended design. Also, it
lmuld be necessary to raise the bottOlr of tLe Ja tel""1 to an e1evation
of approzinately 6 feet above t:.e :uain channel. This ViaS not feasi.ble
as the original design criteria l'estrictecl the verti.cal spacing between
the bottoms of the joining channels to approxim8tel" 2 feet because of
prototype grOlmd confi,.,uratiollS.
Structure C=!l
Struct'lre c .... 4 is a torrace outlet in 'whi.ch local draina;e is acJ·
l~i.tted to C l)itch. The nmcbm1 discharge of the lateral is 25 cfs.
[",e desi.,;n cr:ii;eria furnishec' te' the Eei;ion 3 Engi.neering Division are
listed :Ln 'fahle II.
T'AB1,E II
D8SIGlJ CRITERIA Fml STEWCTURE C-h
Discharge (cfs)
Bot ton \{]dth (it)
Side S1.ope
Slope
lJormal Depth (ft),f
!;ormal Velocit;y (fps)
Fronde Humber ",.
I"anning I s n
~~.
,,<
Inlet ;.:ain
3ch .G
7.0
L5:1
c.ooe6 2.,6:;
J3 .5
2.14
c.015
:aased on maxi.mum disct.arge ~
Lateral
2S.0
8.0
3:1
O.COl
1 .. 22
1 ... 75 0.078
Cl.025
Outlet Uai.n
409.0
7.0
L5:1
0.020
2.20
18.5
1+.[:3
0.015
28
The included angle between the mai.n channel and the lateral was
listed as 90 degrees plus or minus 10 degrees. The suggested vertical
spacing between the bottom of the main and the bottom of the lateral
at the junction was 2 feet 9 inches.
The model was constructed with the lateral at right angles to the
main channel. The scale ratio was 11.63.
The recommended design of Structure c~·4 is illustrated in Figure 19.
The initial model studies, based on a prototype friction factor
for the main channel of 0.015, indicated t.'1at with a lateral discharge
of 25 cfs, a hydraulic j1lJnp formed in the main channel for all dis-·
charges up to and including the maximum (Figure 20a). Wi.th lateral
discharges less than 25 cfs, the formation of a jump was dependent upon
the discharge of the inlet main. For those conditions in which a jump
formed, flow downstream from the junction was good (Figure 20b). When
a jump did not form, waves were created at the junction and the surface
downstream from the junction was rough.
In view of the fact that the prototype friction factor of 0.01.5
was an estimated value and because a decrease in the friction factor
would probably be detrimental to flow conditions at the junction, the , model was tested for conditions equi.valent to a prototype n value of
0.013. It was found that for a lateral discharge of 25 cfs and a maxi-·
mum inlet mai.n discharge of 38h cfs a hydrauli.c jump no longer formed
(Figures 20c and 20d). As a result, the flow downstream from the junc
tion was characterized by waves whl.ch were reflected back and forth
across the channeL A decrease in the di.scharge of the inlet main
resulted in the formation of a jump.
The use of a single submerged pier in the center of the channel
resulted in good flow condi.ti.ons for all discharges (Figure 21). The
vertical spacing between the bottom of the joining channels was in
creased to 3.25 feet to prevent surges from traveli.ng up the lateral.
Profiles of the water surface are shovm i.n Figure 22 for an inlet-main
discharge of 384 cfs and the lateral discharges of 25 and 50 cfs. Whi.le
the maxi.mum anticipated lateral discharge was 25 cfs, measurements ,vere
taken for a discharge of 50 cfs as a matter of general interest.
$;1"" "M -pur $wS'ts1'·tite1~~rlti "weT ''''r C YerIr{'X' Ri(f---r1P',''{Ct''A1'c'''''-''fc 'W'···" 0' "''WIh~''~' -"--
~O ,I ~ . ""lOiI m f~"iWj'W~~'I'\iii" ..... . .. SO - Jii*Yi!wU\\"'· .'. 'v"" < ,. . .
I
,SO" I'lIililM: 4%ii!!lk1ii'!l!!l%\~>'f$!!!M.W#!iiRa1n.-Wf.'f.l¥ .••. · .. --;"." ift14f1 • 1 I -n i . "", !!Ii" -, I .~ _.",,;::--.,/.,.,:,.,.,
, I I -- I -- I t-
, , I
I 1 I I
I
MAIN - - - -
/' L-I
INLET MAIN \ Q .... 384cFS n '"'' .015 f $.... .0086 d····· 2.65 FT
JU TFRNIlTJ I
~ 0 ~ hdtd~~ ~ : ~
I' 5=.0086
ALL DIMENSIONS IN FEET
MN-R-3-209
i
"
I SO
1-4-1 T
I -I. If ~t LATER~ , I Q •.•.• 25 CF:
I I n ...... .025 I
..J. d······ .~F'
Is ~ I' AJ.
PLAN VIEW
~
! -t. - -: I
I OUTLET .NAIN
"!j' .. · .. "T--T· T ..... " ~ ~==~-~'~ I ~ ~'f.; ..... '1 ' 1./ II ~_ ", I ~
I
SECTION A-A
l:ILVt'I:. VI" I II:AIU_ I:N.I ur r-1J;n IV: I f
I i r -t-
I
~ ~ / I ~ Li////J;j /' Y 1 !
///. T T
5:020 LLOCATION OF CHANGE IN GItAOE MAY lIE MY
PLACE BETWEEN THE Jl.NCTION CENTER LlHE
SECTION ON CENTERLINE AND A POINT 2S'DOWNSTREAM
-----.
Figure 19. Structure C-~, Design I - Proposed Design , , "',o"~'"' """'""." "" <,,",, .. ,,.,0 ;",,,._0 ... ,,,,
, .,'" '" ~'O" .. ". '.' '. '"," t ... ,,~.", " .... " 'fl' ",' '"" •• ,< '''''''''" ",,"" " •• , ~'O" .. O"
~
The four photographs illustrate flow conditions corresponding to prototype discharges of 3811- and 25 efs in the inlet main and lateral respectively. The top two photographs illustrate aco'ndition based on a prototype friction factor of 0.015, whereas the condition in the bottom two IS based on a factor of 0.013.
In the top photograph a hydraul ic jump has formed at a pOint 20 feet upstream of the Junction. In the bottom photograph a diagonal wave rather than a jump has been formed.
Figure 20. Structure C-~, Design I - Maximum Discharge Condition v • ~"'"R''' .0 •• """ .... ~ .. , <0 ...... " •• ~ .. ."._~ •••• " • .. ~ .... ,." .... ,. , .... ,. .... f. ,.,."" ... , '>,,"ROO' ......... . ," ~I .... ", .,0>, M,., •• '" "'"'''''' u." .... " " ........ ,.
'", ',A",1iI
"" o
~ 0 O""'~'''.' """".". ,.,' "." .... ,- ..... "-" .. ,.,, .. < ....... ,'" •• ," .......... "" .,. '" ..... ' """~'"' '''''" '"< "'" ",n._. "".M, •.• "., lpO"."',. "''''<'''.'' ", .•• "".
The flow conditions correspond to those of Fjgur~s 20C and 2od. The addition of the Pier has a beneficial effect.
Figure 21. Structure C-ij, Design 2- Pier Design
"" ....
.J
5..-----; -,---~--.- "! ~! .! I I t
i 'I iii J a CENTER LINE ! 41 1--
1" () I -- ! 0 RIGHT WATERLINE ,
I . " i ! ~! I' • LEFT WATERLINE ' , ,0 i ' i : , (lOOKING DOWNSTREAM)
3\-- -, -~I -or '--1---1'- '-r-- -1' ! , ! ""
i -- Ii! ! L---I----\----h.. '" -+-r-: --<---<> 21-----+, - . L_ ---1. --~---~-- +--l--+~ -~-- i : I I i : i I ! .' I i PIER i i ""i ! ! !!IILET 1 MAIN· .. !Q:384 C FS
I ,L IJ----+--.Li----L~--- -----t- J'.., i I LATERAL ........ , 25 CfS ,
I, iii, i i 'I i ' " I' ! 'I 1
' • 'I I , , . '1' I' , I ' , .
!-. Q.~o 40 -do -26 :ib J -,b 20 30 40 J; 60 70 8'0 90 160110 uJ uJ u..
z 5=.0086 T 5=.0200 -----.-;
~ 51 -I ' "- , I ~; I I I i
~ +-- t- -- i - -- + -- --,- -t--- +--+---+--+----+--+----1----1 i I I I iii ! I I r--' 1 . , ' 1 I . I ' , 3 ,-" .... -.,- '--r-- I I , I <p~ ..... , I !: i I -I--\;-I--~---l---+---t 'L.": 0 I r---!---1---~,.
2, I I II I PIER I I " 'INLETIMAIN"'IO:3-84-'~~S i--i i I, ' !! "" LATERAl,.·· ...... j 50 G FS '
i I I I ' . . I ' i " , I ! I ~ , J' I ' l I • , I "J !, o I I l' n l
-"''' _An -"" "" In 0 10 20 30 40 70 80 90 !OO 10
MN-R-3-210
" ',"0< ,~'" •• , ,,,-. ,. •• " ;'" ••• " ..... "
(,> .. ,~." ".""- <"' . """, " u,"· .... ,
DISTANCE FROM CENTER liNE OF LATERAL IN FEET
Figure 22. Structure C-IJ., Design 2 - Depth of Flow '-'" I'\>
.A
33
Ueneral Terrace 01::.tlets -'--~~--'---"~" .. -.-. ------ ~'-,~~ ------
; 0:le1 S tuclies Here de--
be jlsti f'ied for each ten'ace outlet..
rrb,erefor3, :i L \,:ao deci(~8C' tha.t. a ';ei'leral. scnd::]" of J~errace Qu'c.lets l"iould
1x-; wade which -,"o'uld r:Over the ant.ic:ipated ran.:~e'of opGratin[,' conditi,ons
and prov:1.de su:fici.ent infor ltion tel' the Gesif~n :Jf the terrace outlet
strllc tures, fl'r e :.1ei~;i,on 3 E:c:;;h18 :;"C-i":lg L':!.vision 1:'e'lI'E~stec~ that the stuCies
be cOl-':.ductej on n jnn.ction d.e~)~<;'l ["~jr ilc1.l~ to Ltc2t sho1'm i.n t'i';11re G<>
'rYe ·3 esigl': r:r i tel:i.a are shol'm. in f1\9 ~;le Ill"
=_a~::l.mlL'1l !):i.schal\~:O (cfs)
30 t tor;) lVtb (ft)
Sid.e Slope
Slope
1 .an:n:"ng 1 s n
TL?LE In
3nlet ., B.i.1
'lcu·Mo 11 , (;
Lateral.
5,20
10 0
C .005·0.015
0,03')
Outlet Lain
305-420
4.0
1.5:l
o.oh-o.08 0.,015
Thl~ lateral 1'Ia~ to be at ri~~ht anr;les to t.he main channel~ ri11e
SUL;:..;8Stt3(1 \fey tical spacin€: beb,,'een Ule bott,om of" tLe jnai.n a.nd the bottom
of the 1a t"ral v:as J.O feet.,
The ini.tiD J ~es ts yere conducted ," i.th a cha.:lne 1 s ~cl:;e of B per
cent. 31lC.~ :1.,,:'-ilet-<nain disd-,i..~.:r[;es of U to hO(J cfs, TLe co:'.~:;uted depth of
34
'rhe proposed desi[;n for tLis structnre i~l i.llustrated i.n Figure
23. 'j'he baffle walls SLOiffi in l'i':;11re 23 "ere not installed ini.tiall:'
and, Hith a maximmn di.scharge in the lateral, it was noted that the
flow 1'as not evenly distri.buted across the transverse weir. This re···
en1 ted because the la Goral. flow was turned tLrongh 90 debrees before
flowin[; over the weir. 'Ehe addition of a taffl.e wall to one side of
the weir opening greatly improver] the flow. It was found that the Hall
cOllld be placed at right angles to the centerline of the lateral or at
45 de::;rees as shm'n jn FiGure 23.
It was also noted that some sl'rface spra;.- ;enerated b;) the inlet
main ras striking the llpstreac side of the 1a teral. 'Ilhile thi.s was
not necessaril:r indicative of protot;ype performance, i.t was thought
desirable to increase the verti cal spacing of the channels to h. S feet.
'rhe greater clearance also red'lced the possibi1i.ty of the formation of
a hydraulic ;jurnp on the '~pstream side of the lateral.
Figure 2). illustrates the flow conditions for the recommended de
sign, ,iith large discharges in the mai.ll channel there were no appreci-·.
able surface waves, l,ut considerable spray lOOlS created downstream from
the jlmction. With low discharges in the main channel, as i.llustrated
in Figures 24c and 24d, the ·water surface downstrearr was q'Jite irregu·_·
lar, but the tlaxinurn height of the waves was less than normal depth for
large di.scharges. It is doubtf'Jl wLether the model correctl~· simulates
tLe srray condi tions in tl.e prototype; as a result, the recommended
"·0.11 heights downstream from the junction are onl" an estimate.
The moclel tests e-Clphasized the desirabi.1it~' of spreading the top
or lateral floVi unifornl;\ over tLe .. ater surface of the main channel.
nest results were obtained ·when the wic,.th of the je t: as slight1y in
excess of the water surface ,·ridtll in the ;min channel.
Due to time limi to. tions on the study, it was not possible to test
the complete range of channel slopes and discharges that 'ias initiallj
requested. In addition to tile precedinc: stlcdies only one otner test
A~ I
, 45 !.- 'j ~--U5 _. ~ r--- --- ~ l
I ----,_.-:- llf'-lrT~·.J 1 L----1.
" I
! ; (1)&:;1 ! - ~ r-.~ . ' I ,«, l-r~o i ! j "- LId' I "; 1---·--'--·------·----+-1-:----11 Il ._- ; -'-- ------;-i--L-_. ----. ------ -.--_. :p-;-r' rr-y-' , .---1 L -i-r'-- -i'-j-- I . 'i, + ' / '.' I' "'
'- I '" ,/ 1'-) J .'1-.1 m~ :
l-·--- /A-I -~-+ i. -~ t / . .-11-_. \ FOR ALT. BAFFLE WALL
/ If! ''''-''''/'1''/ , , I \ ~, U" 0\ " ! 10---; ~ AJ
INLET MAiN G)...... 400 CFS
2, .. ··· 0.08 "~ ..... " .015 (I" ... ; _88F
LATERAL 25 CFS
ALTERNATE DESIGNS FOR SAFFLE WALL
PLAN VIEW
:-is'1T-! ~ ~ J 1 • W,,,
,-------1
;>;7;7~l?7·'>Y~.-~rmM Ii) 1. . <ot LlIT t. OF ' ATERAL ~ J.5 f ~"C ""'"
U.J l
ALL.. DL,:Et<:~1\:>NS dM FEE"r SECTION Il, - A -~.-~
~\f(i\i'- .,\ -.~" . .,: I
"iglll'B 23. Terrace Out.let - General Design ",.)-~
'-Sl
'" o
'" o ~
'0 C C u
E
" E
:;J E
'" "
a o .p
"0 C 0
" on ?) ;.: c
" '" c a
" '-cr, 0
" 0 "-C\.
a ~ E 0 ~
+' 0 0
~
'" , .
" > -~ C)
'" <>
" " L
" L -1)
'" 0 c "
"-
" E ~ ," c
.~
.C
c
u
>, '7;) > ~ u
" ( ....
'" '" l.
';;j L (i;' F' n
i.'" t~
'J t;:
", E
~
" c
" .r..:: '.-
" ~.
", N
C C ,to;
,,:::>
S '. c
U .-, ~~-~
(j 'h
r";
37
condition 1fas run. 1 L correspOtlcer. to a claxil1Ul c'ischarge of 300 cfs
cUl(~ the lroude nUl':lbel' vras .: 020 Tbe appearance of the flow vd.th dis··
charGes of 2S and 300 efs in the 'Lateral and i.nlet c\a:n respectively
r .. as s:~.ni.1Clr to the precedi.ng tests 0 It, is proLs-hle that. for lor ... di.s-'
charges i.n tLe nain cl:;'·1nnel S ]ll':,e Y,-clVes ;-~i.,_~_ht 1:,3 forrr;e(~~ hat. it :i..s
dOli;:tful -whether the): ~Iould be Seri01)S as l.ong as a generons freeboard
is provided
.Lt ma:' be of interest to noto Hat for the specified cLannel di-
YJensions, C'lD-nae:'- slo,:es of 1; to 6 per cent, a friction factor of O.GIS,
and inlet·'-lain c'iscllar"es of 3CC! to ;"00 cf's, tJie mi:li.J1ul11 computed Froude
nlll1ber lTD-S t. 2 alV! tlee :;lax:L:mIT yas 1(, ,. J . l' or a 1a teral eli scliarge of
25 cis the ratio of the inlet flmr t,o t]-.e lateral floT' ranGed from 12
to 16. For these cOl1(~it,i~ns it ,las est:i<'Dteci that, except for spray,
In tests
of anoth.er junction of this t2'Pe (p" e ) the results ,Jere not too satis,
j"actory> In U;e lc:t ter case tte ,'i scLaree ratio for na:x:imum discharge
Ir2S 13 .. 7, bllt the Frou(:e rnunber l'TClS onl:~- 2,,9,
Br ief tes ts 'here ~onrlllct.ed vrl til the 1a teral di.schar:;;ing over a
weir at the upstream sir:e of tL8 tr~nsverse box The res111 ts nere 1ill-'
satisfactor;' due to the larGe a:,.ount of s,Jr-aJ createc' anc' an increased
tendenc;) toward the format5..on of a L;yr:ranlic j1JmP,
Structure p,,,.c
Strnctllre P-t COllsis Ls of a jlUlcti 0::1 between a chamw1 1d.th a maxi
Dl111 discLarse of 70 cfs and P Di teL uLich has a L'~axi.mlJ.fl discharge of
S\)() efs" it \"'"3S req1.1csted that tects -:=:8 conducted on tLe bransverse
."reir .. "type j1;nction sinilar to kat i3L01m i.n Fic;',re (3" TLe i.nitial de-·
sign condi tions are listed in Table IV,
Y1-18 to limitations elll t;-,e tire available for ti:e stud;), the initial
tests were cODrlucted wi.th a {;.cl::::iJ::UJU dischar'::'8 in the inlet nain of h32
cfs, as op:)osed to 3. design maXimlITl ai'
conducted v,ri.Lh a rnaxinu:::rl 0-;:- 632 cfs~
Subsequent tes ts 1::rere
: a::imUJIl :lisclwr,;e (ds)
nornal Depth (ftt
::ormal VelocU;y (fps)"
loot to", 1'Ii c: th (f't)
Slope
Side Slope
Fr- oude ~r'mn ~er'{'
I ianning 1 s n
TM'LE fiT
Inlet .,~ain
9cO.0
il.09
19 .L~
6,0
C.0l2
2.26
-k~:,(1sed on maxirrrnm discharce Q
Lateral
70.0
20.0
0,005-0.01;'
Tronqui.l Flow
38
Outlet Itain
1030.0
4.23
19.8
6.0
(.012
1 .. 5:1
2.U:
0.01~
'V'ith t;jscharLes of 432 ane' 70 cfs in the inlet oai,n and lateral
res~)ectively, the dmmstrean water surface VIas ver; rough, Hith larGe
,',aves developing and continllin,; dmmstreau. The ;;;ave crests were 4 to
L,.~; feet above tte channe 1 flow onG the hol lows were 2 feet above the
floor (Figure 25a).
It was thol1ght tLo t floy;, cone,i tiona could be improved b~ increasing
the Froude mmher of tLe inlet nain, On the basis of tLe croLmd pro·,
file of P Ili tell, the slope of tlle di toh u;ostream from the jlIDction Vfas
decreaset~ for a distance 0 f 666 feet and then increased for 0 distance
of 460 feet. The slope e'ata are as f01101[S:
t:ps tream froyn Station ;-iJ + 54
sta tion lJ ~ ~L, to Sea ti.on 50 .; 20
Station 50 • 20 to Station 54 + ~o
::JOTi1lstrGi:m irom Station 54 + GO
(The J'-nction Vias located at stc,tion
Slope = 0.012
STope 0.0062
Slope = 0,0204
Slope = O§012
51., + 70)
39
Dro1J,,,·c'01'm C1.1IVeS i·';ero computed to c:eterrrine the depths at t.he
junction. The results indicate that l10rnal depth would be obtained.
The cO::Jputed depths allc related ca ta on tlJe inlet main for the
above conditions are r;iven in Table V.
TABLE V
DEPTHS AiD EELii.TED DATA ON TEE; EJLET l'ilIIJ
i~
(efs)
960
632
432
d (ft)
3,.S8
2.90
2.38
v (fps)
23.6 21.1
19.0
F
4.83 1.;.77
4.71
It '1',ay be noted that the slope chan.;es resulted in an increase
:i.n tlle Froude mmlber fr om 2. ';6 to h.71 for a cci.scharge of h32 cfs. The
flo\[ "ondlticn for c'iscl18r ges of 1+32 and 70 cfs in the inlet r.lain and
lateral respectively are shown in Figure 25b. Some improvement of the
flow v'ras noted, out the surface was still considered rough. liith a
discharge of 632 cf's, the flow was good wl.th onl~ slight waves.
V,1hi.le the floYT condi ti.ons with an inlet-main discharge in the
vicinHy of 1+.32 cfs were not satisfactory, no further increase in the
Froude nu~nber ·was considered because of limitations imposed b;j" the pro
totype ground configurations. Instead the use of' submerGed piers was
investigated. 1t was experimenta.ll;) determined tLat two piers located
cJownstreaLl from the junction greatly improved the floW"> Fignre 25c
illustrates tLe flow condi.ti.ons for a dischar6e of il32 cfs. With a
dischar~e of 632 efs (E'i.gure 2S) the flow was 1i.kewise improved> At
a discharge of S6c cfs in U"e inlet main, it Vias estimated that the
only objectionable feat'lre of the junction 1'1Oulc. be spray.
On the basis of the tests, the junction desi~n was c)l1sidered
sa t:..sfa.etory a.fter tLe a,:'cdi b.on of the subner ;=ed piers .;1:.e recommended
(a) Design 1 (b) Design 2 (e) Design 3
The discharge of the inlet mal'n corresponds to 432 efs (Max. Q1:= 96'O'cfs), and the lateral to 70 efs. The three designs are similar except for difference in slope of the in1et main and the addition of piers In Design 3.
Figure 25. Structure P- 8 - Comparison of'Three Designs
" , 0.,<" ... " ., ~""'''.'', ,.', C'.""''''. ,,, •. ,, ...... ,, • .• , .... ".·0' .," , ..... "" ••••• ""0."".1 £ ......... , "." •••••
,,, ........ r '"'' .,., •• ,,, , .... " •••• Y.""'''' Of ........ "
f;
--------------------,-~~~;1"~.,lillhr&!Jllflli%1l1'£l.'l.!li'1iillWU1\i.@~
I. 15~
I i
II' i
i! J, lSi
'" 1 ~ ! I ' I I I +-1 j -----1 '" I
---i I
-~r~ t: I ii' t IJ r 1
I I
~9 ---+ 9~
//
/I
, - ----1 __ ~------==~~====-45 j
I ------30 .J.. SlOE SLOPE 1,5:1
I ~ -JII I
I "'~ I I [ -'-~5! 50 I 'j j
'I i ,£----.::-~--:.:;=!N ~~~t I -lI----¥-- t. --\ '1..: '---1
J '-PRISM LINES":' \ PIERS ; t I 1 I : I ob \ Ii! - \ lJ I I
ROUND LEADING AND TRAILING ENDS OF PIERS
ALTERNATE/ ;'
PLAN VIEW
(4' TO 6) :;; DR~IN: ...u
~ Ii I U~ Ii! : Ii f f ! i '" \... 1 I 1 I /l 1 rl -----.--1 j' 1 'I 17'" /~' 1 I!
-'-/." ; I . ~ ~: .~.., l t7:::r/./.7d;/h/7»/))/74//,j»;?;///~) i k M J JR. i J , S=.020:~Jt<:WM?//; Y/);;;;/7,w,.;r))~ ~:?o:~,.;r////h/TM7;;;N/ff4 ::?&M)/7/,.;r;;:;:.1
ALL DIMENSIONS IN FEET STA. 54 + 801 SECTION ON CENTER LINE -
MN-R-3-212
", " , .,,,,,, ,., .", '"' ~.",,,, ,"0"' 'C""" .. "
Figure 26. Structure P-8, DeSign 3 - Recommended DeSign ~
~
i-'
10
9
8
7
.... 6 \IJ \IJ ~
5 :z
:z:: 4 .... I:L \IJ
o 3
2
I !
l I
I I
L !
I
1 I
,
1 i I I
I
J I I I ! 1 i
I I
• 1 !
1 ... I
I 1 i I !
• , i I I I I I
i
LATERAL~\ i
I ~~ i
I I I I \ \ I . , \ I \ \ t I J I i
I I I ! I I j j I
! ! . I I l ! i
I I ,
I v,-i !
--1---- -- I ! I f
, I j ! I , I ! !
i I I I i J I J I I i
I I 1 j I DISCHARGE 1 I I
J I i , i I •
INLET MAIN - 632 CFS I I
J LATERAL - 70 CFS
! •
i I ! I i I J J I 1
I ! •
1 I 1 I I J I I
J J ! I I i I i I
1 J ! I I i ! I I ! 1
t t -I • --t-- , k t r I
I ('_jPlERS I I I I ' 1 i
I I i r,. "' I
'" I ,! I
1- 5=.0204 5=.0120 I '>.',J ., o -40 -30 .!.20 -10 0 10 20 30 40 50 60 70 80 90 100
DISTANCE FROM CENTER LINE OF LATERAL IN FEET
MN-R-3-213
Figure 27. Structure P-8, Design 3 - Depth of Flow ",",,'<.,. 00"'" ,.,,"'_,
", '" ~,".,,,,, ," "" ~.' '''' "''''','' •. ", '"' .. ,d. "W.",,,,,,
fu
This represents a prototype discharge of 632 cfs In the inlet main and 70 cfs In the lateral. The maximum anticipated discharge of the inlet main is 960 cfs.
Figure 28. Structure P-8, Design 3 - Special Discharge Conditions u 0 u .. '",. ... " """".'" So" c." •• " .......... " .•••• "." ,. c ........ " .," ..... '" •••••• a ••. , ... " •• '0.,,, .. , •.• " .... '"' '" ~, .".0 ••. '''. ~"".'" co ... " •••• J .... " .. , " .. '" ••••••
{;;
44
desi"n i.s sh01m in FiLure 26, The depUe of flow for di scharges of 632
and 70 cis in the inlet main and lateral res;Jective1y is shown in
It is possible that a juncti.on design simi.laT to that used for
Structures c-·4 or 0-5 nay have wnrranted investigation, but time 1i.lILi.
tations prevenGed further tests.
etructure_P-T
structure P-7 consists of the junction of 0 Ditch and F Ditch,
both of wLich contain flow with velocities greater than the critical.
The included angle betvleen the inlet main and lateral could be varied
somewllat, but an angle of 51 degrees 2 minutes was considered desi.rab1e
since this permitted the best topographical location of 0 Ditch. The
design criteria are listed in TableV1.
TABLE VI
DESIGN CRITERIA FOR STRUCTURE p-·7
Inlet Main
Lateral Initial Final
Outlet Main
Initial Final --------, ... _ •.. _._------------_._----------------::aximmn Discharge (ds)
lJorma1 ::Jepth (ft) If
Ilornal Veloei.t) (fps)"*·
Bottom Width (ft)
Slope
Side Slope
Froude thmber
EanningT s n
630.0 330.0
3·31
17·3 6.0 6.0
0.012 If-Ji
1.5:1 1.5:1
2.81
0.015 0.015
~~D • based on maJCl.mum discharges.
~H(-Can be varied.
33C.O 2.16
16·5
6.0
0.017
1.5:1
3·91 0.015
960.0
4.08
19.4 6.0
0.012
1.5:1
2.86
0.015
960.0
4.79 15.2
6.0
0.0062
1.5:1
1.50
0.015
Both the initial design cri.teria supplied by the Regi.on 3 Engi
neering Division and the final design crHeria developed on the basis
of model tests and conferences w'i tll the above orGanization are shovm
h5
for the lateral and outlet main. The change in slope of the out1et
main was made for the purpose of improving flow conditions at Structure
p-·e which is located dO'l'ffistream from Structure P-7.
The proposed design of Structure P-,7 shov;n in Figure 2? was based
on the assumption that the flow in both channels would pass through a
hydraulic jUl11p and joi.n at ve1oci.ties less than critical. Preliminary
computations indicated that this was the simplest and pr'obab1y the most
economical design. Si.11s or other means would be adder! to induce the
formation of a jump if necessary.
As a first approximati.on it was assumed that for the maximum dis""
charge condi tion the depth a t the jlmcti.on wo'~ld be equivalent to the
alternate pressure--momentum depth of the inlet main, with a hydraulic
jurrp forming just upstream of the jlmction. As the alternate depth
of the lateral was considerably less than that of the inlet main, a
;jump should form at some distance upstream from the junction i.n the
lateral chmme1. On this basis the computed depth at the jlmction was
6.9 feet. ICodel tests subsequently indicated a depth of 7.2 feet at
the junction. Figure 30 shows photographs of the flow condi ti.ons at
the maximum discharge and Figure ,31 illustrates the water surface pro
fi.1e based on model tests.
Subsequently an attempt was made to compute the channel depths
using the pressure-momentum theory. The results, whi.eh are discussed
i.n a later secti.on of this report, were not too successful. but did
assist in explaining the performance of the junction.
As noted in Table VI, the design discharbe of the in1et main was
630 cfs while that of the lateral was 330 cfs. The model tests indi
cated that for an inlet-main discharge of 630 cfs, hydraulic j1l11!ps
formed in both channels for all lateral discharces in excess of 167 cfs.
With a lateral dischar[;e of 330 efs, the same condition existed for
a11. inlet-main discharges in excess of 1:36 cfs. Two views at i.nter
mediate flows are shown in Fi.gure ,32. The nri.nimmn values ;just cIted
were dependent on visual observations and are somewhat arbi trar3' For
those condHi.ons in which the hydraulic jumps formed, the 'water surface
at the jtffiction and downstream therefrom was reasonably smooth and was
STA. 30 + 22,
+
~~
Inllllllllilli
MN-R-3-214
~, ~ ':';:':,'.~;:':2;,::' ~~~',~:'~:~:::;: ::~'. ,;.:~:,:,:,.:oy:':': :~,7:"";:~~;~:; ::::
STA. 43 + 37.4
I I 1
~ I I I
/
7}' \ 7..':1 X " \
. "" ~I "I
o DITCH
A...., /P DITCH !
• I I ;
t~ - -<0
:t
A..J SECTION A-A
NOTE
I. 51= 0.012, 50= 0.0062. SL= 0.017 CHANGE IN GRADE OF OUTLEi MAIN
IS AT STA. 43 + 54 2. SIDE SLOPE = 1.5' I
Figure 29. Structure P-7 - Proposed DeSign
t:
Hydraul ic jumps take place upstream fron; the channel junction"
Flow at the junction is therefore subcr'itical,
Figure 30. Structure P-7 '- Maximum Discharge Conditions
u , O""I~".' ,j " ., ''''''. '0, (.0,'" """'" ,_e"""., • . ,e.,'".".," •.• " ••• ,· ... "., c.""" ",,,,.,""'"'""''' '" """,,. ", • ",,,.,,., ''''-''''', "'"'''''' ,,' , .. " ot,
47
130
128 !-LJJ LJJ .... 126
~JC I.LTERHiTE SIDEW"'LL HEIGHT ! , ,
i I i !
i ----- ---'--..j. ..J. ! J ! I I ,
I "- RECoMMENDEO SIDEW ... LL HEIGHT ./ I I I
- 'r-
l i I
I - - ·1· . -- 'G.. --- .... ~ MAXIMU,", HEIGHT Of SURGES
z
z 124 0 i= <:(
122 >
"'" ..... w
120
I I ! /' 1 -1 -.... -~ f-="'Y.l~~E _ ~I~:~C: I I I I i '9... '" I~ i 0 ....
.", !'7 ;:: ~
I T_ I" ~ l ~ i , i ~HLETM"'IN_ i , "" i ~ I ",," I i I 630 CFS I ' I I' , 960 CFS . j ,
I I I ! i I I . . L ; 1
I I I c: i I '" I ,
•
II. I I , I ,
i 5' .012 I I . I I 1
S '.0062 .
I
4230 40 50 60 10 80 90 4300 10 20 30 40
STATION ON P DITCH 50 60 10 80 90 4400 10
130
itS !-LJJ LJJ .... 126 Z
Z 124 Q 0-« (;j In ....J LJJ
120
II e
MIII-R-3-215
-, 1<,' . '" ~
r--i---i- I I I - --- - ! i I ' - -1"'-- - J I ! "\
I ~
! !) ! I I \ I
I I I I .1 •. _ - ,.. -I- - --1..---l I ..... +-- -- ,---- .t'"
I Ii ~;:":-, 'I .! i I I I \ I I 1.......-- i, I I ! i·;:: I ~ i LATERAL..f ! I I I II! \ ~ L.1 ! 330 CFS !' I ~ I I I ! 1 \.,
I I .1 J '! i I \ I I 11 r II . I' 5 ' .0 17 ! I I I
Ii! ! I I I • II ~_l I ~1.. I I I I I 1 i --n
90 :1.900 10 20 30 40 50 60 10 80
STATION ON 0 DITCH 90 3000 10 ?-O
- NOTES-
I. JUNCTION LOCATED AT ST .... 43 +37.4 ON P DITCH AND ST .... 30 + 22 ON 0 DITCH.
2. JUNCTION ANGLE • 51° 02'
3. BOTTOM WIDTHS Of CHANNELS , 6 FEET.
4. SlOE SLOPES - 1.5'1
Figure 31. Structure P-7 - Water Surface Profiles and Sidewall Heights -§;"
··~'-'"·-"">_~_~!"C'*_"'""#'.!'~~"'~~~~~4
.,'.'
The discharge of the lateral is equivalent to JJO cfs and that of the
inlet main to 160 cfs. There is a hydraul ic jump in both channels
The later-a1 has a discharge of 8l1- cfs, the inlet main a maximum of
630 cfs and there is no hydraulic jump in the inlet main,
Figure 32. Structure P-7 - Intermediate Discharges
O. O,,","m, .. " "., "."''". ~ •. , c,",,,',,,, ,,.. >0'" ,_R .... ".
" c . .,,, ,I,.. " .• '" ~ .... " ... ,' '"".' " ,,"',~,,' ,,", ... .. ". , ." '0', " •• ,d .,,' ., t,,",·, ''''r, " ""'" 0' ~"" .",.
49
50
characterized by a minimum of surging. With a maxi.m1L'11 discharge in one
channel and discharges i.n the other less than the rni.nimum value just
cited, the flow at the junction had velocities greater than cri.tical,
and rather large waves developed at the juncti.on and immediately down
stream therefrom, as is sho"l'm in FiGure 33. However, their height was
less than the freeboard required for the maximum discharge condition
and they were not considered objectionable.
Beginning wi th a maximUlll discharge in both channels, a decrease
in the discharge of the inlet mai.n caused the jump in that channel to
move upstream, caused the jump in the lateral to move downstream, and
resulted in a decrease in the depth of flow at the junction. A similar
phenomenon resulted if the flow i.n the main channel were held constant
and that of the lateral decreased ·wi th the jump in the main channel
moving downstream and that of the lateral upstream. Figure 34 illus
trates the depth of flow at the j1llction for various discharges.
In the tests just described the hydraulic jumps formed naturally
without the use of sills. In one series of tests, sills were inserted
for the purpose of forcing the formation of a jump for those conditions
in whi.ch one had not formed previously (large discharge in one chan-·
nel and a small discharge in the other). The sills were successful in
insuring the formation of a jump for all discharges, but the"T resulted
in a serious increase in the depth of flow at the junction with a maxi.-
mum discharge in both channels. This more than offsets any beneficial
effect that the;y rni.ght have, and they were orni.tted in the recommended
design.
The plan of the recommended design for Structure P-7 is illustrated
i.n Figure 29, while the recommended channel wall heights are shown in
Figure 31.
PRESSURE-MOMENTUM RELATIONSHIPS
General
An analysis of the junction of two channels based on pressure
momentum relationshi.ps was attempted in an effort to explain and assist
1
A discharge of 330 cfs in the lateral and no flow in the main.
A discharge of 630 cfs in the main and no flow in the later'al"
Figure 33. Structure p- 7- Special Discharge Conditions.
u S o ... 't~",,'.< .".," ",", So. <" .. " ''','', ,'-. ", "" ," co •• "."," .... '" w " ... " •• ,' '0""'''' " .. ,',~"," ,,,._,, '"' .. , ., ""'''' " , .• " .,,',' "'''''''''. 0' .,"'" .,' ~"., ".
51
I: , r,
7r----r---+----~--~--_r--_+~~~
6r---~--_+--~r----+-----r----+~~+---~~--+--~18
5r---~--_+---~~--·+_--~--_4----+_+_~--_+--~
z o
4r---~----+~~~--+_--~--_4----+---~--_+--·~
fo()
Z ::> ~
~ 3r-----+----~---~~--~----~--~-----~·----+-----+----~
:J: f0-Il. W o 0-- Q I. :330CFS, Qt: 136 TO 632CFS
2 I-----~
O--Ql.: 110 TO 330CFS, QI: 632 CFS
O~--~--~--~--'--~--~---~----~--~--~--~
MN-R--3-216
,." .. ".,., "", •• ".", $ ... c ....... " ....... , .. _~ .... ". ",I',. _n. ' .. ~" .... ,. """".," h •• " .. , .. , ""'" •• , > .. " •• , •• EO. H".a"',e C"",,,,,, U", .... ,' ..... " .... "
o 200 400 600 800 1000
Qo : OUTLET DISCHARGE -- CFS
Figure 3~. Structure P-7 - Depth of Flow at Junction
in the prediction of flow conditions in the vicinity of thejunetipri.
Basically this analysis consisted of equating vectorialJ¥ the pressure
plus momentum of the incoming stream to that of the outgoing stream •.
Considering first the pressure-momentum relationships between two
stations in a straight channel with zero slope, the difference in hydro
static pressure exerted on the two ends of the segment of water between
the stations is equal to change of momentum per unit time, or
and
where P
M
Fm
Q
V
w
y
= = =
= = = =
=wF m
the total hydrostatic pressure in the end of the segment,
the momentum flux, .Q:WV, g
the pressure plus momentum divided by the unit weight of
fl °d P + M mor w'
the discharge,
the average velocity across the section,
the unit weight of fluid, and
the depth of flow.
If the stations are an appreciable distance apart, it is necessary
to include a term for the fricti.onal drag in the above equation, and
if the channel has a slope, it is necessary to add a term for the com-'
ponent of gravity.
In applyi.ng the same considerations to a juncti.on, the sums of
the pressure p1us momentum of the inlet main and lateral are equated
vectorialJ¥ to the pressure plus momentum of the outlet main. The
reference stations for these computations are taken at the upstream and
downstream edges of the junction. For the case in which the inlet main
and outlet main have the same cross section and the same alignment, as
in the present study, the hydrostatic pressure force exerted by the
flow in the lateral is counteracted by the pressure on the opposite
54
wall, provided the water surface in the juncti.on is essentially flat.
Thus, the only force the lateral flow can contribute to the main flow
i,s its component of the momentum parallel to the main channel.
It is necessary to know the depth of flo,,\ at some point in the
vicinity of the juncti.on to provide a starting point or control for the
subsequent computations. Thi.s control may be either upstream or down
stream from the junction dependi.ng on the :flow conditions. If the flow
in all channels is tranquil, the control will be at the downstream edge
of the junction (the depth at this point will be determined by flow
conditions downstream from the juncti.on). Presumably it is possible
to equate the pressure plus momentum at this point to that of the in
coming channels and so determine their depth and velocity, provided
the discharge of all channels is known. It is usually necessary to
make the assumption that the depth of flow is the same in both the inlet
main and lateral. for tranquil flow.
If the flow in all channels, including the junction, has a veloc
ity greater than the critical, conditions upstream from the junction
will presumably determine the depth of the inlet main and lateral im
mediately upstream from the junction. The depth downstream from the
junction can then be computed. However, if hydraulic jumps form up-'
stream from the junction with tranquil flow at the junction, the problem
becomes more complex. For example, assuming that the control is at the
upstream side of the junction, if the hydrauli.c jump in the lateral is
a considerable distance upstream from the junction, either its position
must be known or the depth in the lateral at the edge of the junction
must be known in order to compute the momentum contri,buted by the
lateral. Likewise, if the jump in the main charmel is a considerable
distance upstream from the junction, the pressure plus momentum at that
point is not the same as at a point immediately upstream from the junc-'
tion, and it is necessary to know either the positi.on of the jump or
the depth of flow at the junction in order to compute the pressure plus
momentum contributed by the inlet main. During the course of the pre
sent studies it was noted that in those instances where hydraulic jumps
formed <and where ~rmal flow in all channels had a velocity greater
than the critical) the flow accelerated and passed through criti.cal at
the downstream edge of the junction. Thus it was possible to compute
the pressure plus momentum at this point and use this value in deter-
mining the depth of flow and the position of the hydraulic jumps in
the inlet main and lateral channels. While the computed results were
in fairly close agreement with the model performance, the data were
quite limited and do not constitute an adequate confi.rmation of the
theory. It should be noted that even though the above theory i.s ac-
cepted, it is first necessary to determine whether or not flow at the
junction is tranquil. If shooting flow exists at the junc ti. on, the
control or known depth is at the upstream edge of the junction and the
preceding theory cannot be applicable.
An attempt was made to apply pressure--momentum theory to . the
analysi.s of the performance of Structures c·-5, P-7, and P-8. The pri
mary objective in the case of Structure C·..:5 was to obtain an explana
tion of the conditions under which a hydraulic jump would form in the
junction as a check on the model performance. With Structures P-7 and
P-8 the same information was desired plus computed values of the depth
at various points.
Structure C-5.
As noted earlier, the lateral at Structure C-5 intersects the main
channel with an included angle of 85 degrees. As an approxi.mation it
was assumed that the lateral contributed neither pressure nor momentum.
This assumption was made because the velocity in the lateral was rela
tively low, which was indicative of a low value for the momentum; in
order to compute the momentum contributed by the lateral it would be
necessary to multiply this low quantity by the cosine of 85 degrees,
giving a much smaller value to be added to the momentum in the outlet
main. While the water surface at the junction was quite uneven, it was
considered expedient to disregard any pressure component of the latera1.
The problem was greatly simplified by the above assumptions and
consisted of equating the pressure plus momentum at two stations in
the main channel, one above the junction and the other below. The
56
discharge at the lower station was larger than that of the upstream
station by the amount contributed by the lateral.
Using the maximum lateral discharge of 181 cfs, the pressure
momentum curves of Figure 35 were computed for four inlet-main dis-,
charges. The basic curves represent the pressure plus momentum of the
inlet main and the outlet main as a fUllction of the channel depth for
Design 6 of structure c-5. The values of d noted in Figure 35 are the
computed normal depths of the inlet main for the specified inlet dis
charges.
Referring to Figure 35a, it may be noted that the inlet value for
Fm1 of 65 is less than the minimum value that must exist in the outlet
channel. The only way i,n 1IIhich the inlet main may have the minimum
value for Fm of 120 computed for the outlet main i.n order to equate
the values of Fm of the inlet and outlet channels is for a hydraulic
jump to form in the main channel at some point upstream from the junc
tion. When this occurs, a force acting downstream will be created
which will be equal to the difference between the frictional drag
(acting upstream) and the component of gravity (acting downstream) on
the segment of water between the hydraulic jump and the upstream edge
of the junction. The result will be a new value of F at the upstream m
edge of the junction which will be equal to the minimum or critical
value required at the downstream edge of the junction. In other words,
dl at the upstream side of the junction will not be the normal depth
of flow in the inlet main but will be the depth d'l in Figure 35a 1IIhich
has the mini.mum pressure plus momentum required by the flow in the out
let main.
Referring to Figure 35b, it is apparent also that a hydraulic jump
must form for an inlet discharge of 207 cfs if the lateral discharge
is 181 cfs.
With an inlet discharge of 310 cfs and the same lateral discharge
of 181 cfs, it is noted in Figure 35c that the value for F is just m
equal to the minimum or critical di.scharge in the outlet channel. This
represents the borderline case.
i'
ii'
n ; 0 _ 0 13. dl ; DEPTH IN INLET MAIN
400 .----....--0 .. · --.-.l'"'0...----.1""'03.--,.---.----, 400
(a) INLET • ~ WAX· I (b) I \ I 0 ; 207 0LATERAL; 181 . I
o ; 181 .. 103 ; 284\ 0 0 = 388
300 300 .
!I~ 200 ... E 200 1 I ___ ~_ - I ). --L---l----I--• !~. , E 100 I 100
... I I' I· _ ------ .-0: I -0: I I-J
o -01 1 0 _ I I _ i:
o 234567 0 1234567
d -FT_ d - FT.
400 I (e) \ 1\ puiUiJ400 I (d)
300 I I.. ',<I ...... 'F 74 300
.,!= 200 I I: \,,1 L./ 1---- 1 .E 200 I
100 I I i I I I I- - 100
o Ii; ~~: !~~ I 0 I ~~: ;~~ 01234567 0 234567
MN-R-3-217 d - FT. d - FT.
The rel at j t!tnsh I p between i n1 et and out 1 et discharges is based on a constant 1 ateral discharge of 18.1 cfs.
u. o •• "'~ ... o. AI".'''''', 5", " .... , ...... ~.,.,"-..... " • .. c ...... "'." .,," ,., ... .,,,.,, £""'"'''' « .. ,,,.,,, ""'" 0., '" ;. .""" ".,,, """'''' lo"_'''',. v.· ......... " .• ""t.
"-00· ---"-''-_-'Y_:"'_~,:,:_-,, ":,--jC,~
Figure 35. Structure C-5 - Pressure Momentum Curves U1 --.J
In Figure 35d the value of F for the inlet channel m
of the minimum required in the outlet channel, thus no jump wii.l Oc(~UZ;;
there m.ll be a transi.tion from the inlet depth of approximately 1.7
feet to an outlet depth of 3.3 feet. The model studies indicated that
the transi ti.on was in the form of a shock wave which was quite turbulent.
The essential information of Figure 35 nas been replotted in
Figure .36. As mentioned in the preceding paragraph, the curves indi
cate that for a lateral di.scharge of 181 cfs, a hydraulic jump win
occur for all inlet discharges less than 310 cfs (outlet discharges
less than 491 cfs). The model studies indicated that the above is true
for all inlet di.scharges less than 260 cfs (outlet discharges less than
441 cfs); this figure is based on visual observations and is somewhat
arbitrary.
No special effort was made to compute the depth of flow in the
vicinity of the junction, but l.t is thought that for those instances
in which the flow at the junction was tranquil the assumption could be
made that critical depth occurs at the downstream edge of the junction;
it should then be possible to compute the depth at the upstream edge
of the junction and thereafter the position of the hydraulic jump.
When shooting flow exists at the junction, it i.s accompanied by a shock
wave and a very turbulent surface; it is doubtful whether depth compu
tati.ons would be of much practical value for this condition.
It is thought that the primary value of the preceding computations
was an explanation and conformation of the model behavior. The model
studies were the primary basis for the selection and design of the
prototype junction.
structure P-8
Wi.th regard to Structure P-8 pressure-momentum computations were
made for discharges of 632 and 70 cfs in the inlet main and lateral
respectively. In this structure the lateral flow passes over a trans-·
verse weir, entering the main channel from the top. While the lateral
flow has a small downstream component at the point where it strikes
the surface of the main stream, it was assumed that the lateral
500
DISCHARGE OF LATERAL=18ICFS
...
:. ::;) 300 ~ Z
IN. Fm
ILl :.
FOR OUTLET
0 :.
+ 200
ILl II: " ::;)
lit lit ILl
I I· I ,- °L HYDR. JUMP NO JUMP
II: 100 ~
..,~
• e ~
o L--0
MN-R-3-218
u S U' •• ,,~ •• ' o. ~'"'.''.''' ••.• <0.,,, .......... '''_~ ... " .. .. ~ ••• "., ....... '" w, ..... " .'0 ......... , ••• " ..... ""',,. 'ft' ' .... a." •• , "", ~", .. h. , ....... ,', u .... ,," •• , .. , ••••• "
100
Figure 36.
200 300 400
00 - CFS
500
structure C-5 - pressure-Momentum Relationships
for Various Inlet Main Discharges 'C0~b'~
~,~~~c=~===c~""~~=_~~~~~'"~ ____ ~ _____ ~ ~_"' ~~~~
6Q
contributed neither pressure nor momentum to the main stream. The
computations were quite simple; the results indicated that there was
little possibility of a jump forming. Assuming that the above was true,
the control or known depth would be on the upstream edge of the junction.
Equating the pressure plus momentum at this point to that downstream
from the junction, it was determined that the downstream depth should
be 3.4 feet. This may be compared with the results of the model tests
(Figure 27) which indicated a value of .3.S feet.
structure P-7
The lateral at Structure P-7 intersects the main channel with an
included angle of Sl degrees 2 minutes; thus it was necessary to include
the momentum contributed by the lateral in the pressure-momentum cal-,
culations.
An attempt was first made to determine analytically the operating
conditions for which a hydrauiic jump would occur in the vicinity of
the junction. The momentum of the lateral at normal depth waS! multi.
pli.ed by cosine Sl degrees 2 minutes and added to the pressure plus
momentum of the inlet main. Whenever this sum was less than the criti
calor minimum pressure plus momentum of the outlet main, it was assumed
that a jump would occur. The computed results agreed wi.th the model
performance for approximately one-half of the proposed operating range.
One possible explanation for the lack of better agreement is the failure
to consider the velocity distribution in the analysi.s. A uniform
velocity distri.bution was assumed. If the velocity distribution were
to be considered, it would be necessary to include a momentum correc
tion factor in the above calculations.
An effort was also made to compute the depth of flow in the vi.
cinity of the junction for several cases .in which the flow at the junc
tion was tranqui.l. Fair results were obtained, but the computations
were discontinued when the model studies were completed. The latter
indi.cated that the proposed design was acceptable.
COMMENTS
The present study was undertaken for
taining information that would assist in the design of open~c]n!lJqn,~~·
junctions in the drainage system at Whiting Field. Due to severe tillJi6.<
limi.tations imposed on the study and the numerous structures requiI-ing
investigation, it was necessary to arrive at sati.sfactory des:i.gnsfor·
the various junctions as expeditiously as possible.
In view of the limited amount of information available on the de-·
sign of junctions of this type, i.t would have been very interesting
to conduct a more extensive investigati.on with the objective of ob
taining sufficient data to assist in the general design of high-velocity
open· .. channel junctions. While thi.s was not possible, it is thought
that in addition to supplying information on the specific junctions
being investigated, the studies reported herein may be of some value
as an indicati.on of some of the problems which may be encountered in
junctions involving shooting flow.
During the course of the studies it became increasingly apparent
that model studi.es of junctions of this type are necessary until more
information is available to assist in their desi.gn. Pressure-momentum
relationships were utilized in an attempt to analyze the behavior of
the junctions; while the results were of considerable interest, parti
cularly in the case of Structures C-S and P· .. 8, they gave only a partial
solution to the problem. With additional background information on
whi.ch to base some of the assumptions employed in the analysis and
additional time to make the necessary computations, particularly in the
case of Structure p .. ?, it i.s thought that closer agreement with the
model performance could have been obtained.