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NATIONAL ENGINEERING HANDBOOK
SECTION
HYDROLOGY
CHAFTER 21. DESIGN HYDROGRAPHS
Victor Mockus
Eydraulic Engineer
Revisions by
Vincent McKeever
William Owen
Robert Rallison
Hydraulic Engineers
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NATIONAL ENGINEERING HANDBOOK
SECTION
HY ROLOGY
CHAPTER 21 DESIGN HYDROGRAPHS
Contents
In t roduct ion 21 .1
P r i nc i pa l S p il lways 1 . 1
Runoff cur ve number proc edu re 21.2
S ources of r a in f a l l da t a 1 .2
Areal adjustment of r a i n f a l l amount 1.2
Runoff cu rv e numbers 21 .2
Climatic index 21.3Channel lo ss es 21.5
Q u ic k r et u rn f lo w 2 .5
Upstream re le as e s 1.5
Combination of channel lo ss . quick ret ur n f low.
and upstream re le as e 1.5
Runoff volume maps pr oc ed ur e 21.8
Areas of mapped run of f volume 1.8
Deep snowpack a r e a s 1.8
Cons truc tion of p r in c i p a l spi1lwa;- hydrographs andmass cur ve s 21.9
Development of Table 21.10 21.9
Use of Tab le 21.10 21.10
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Figures
Figure
Mass curves of runoff . . . . .ES-1003
. . . . . . . . . . . . . . . . . . . . . . .323-1011 . . . . . . . . . . . . . . . . . . . . . . .ES-1012 . . . . . . . . . . . . . . . . . . . . . .ES-1020 Contiguous s t a t e s
Sheet of 5 . . . . . . . . . . . . . . . . . . . .Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . . .Sheet 3 of . . . . . . . . . . . . . . . . . . . .
heet of
heet 5 of
ES-1021 Hawaii)Sheet of 5 . . . . . . . . . . . . . . . . . . . .Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .heet of
Sheet of 5 . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .heet of 5
ES-1022 Alaska)
Sheet of
Sheet 2 of 5 . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .heet 3 ofSheet of 5
Sheet 5 of 5
ES-1023 Pu er to Rico)
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Table
Tables
Arrangement of increments befo re c on st ruc tio n of
PSHandPSMC 1.11PSH and PSMC f o r example 21.1 21 .14
PSH and PSMC f o r example 21.2 21.16
PSH f o r example 21.3 21.18
S e r i a l numbers of PSH and PSMC 21.19
Time, r a t e , and mass tabu la t ion fo r p r in c ip a l
spillway hydrographs PsH) and mass cu rv es PSMC) 21.20
Equations used i n co ns tr uc ti on of ESH and FH 21.52
Hydrograph comp utatio n 21.54
Hydrograph comp utatio n 21.56R a i n f a l l p r i o r t o e xc es s r a i n f a l l 21.57
R a i n fa l l an d time r a t i o s fo r d e te rmining To
when storm durat ion i s gr ea te r than 6 hours 21.58
Hydrograph fa mi lie s and To/Tp r a t i o s f o r which
dimensionless hydrograph ratios a r e g iv en i n
Table 21.17 .2 1. 59
Time, d is ch arg e, and accumulated runoff :-atios
f o r dimensionless hydrographs 21.60
Ex h ib i t s
Exhib i t
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NATIONAL ENGINEERING HANDBOOK
SECTION
HY ROLOGY
CHAPTER 21. DESIGN HYDROGRAPHS
In t roduc t ion
This ch apte r contains a sys tema tic approach t o th e development of
des ign hydrographs fo r use i n propor t ioning ea r th dams and th e i r s p i l l -
ways according t o SCS c r i t e r i a . Include d a re da t a o r sourc e s of da t a
fo r des ign ra i n f a l l amount, dura t ion , and d is t r i bu t io n; methods of
modifying design runoff t o include eff ec ts of channel lo ss es , quick
re tu rn f low, o r ups tream re leases ; and methods fo r rap id con s t ruc t ion
of hydrographs..
The methodology presented i n t h i s chapter i s s u i t a b l e f o r t h e d e s i g n
of many type s of water c ont ro l s t r uc tu re s, inclu ding channel works,
but the emphasis i s on hydrology f o r design of ea rt h dams t h a t pro-
vide temporary s torage f or f lood prevent ion i n a ddi t ion t o permanent
s to ra ge fo r o the r use s. t s chief purpose i s t o c o n tr i bu te t o s a f e
des ign . Although th e methods are based on da ta of a ct ua l s torms and
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Any one of four methods of runoff determination is suitable for thedesign of principal spillway capacity and retarding storage. They are
1)the runoff cunre number procedure using rainfall data and the water-shed s characteristics, 2) the use of runoff yolume maps covering
specific areas of the United States, (3) the regionalization and trans-
position of volume-duration-probability analyses made by the SCS CentralTechnical Unit, and (4) the use of local streamflow data with provision
of sufficient documentation on the method and results. The latter two
methods are not discussed in this chapter because they vary in procedurefrom w e to case, due to conditions of local data, and standard pro-cedures have not yet been established.
Runoff Curve Number Procedure
The runoff curve number procedure uses certain climatic data and the
characteristics of a watershed to convert rainfall data to runoff vol-m e. This procedure should be used for those areas of the country notcovered by runoff volume and rate maps. (Exhibit 21.1 through 21.5.
SOURCES OF RAINFALL DATA. Rainfall data for the determination of di-
rect runoff may be obtained from maps in U.S. Weather Bureau technicalpapers
For durations to 1 day.--
TP-40. 48 contiguous States.TP-42. Puerto Rico and Virgin Islands.
TP-43. Hawaii.TP-47. Alaska.
For durations from 2 to 10 days.--
=-49. 48 contiguous StatesTP-51. Hawaii.
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Table 21. i . -- ~ at io s f or ar ea l adjustment of r ai n fa ll amount
AreaArea/point ra t io fo r Area/point ra t io fo r
day 10 daysArea
day 10 days
10 o r l e s s
1520
25
30
3 m i .
r a i n f a l l f o r t h e s t r u ct u r e s i t ei s
6 or more inche s, th eN
fo r t he 10-day storm i s taken from table 21.2. If it i s . l e s s th an 6 inches , the CN
fo r the 10-day storm i s th e same as t h a t fo r the 1-day storm. The10-day N i s used only with the t o t a l 10-day ra i nfa l l .
CLIMATIC IIVDEX. The climat ic index used i n th i s part of the chapteri s
where C i=
climatic indexPa = average annual precipitation in inchesTa average annual temperature i n degrees Fahrenheit
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Ta ble 21 .2. --Ten-day ru no ff curv e numbers
Runoff curve numbers for:
day 10 days l d a y lo da ys day 10 days
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Climatic Maps f o r th e Nation al Atlas . Maps with a scale of one
in t en mi l li on . map fo r ayerage annual pr ec ip it at io ni s
avai l -able but there i s no map f o r avera ge annual temp eratu re.
SCS person nel may ob ta in the se p ub lic at io ns thPough t h e i r Regional
Technical Service Center.
CHANNEL LOSSES. If th e dra inage a rea above a s t ru c tu re has a c l imat ic
index le ss than 1 then th e di re ct runoff from r a i n f a l l may be decreased
t o account fo r channel lo ss es of inf lu en t streams. Channel lo ss es can
be determined from lo ca l dat a but t he lo ss es must not be more than de-termined by use of ta b le 21.3. When adequate lo ca l da ta ar e not a va il-
able , t ab le 21.3 i s t o be used. Example 21.1 gives th e procedure for
making th e channel lo ss reduc tion of d ir ec t runoff.
Channel los ses in areas where the cl im atic index i s 1 or more w i l l
requ ire s pec ial s tudy; r es ul ts must be approved by th e Dir ector ,
Engineering Division, before being used i n f in a l design hydrology.
QUICK RETURN FLOW. Quick retu rn flow (QRF) i s t h e r a t e of discharge th a tPe rs is ts fo r some period beyond th a t f o r which th e 10-day PSH i s derived.
t includes base flow and other flows that become a part of the flood
hydrograph such as ( 1) ra i nf a l l th a t h as i n f i l t ra te d and reappeared
soon afterwards a s sur face flow; ( 2 ) drainage from marshes and potholes;
and 3 ) delayed drainage from snow banks. I f th e dra inage a r ea above
a s t ruc tur e has a c l imat ic index gr ea te r than 1 then QRF must be
added t o the hydrograph o r mass curve of di re ct runoff from ra in fa ll .
QRF can be determined from lo c a l d at a bu t it must not be le ss than the
steady r a t e determined by use of ta b le 21.4. When adequate lo c a l dataare not avai l ab le , ta bl e 21.4 i s t o be used. Example 21.2 give s the
procedure f or adding QRF t o th e hydrograph or mass curv e of d ir e c t run-
off d erived from rai nf al l .
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TABLE 21.3--CHANNEL-LOSS FhCTGRS FOR REDUCT ION O f DIR EC T RUNOFF
.......................................................................C L I R A T I C IN DE X C I
O R A l N G t :AREA
1.0 0.9 08 0.7 0.6 0.5 0.4 OR
L E S S
SP. MI .
1 OR LESS
2
3.
4.
5.
20.
SO
40.
SO.
60.
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Sable 21 4 Minimum quick return flow f or PSH derived from
r a in fa l l
C i Qm C i RF
in /aax p i n 1 ~
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pa rt s by use of a pprop riate CN and then combined, the channel loss re-
duction i s based on th e ar ea of th e semiarid pl ai n and i t s c l imat i c
index, the hydrograph or mass curve of d ir ec t runoff i s cons tructed ,
and QR from th e mountain a re a i s added.
I f th ere are upstream str uc tur es , th ei r releas es a re always added re-
gardless of the downstream climatic index or other considerations.
Rmoff Volume Maps Proced ure
The runoff volume and r a t e maps, ex hib its 21.1 through 21.5, ar e pro-
vided fo r a rea s of th e United S ta te s where measured runoff volumes vary
significantly from those obtained from the curve number procedure forconvert ing r a in fa l l t o runof f. The mapped areas are of two gener,altyp es: (1 ) the are as where runoff from e it h e r snowmelt, dormant season
r a i n f a l l , or a combination of th e two produce gre at er runoff volumes
than growing season rainfall and ( 2 ) the deep snowpack areas of high
mountain elevations.
AREAS OF bIAPPED RUNOFF VOLUME. The 100-year 10-day runoff volume maps,
ex hi bi ts 21.1 and 21.4, repr ese nt regio nalize d value s derived from
gaged streamflow da ta d sup ple me ntk with clim ato log ica l da ta andlo ca l observat ions . These values should be used for estimating flood-
water deten tion sto rag e within th e map a re a where lo ca l streamflow
data ar e not adequate.
Areal reduction should not be made on the 10-day runoff volumes shown
i n th e maps. Since these -amo unts were derived from stream gage da ta ,
base flow nd channel l os s w i l l be automatical ly included i n the map
val ues and i n Table 21.10.
Quick retur n f low i n th i s procedure i s used as th e ra te of discharge
expected t o pe rs is t beyond th e flood period described under th e 10-dayPSH The r a t e s of d ischa rge, ex hi bi t 21.3, were deriv ed by averaging
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TIM D YS
Figure 21. la uick Return Flow Combined with Principal Spillway
Hydrograph fo r th e Runoff Volume Maps Pro cedure .
such as seasonal pre cip ita t io n range of elev ation aspe ct cover
geology so il s et c. es t imating equations can be developed witha minimum number of independent variables. Unt i l techniques are
developed t o properly analyze the ef fe ct s of a number of va ria bl es
the selection of homogeneous gaged watersheds with as much similarity
t o t he ungaged watersheds as po ssible i s recommended for estimating
volume-duration-probability data. Sta t i s t i c s from volume-durat ion-
pro ba bil i ty s tud ies of gaged watersheds can al so be used t o a s si s t
i n developing est imating equations.
Construction of Principal Spillway Hydrographs and Mass Curves
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rate of flow and then accumulated to form a mass curve, it has theappearance of c m e in figure 21.1. Such a curye is a straightline on log paper and it has the equation:
D Qio ~ ~ / 1 0 1 ~ (21.2)
where QD total runoff at time D in daysQ ~ Qtotal runoff at the end of 10 daysD time in daysa log ( Q ~/ ), in which Q1 is the total runoff at the
end of 1 day
Thus, knowing only the 1- and 10-day runoff amounts, a continuous
mass curve can be developed for the entire lO-day period.
Examination of such mass curves of runoff from streamflow stationsin m ny locations of the United States showed that the exponentvaried from 0.1 to 0.5. Extremes of 0.0458 and 0.699 were chosen forthe standard curves; these extremes correspond to Qi/Qlo ratios of0.9 and 0.2 respectively. The ratio Ql/Qlo is used hereafter in thischapter as a parameter in preference to or Qlo/Ql because Qlo ismore satisfactory as a divisor in preparing PSH and PSMC with dimen-
sionless rates and amounts of flow. Ql/Qlo ratios of 0.2, 0.3, 0.4,0.5, 0.6, 0.7, 0.8 and 0.9 were selected to give representativedegrees of curvature for the runoff curves.
The 10-day on-site runoff for each Qi/Qlo ratio was rearranged as shownin table 21.5to provide a moderately critical distribution of the10-day runoff. This gave a distribution midway between extremes thatare theoretically possible. On figure 21.1, curves A and B show theextremes and c w e shows the rearranged distribution for a Ql/Qlo
ratio of 0.4.
The effects of watershed lag were included by taking increments ofrunoff for each of the eight typical mass curves, making incremental
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Table 21.5.--Arrangement of increments before construction of PSHand PSMC
Time Increment
19th largest 1/2 day17th 11 1
15th ,I I,
13th 11 I t
11thI ? 1
9th I I
I t
7th ,,T i t
5th II 11
3rd t t
9th largest 1/10 day
7th I, 1
5th 11 I
3rd I 11
Largest 1/10 day2nd largest 1/10 day
4th II I
6th It i t
th It 11
10th It 1
4th largest 1/2 day
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which the t ab le i s prepared, ther efor e choose th at se t having a Q i / Q l o
r a t i o and Tc nea res t tho se of the watershed. I t i s eas i e r t o make
t h e choice on t a b l e 21.9, which gi ve s av ai la bl e PSH and PSMC and t h e i rs e r i a l numbers, and then t o look up th e s e r i a l number i n tab le 21.10fo r th e t abu la t ions.
Examples
The proced ure by which a PSH o r PSMC i s developed w i l l b e i l l u s t r a t e d
by fou r examples. I n example 21.1, channel lo ss es ar e taken from
d i r e c t runoff befo re development of a PSH and PSMC; i n example 21.2,
i s added to a PSH and PSMC; i n example 21.3, ru noff volume andra te maps ex hi bit 21.1through 21.5) are used t o obtain runoff ; and
i n example 21.4, upstream r el ea se s a r e added t o a PSH.
Example 21.1.--Develop t h e 50-year fre quency PSB and PSMC f o r a
watershed located a t la t i tude ongitudeThe watershed has a dra inage a re a of 15 .0 square mi le s, time of
conce ntratio n of 7. 1 hours, average annual pr ec ip it at io n of 22.8
in ch es , ave rage annu al temp eratu re of 61.5OF, and a runoff curve
number CN) of 80. There a re no upstream str uc tu re s.
1. Compile the 1 and 10-day po int r a i n f a l l amounts from U.S.
Weather Bureau maps. For t h i s lo ca ti on TP-40 and TP-49 are used.
The 50-year frequency 1 and 10-day amounts ar e 6 8 and 11.0
inches respectively.
2. Determine th e a re al r a i n f a l l . Get th e adjustment fa ct or s from
table 21.1. For the drainage are a of 15.0 square miles they ar e
0.978 and 0.991 f o r th e 1 and 10-day r ai ns res pec tive ly. Thea r e a l r a i n f a l l i s 0.978 6.8) 6.65 inches fo r th e 1-day ra in
and 0.991 11.0) 10.9 inches f o r th e 10-day rain .
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ta b le 21.3 with the drainage area 15.0 square miles and th e C i
of 0.603 and by in ter po lat ion f in d a reduction fa ct or of 0.75.
Multiply Q1 and Qlo of s t ep by the f ac to r t o ge t ne t runof f s
of 3.28 and 4.76 inches res pe cti ve ly. The ne t runoffs w i l l beQ1 and Qlo i n the re s t of t h i s example.
7. Compute th e Q Q O at io . From ste p 6, Q1/Q10 3.28/4.760.689.
8. Find th e PSH and PSMC ta bu la ti on s i n ta b le 21 J.Q . Enterta b le 21.9 with th e ra t i o 0.689 and Tc of 7.1 hours and f ind th a t
t h e PSH with value s nea res t tho se s No. 22. Locate th e appro-
p ri a t e ta bu la ti on s i n t a b le 21.10 by looking up PSH No. 22. Col-umns 1 2, and 4 of ta b l e 21.6 show th e time, r a t e , and mass
tabulat ions taken from table 21.10.
9. Compute PSH disc harg es i n c fs . F i r s t f in d th e product of
drainage area and 810 This i s 15 .0 4 .76) = 71.40 mile2-inches.
Mult iply th e en tr ie s i n column 2, ta bl e 21.6 by 71.40, t o get
th e discharges i n c fs i n column 3.
10. Compute PSMC amounts i n inches. Multip ly t h e en tr ie s i ncolumn 4 table 21.6, by t o get accumulated runoff i n
inches a s shown i n column 5. I f amounts i n acre-fe et or another
un i t a r e des i r ed , conver t Q l o t o th e d esi red u ni t before making
t h e s e r i e s o f m u l t ip l i ca t io n s .
The example s completed with step 10. m e n ex t s t e p i s t h a t of r ou t-
ing th e PSH or PSMC through th e s tru ct ur e; see ch apter 17 fo r rou tin g
methods.
In th e second example t h e s te ps concerning channel lo s s a re omitted
and steps concerning RF are included.
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Table 21.6. PSH nd PSMC f o r example 2l.1
cf sTime PSH Acc ppsm
4 0 4
csmlinch fs inches
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3. Determine t h e CN fo r th e 10-day ra in . The 10-day amount i n
s t e p 1 i s over 6 inches th er ef or e th e 100-year 10-day amount i s
to o, and t a b l e 21.2 may be used. E nt er t h e t a b l e w i th t h e CN of75 for 1 day and f in d th e N i s 58 a t 10 days .
4. ~ 6 t i m a t e h e d i r e c t r u no ff f o r 1 and 10 days. En t e r f i gu re
10 .1 wi th th e r a i nf a l l amounts f rom s tep 2 and th e approp r ia te
N from step 3 and f ind Q1 = 2.94 and Q l o 6.68 inches. Because
the r e a re no channe l l o s ses , t h e d i r ec t runo ff i s t h e ne t runo f f .
5. Compute t h e QlIQlo at io . F rom s tep 4 Q 1 / Q l o 2.9416.68
0.440.
6. Find th e PSH and PSMC ta bu la ti on s i n ta b le 21.10. Ent er t a b l e
21.9 wi th th e ra t i o of 0 .440 and T of 2 .0 hou rs and f i n d t h a t t he
PSH and PSMC wi th v alu es ne ar es t tho se i s No. 3. Locate the
app rop riate ta bu la t i on s i n ta b l e 21.10 by looking up PSH No. 3.
7. Compute PSH dis ch ar ge s i n c f s . F i r s t f in d th e product of
drainage area and Q l o . This i s 8.0 (6.6 8) 53.44 mile2-inches.
Mul t ip ly th e e n t r i es i n t a b l e 21.10 for PSH No. 3 by 53.44 t oget a i scharges i n cfs . These a r e shown i n column 2 , t ab le 21 .7 ,
under t h e head ing of ~ r e l im in a r yPSH becau se t h e f i n a l PSH must
contain QRF.
8. Compute PSMC amounts i n inch es. Mu ltipl y th e en t r i e s i n t a b l e
21.10 f o r PSMC No. by Q l (6 .68 inches) t o get accumulated
runoff i n inches. The r e s u l t s ar e shown i n column 5 t ab le 21 .7 ,
under t h e hea din g Pr eli mi na ry PSMC bec aus e t h e f i n a l PSMC must
con tain accumulated QBF. I f t h e PSMC i s t o be i n a c r e- f ee t o rano the r un i t , conver t 10 t o t h e d e s ir e d u n i t b e f o re making t h e
s e r i e s of m u l t i p l i c a t i o n s .
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21.16
Table 21.7.--PSHand PSM for example 21.2
PrelimPSH
PrelimTime
inary QRF inary Acc.PSMC
PSH PSMC QRF
0
.1
.51.0
2 o
3 0
3.54.04.24.4
4.6
4.74.8
4.95.0
5-15.2
5.35.45.5
5-65.86.o
cfs
0
4860
6978
100118146181
230
259298
3705121992
1039567383302
257
207174154
cf
10
10
10
10
10
10
10101010
10
10
10
10
10
10
10
1010
10
10
1010
cf
10
58
707988
110128
156191240
269308
3805222002
1049
577
393312267
217184164
inches
0
.01
.11-2660
1.001.261.581.721.91
2 132.252.402.603.16
3.844.20
4.42
4.574.69
4.80
4.975 U
inches
0
oo
.02
.04
-09
.14
.16
.18
.I9
.20
.21
-21.22
.22
-22
23-23.24.24
-25
-25.26
-27
inches
0
.01
-13-3069
1.141.421.761.912.11
2.342.462.622.82
3.38
4.074.434.664.81
4.94
5 0055-235.38
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In th e th ir d example the use of the runoff volume maps i s i l l u st ra te d.
Example 21.3--Develop t h e 100-year frequency PSH f o r a wa ter -shed loc ate d a t 43 la t i tu de and 77 longitude. The watershed
has a drainage are a of 12 square mile s, time of conc entra tion of
3.5 hours.
1 Estimate 100-year 10-day runoff volumes from exhibit 21.1.
The inte rpo late d value i s 8.8.
2. Sele ct the Q ~ / Q ~ Oa t i o from exh ibi t 21.2. For th i s a r ea
the value i s 0.4.
3 Ca lcu lat e 1-day volume of ru nof f. Q l / Q l o 0.4 , Q i (0 .4)(8.8 ) 3.52 inch es .
4. Find t h e PSH ta bu la ti on s in Table 21.10. Ente r ta b le 21.9
wi th the Q l / Q l c r a t i o of 0 4 and Tc of 3.5 hours and fi n d t h a t
th e PS Ht i th values nea rest i s No. 11 Locate appropriate tabu-
l a t i o n s i n ta b l e 21.10 by look ing up PSH No. 11
5. Compute PSH di sc ha rg es i n c fs . Find t h e product of dr ain age
area and 4 1 0 This i s (12) (8.8) 105.6 mile2-inches. En tri es
f o r PSH No. 11 are mul t ip l i ed by t h i s va lue t o ob ta in d ischarge
i n c fs . These a re shown i n column 2, t a b l e 21.8.
6. Determine the quic k-ret urn flow ra t e . From ex hi bi t 21.3 t h e
in terpola ted value i s 5.3 csm.
7. Extension of quick-return flow r a t e s beyond t h e PSH Thequick-r eturn f low ra t e i s (1 2 ) 5 . 3 ) 63.6 cf s, round t o 64cfs. This constant ra te of discharge i s an extension to the
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Table 21.8.--PSH for Example 21.3.
Prelim-inary
Time PSH QRF PSH
cf cf cfs
0 0 0
1 61 61
5 116 116
1 0 134 134
2.0 151 151
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2. Flood route the upstream structure releases or outflows to
the lower structure. Chapter 7 discusses flood routing
procedures.
3 Add the routed flows to the preliminary PSB to get the PSHfor the lower structure.
Note that if an upstream structure is itself a lower structure in aseries then the procedure of example 21.4 must be followed for it
first.
Table 21.9. Serial nlahbers of PSH and PSMC
hours
Serial numbers
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Table 21.10.--Time, r a t e and mass tabula t ion s f o r Pr i nci pa l Spi l lway
Iiydrographs PSH) and Mass Curves PSMC)
Tc 1.5 hours
S e r i a l No. 1 2 3
Q ~ Q ~ ~ 0 0.3 0.4 0 05
Time PSH PSMC PSH PSMC PSH PSMC PSH PSK
cfS/AQl0 C ~ S / A Q ~a1 fSIOa1 fs/A OeO
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Table 21 lo. -- Continued)
T 1 5 hours
Serial No. 5 6 7 8
0 6QJQ lo 0 7 0 8 0 9
Time PSH S PSH P S E PSH PSMC PSH PSMC
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Table 21 10. - Continued)
T, ours
Serid No.. 9 10 12
Q o 0 2 0 3 0.4 0 5
Time PSH PSM PSH PSM PSH PSMC PSH P S E
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Table 21LO -- continued)
Tc hours
Serial No 3 4 5 6
~ ~ 1 ~0.6 0.7 0.8 0 9
Time PSH PSW PSH PSMC PSH PSMC PSH PSMC
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U.24
Table 2 l LO. -- continued)
T 6 hours
S er i a l No. 1 7 1 8 1 9 20
Q ~ / Q ~ o 0 2 Oe3 0.4 0 5
Time PSH PSMC PSH PSMC PSH PEW PSH PSK
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Table 21 lo -- continued)
c 6hours
Serial No. 2 23 24
Q I / Q ~ ~ o .6 0 7 0.8 0.9
Time PSH PSMC PSH P SW PSH PSMC PSH PSMC
days
0
2
.51 0
2 0
3.0
3 h4.0
4034.6
4.8
4.9
500
5.1
5.2
593
5 45.5
5.6
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21 26
Table 21 10 -- continued)
hours
S e r i a l No 5 6 8
Time PSE PSMC PSH PSH PSB PSMC
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Table 2 lo -- continued)
T 1 2 hours
S e r i d No. 29 30 31 32
Q ~ / Q ~ ~0 6 0.7 0 8 0.9
T i m e PSH PSI42 PSH PSMC PSH PSW PSH PSMC
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Table 21.lo. -- Continued)
i?,18 hours
Serial NO 33 4 35 36
/Bl0 0 2 0 3 0.4 0 5
Time PSR PSMC PSH PSMC PSH PSW PSH PSMC
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Table 21.10. --(continued
T = 18 hours
Serial NO 37 38 39 40
Q ~ / Q ~ 0.6 0.7 0.8 0.9
ime PSH PSM PSH PSK PSH PSK PSH PSM
c f s / ~ , ~ l fs/AQIO a1 &lo cfs/A o L ~
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Table 21.lo.-- continued)
T, 24 hours
S e r i a l No 4 42 43 44Q ~ Q ~ ~0 2 0 3 0 4 0 5
Time PSH PSW PSH PS E PSH PS E PSH PSM
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Table 21 10 -- continued)
Tc 4 ours
S e r i a l No. 45 6 7 48
Q l / ~ l o 0 6 0 7 0 8 0 9
Time PSH PSMC PSH PSMC PSH PSMC PSH PSbC
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2l.32
Table 21.10a--(Continued)
Tc= 30 hours
Serial No. : 4g
Ql/Qlo50
: 0.2 0*3 51.4 52.5
Time PSH PSI.c PSH PSE PSH PSIE PSH PEW
e. Q/Q-~ -/AQlo Q&o dAQ,o so cf4AQ1.o%o
0
A50.Y55
1.6%l.y55
0
.OOO?
.0103a0407.0747
2.252 .15272-574 -24162.99 .30223.228 -3363
3.579 .3614
3.8%4.124404384.7244.935
5.052
K84:845
0
-0005.0077.0306.0568
0 0
-538 .0057,998 .0233
1.195 .0437
0 0
*067 .0003.425 .0046.764 *0181.937 .Q339
.1201
.lY55-2528.2865
-3133
.32P
.3474
.3682
.m6e4171
.0932
.1567
.2068
:g
1.229 -0738~6% .12632.274 SW322339 .1975
4.249 .2232
.2823
.3032
:gE.3913
5.520
kgi10.535U.666
.2412
.2645443.3299.3708
.444G Y-779 .4266 12.218 .4148
04713 9.730 .4626 12.098 .4597.4982 9a348 .W8 n-502 .5032.5241 8e761 .5312 10.630 .544c
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Table 21.lo. -- continued)
T3 hours
Serial NO. 5 54 55 56
QI/Q~O 0 6 0.7 0.8 0.9
Time PSH PSMC PSH PSMC PSH Pix PSH PSMC
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Table 21.LO. --(Continued)
T, 36 hours
S e r i d No 57 58 59 6
Q O 0 2 3 Oak 0 5
Time PSH P a PSH PSm PSH PSM PSH PSW
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Table 21 . lo. --(continued)
T 36 hours
S e r i a l No. 61 62 63 64
Ql/Q- o 0.6 0.7 0.8 0.9
Time PSH PSMC PSH PSMC PSR PSMC PSH PSW
C ~ ~ / A Q ~ f ~ / ~ ~10fs/A5iOU1 a1
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Table 21 10.- continued)
T, 42 hours
erial NO 65 66 67 68
Ql/Ql0 0.2 0.3 0.4 0 5
Time PSH PSMC PSR PSMC PSH PSMC PSH P S K
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Table 21 10 -- continued)
T, 4 ours
Serial No. 69 70 7 72
Q1/Ql0 0 6 0 7 0 8 0 9
Time PSH P SE PSH P S E PSH P S E PSH PSE
21.38
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Table 21.lo.--(continued)
T 8 hours
S e r i a l No. 7374 75 76
Q 0.2 0.3 o 4 0 5
Time PSH PSW PSH PSM PSH PSbE PSH PSW
s.ZL%10 a 1 0 *lo Ql0 cfs/A 30 L5L fs/A 30 &30ays
0
.61.32 0
3 0
4 o
4.8
5.0
5-2
5.4
5.5
5.6
5.7
5.8
5.9
6 o
6 l6.26.3
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Table 2120 - Continued)
T, 48 hours
Serial NO 77 78 79 aQl/Qlo 6 0 7 0 8 0 9
Time PSH PSMC PSH PSMC PSB PSKC PSH PSKC
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Table 21 lo -- continued)
T 5 ours
Serial NO 81 82 83 84
Q ~ / Q ~ o 0 2 0 3 0 4 - 5
Time PSH PSMC PSH PSMC PSH PSMC PSH PSM2
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Table 21 -10. -- continued)
T 54 hours
S e r i a l No 85 86 87 88Q1 Q1o 0.6 0.7 0.8 0.9
Time PSH PSMC PSH PSMC PSH P S E PSH PSMC
21 42
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Table 21 10 -- continued)
T = 6 hours
Serial No. 89 91
Ql/Q l~0 2 0 3 0 4 0 5
Time PSH PSMC PSH PSM: PSH PSM: PSH PSMC
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Table 2 .lo. -- Continued)
T = 6 ours
Serial No 93 94 9
Q 0.6 0.7 0.8 0.9
Time PSH PSMC PSH PSMC PSH PSK PSH PSMC
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Table 21.lo.-- Continued)
T = 66 ours
d ys
0
.61.32.0
3.0
4.04.8
5.05.25.4
5.65.86.06.26.4
6.56.6
6*76.8
7 0
Serial NO 97 98 99 100
9/Q10 0.2 0.3 0.4 0.5
Time PSH PSM PSH PSM PSH PSM PSH PSMC
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Table 21.10. -- continued)
c 66 hours
Serial No 101 102 103 104
Q ~ / Q ~ ~0.6 0.7 0.8 0.9
Time PSH PSMC PSH PSE PSH PSI42 PSH PSMC
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Table 21.10.-- continued)
Serial No 105 106 107 108
Ql/ O 0.2 0.3 0.4 0 5
Time PSH PSMC PSH PSMC PSH Psi PSH PSMC
days cfs/AQ10 a1 fs/AQlo
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Table 21.10. -- continued)
T 72 hours
S e r i a l No. 109 l l 0 112
Q1/~ 0-6 0.7 0.8 0.9
Time PSH PSMC PSH PSMC PSH PSMC PSH PSMC
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R A T ~ O S OR 50 AND 26 -YEAR 10 -DAY RUNO FF VOLUMES
TO ob ta in : M u l l i ~ l y p values b y .
~ r e a A re a 2 A re aW-Y EA R IO-DAY RUN OFF 0.85 0.90 0.92
25-YEAR 10-DAY RUNO FF 0 70 0.80 0.85
JANUARY 1971. REV. APR iL 1976
F IGU R E 2 1 A )
100-YEAR. 10-DAY RUNOFF INCHE S)
PR IN C IPAL SPILLWAY H YD R OGR AP H
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L E GE N D
Q1 1-Day Volume Runoff
Il0. 10-Day Volume Runo f f
FIG URE 2 1 El)
R TIOS OF VOLUMES OF RUNOFF Ql/Q1,,)
P RINCIP A L S P IL L WA Y HY DRO G RA P H
-NUARY 1971. R E V . A P R I L 1 9 76
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.ANUARY 1971 REV APRIL 1976 P RINCIP AL S P ILLWAY HYDROGRAP H SNOWMELT PRODU CI NG FLOOD ARE AS
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Emergency Spillways L/
Flows larger than those completely controllable by the principal spillwayand retarding storage are safely conveyed past an earth dam by n emer-
gency spillway.The emergency spillway is designed by use of an Emergency
Spillway Eydrograph (ESH) and its mi n i m freeboard determined by use ofa Freeboard Hydrograph (FH). Both kinds of hydrographs are constructedby the same procedure. There is a small difference in that procedure de
periding on whether a watershed's time of concentration is or is not oversix hours.
This part of the chapter presents a manual method of developing ESH andFH. The method requires the use of the dimensionless hydrographs given intable 21.17. Methods of routing the ESH or FH through structures are givenin chapter 17.
Alternatives to developing and routihg the hydrographs manually are i)
use of the SCS electronic computer program, in which basic data are inputand the ESH or FH, the routed hydrograph, and reservoir elevations are out-put; and (ii) the Upper Darby or U method, in which no hydrograph is neededbut which uses the hydrograph characteristics of ESH or FH in an indirectrouting procedure with results in terms of spillway elevation and capacity.
The hydrologic criteria given below apply to the manual method and its al-ternatives. The examples that follow apply only to the manual method.
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ES -1020, 5 sheets. 48 contiguous States. Supplementary sheetsfor California and Washington-Oregon are also given.
ES-1021, 5 sheets. Hawaii.
ES-1022, 5 sheets. Alaska.
ES-1023, 5 sheets. Puerto Rico.
ES-1024, sheets. Virgin Islands.
The rainfall amounts on these maps are minimums allowed by SCS criteria for
various classes of structures.
DURATION DJUSTMEW OF RAINFALL AMOUNT. If the time of concentration ofthe drainage area above a structure is more than six hours, the durationof the design storm is made equal to that time and the rainfall amount isincreased using a factor from figure 2.2, part (c).
AREPL ADJUS lNEWt OF R INF LL AMOUNT. If the drainage area above a struc-ture is 10 square miles or less, the areal rainfall is the same as the rain-fall taken from the maps of ES-1020 through 1024. If the area is over 10
square miles but not over 100 square miles, the areal rainfall is obtainedby use of a factor from figure 21.2, part (a). If the area is over 100square miles, the adjustment factor for the area is requested from the En-
gineering Division, Washington, D. C. When a request is submitted the
following info-%ion about the area should also be submitted: (lj location,
preferably the latitude and longitude of the watershed outlet; 2) size in
square miles; 3 ) length in miles, following the main valley; 4)time ofconcentration in hours; (5) runoff curve number; 6) proposed value of theadjustment or adjustment factor. If a factor is also needed for a subwater-
shed of that watershed, then similar information about the subwatershed shouldalso be submitted.
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the second when i t i s . There i s no dif fer en ce i n procedure f o r ESR and FH.
Equations used i n the examples ar e li s t e d i n tab le 21.11.
Example 2l.5.--Construct an ESH f o r a c la ss (b) s tr uc tu re wi th a dra in-age area of 1.86 square miles , time of c onc ent rati on of 1.25 hours,
CN of 8 2, and l o c a ti o n a t l a t i t u d e , longitude-.
1 Determine th e 6-hour design storm r a i n f a l l amount, P. Fo r th i s
st ru ct ur e c lass t he ESH ra in fa ll amount i s take n from ES-1020, sh ee t
2 of 5. For th e given lo ca ti on t he map shows t h a t P 9.4 inches.
2 . Determine the ar ea l ra in fa l l amount. The ar ea l ra in fa l l i s t h e
same as i n s tep1
because th e drainage area i s not over 10 square miles.Step 2 of example 21.6 shows th e pr oc es s.
3. M e h e d u ra t io n ad ju stment o f r a i n f a l l amount. No ad justme nt i s
made because th e time of co nc en tra tio n i s not over s ix hours. Step 3of example a 6 shows the process.
4. Determine th e -off amount, Q. Enter f ig ure 10 .1 wi th P 9.4
inches and CN 82 and find Q 7.21 inches.
5 Determine th e hydrograph family. Enter fi g ur e 21.3 (ES-1011) withCN 82 and a t P 9.4 read hydrograph family 2.
6. Determine the dur ation of excess ra in fa ll , To. Enter figure 21.4
(Es-1012) with P 9.4 inches and a t CN 82 read by in terp o la t ion
t h a t To 5.37 h o y s .
7 . Compute the i n i t i a l value of Tp. By equation 21.4 t h i s i s O.T(l.25)
0.88 hours.
8. c o m p u t e d % a t io . Th i s i s 5.37/0.88 6.10.
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Table 2l.U--Equations used in construction of ESH and FE
Equation No.
Rev. Tp To
I W T p rev
sp484 A
Rev. Tp
where A drainage area in square miles
q hydrograph rate in cfs
9c hydrograph rate in cfs when Q inch
9p hydrograph peak rate in cfs when nch
Q design storm runoff in inches
Rev. Tp revised time to peak in hours
t time in hours at which hydrograph rate is computed
Tc time of concentration in hours
To duration of excess rainfall in hours
To/Tp)rev. revised ratio from table 21 16
Tptime to peak in hours for TU design hydrographs
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14. Compute the hydrograph rates. Use equation 21.8 and the qc/qp
column of th e sel ec te d hydrograph in t a b le 21.17. The computed
r a t e s a r e shown i n column 3 of t a b l e 21.12.
The hydrograph i s completed w ith s te p 14 Bow th e hydrograph i s furtherr e t d ~ U h t e d r plot ted f or routing through the spil lway depends on the
rout ing method t o be used. See chapter 17 fo r routing de ta il s.
The mass curve for the hydrograph can be obtained using the Q t / ~ column
of t he se lec ted hydrograph i n ta bl e 21.17. Ratios i n th a t column ar e
mult ipl ied by the Q of s tep 4 t o give accumulated runoff i n inches a t th e
time computed i n s te p 13. For accumulated runoff i n acre -fee t or another
unit , convert Q t o th e desired un it before making the s er ie s of m ult i pl i-
ca t ions .
In the following example th e storm duratio n i s increased because the time
of concentrat ion i s over six hours. Increasing the durat ion als o requires
increas ing the ra in fa l l amount bu t i f the d ra inage area i s over 10 square
miles the increase i s p a r t l y o f f se t b y th e decrease i n a r ea l r a in f a l l .
Example 21.6.- -Con struc t a FH fo r a c lass ( c ) s t ru c tur e wi th a d ra in -age a re a of 23.0 s quare mil es, time of c onc ent rat ion of 10.8 hours,
N of 77, and lo ca ti on a t latitude-, longitude-.
1 Determine t h e 6-hour design storm r a i n f a l l amount, P For th is
s t r u c t u r e c l a s s t h e K ra in fa l l amount i s taken from ES-1020, shee t
5 of 5 For t he given lo ca ti on t he map shows th at P 25.5 inches.
2 Determine th e ar e al r a i n f a l l amount. Use the approp riate curve
on f i g u r e 2l.2.a (Es-1003-a). For t h i s loc at io n th e Humid and sub-humid climate curve app lie s and the adjustment fac tor f o r the drain -
age ar ea of 23.0 square miles i s 0.93. The adjust ed ra in fa ll i s
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SCS EIIG 319
Rev. 1 70
File Code ENG 13 14
DATE
OMPUTED BY--YDROGRAPH COMPUTATION CHECKED BY
WATERSHED OR PROJECT zMmm z *)
STATE
STRUCTURE SIT OR SUBAREA
OR. AREA A36 SQ MI. STRUCTURE CLASS^
LZ HR. STOW U R A T I O N R.
POINT RAINFALL N.
ADJUSTED RAINFALL.
AREAL : FACTOR
DURATION: FACTOR
RUNOFFCURVE NO. B
HYDROGRAPH FAMILY NO. 2
7. Compute the i n i t i a l value of Tp.o.T(l0.8) 7.56 hours.
By equation 21.4 t h i s i s
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8. Compute the TO/ a t i o . This i s 10.26/7.56 = 1.357.
9. Select a revised T,/T r a t i o from ta bl e 21.16. Enter ta b le 21.16with the ratio from step and select the tabulated ratio nearest it
For t h i s example t he s el ec te d r a t i o , ( ~ ~ / T ~ ) r e v . ,s 1.5.
10. Compute Rev. Tp.i n r a ti o . By equation
This
21.5,
i s a revised Tp usedRev. Tp 10.26/1.5
because of the= 6.84 hours.
change
ll Compute a By equation 21.6 t is i s 484(23.0)/6.84 1627.5cf s. Round to 1628 cf s.
2 Compute Qq Usin@vesw2t: 7 (16287
the Q from step 440,W.6 cfs .
and th e q fromRound to , a 2
s tepcfs .
13. Compute the times for which hydrograph rates w l l be computed.Use equation 21.7 with the Rev. Tp from s tep 10 and th e e nt rie s in
the t /Tp column of the sele ct ed hydrograph i n t ab le 21.17. The com-
puted ra te s ar e shown i n column of t ab le a 13
14. Compute th e hydrograph ra te s . Use equation a . 8 with Qqp of st ep
12 and the qc/q column of th e se le ct ed hydrograph i n Mole 21.17.The computed r a fes a re shown in coLumn 3 of t ab le 21.13.
,;.1-70
l e Code ENG-13-14
DATE
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YDROGRAPH COMPUTATION COMPUTED BYHECKED BY
Q =IP /QR
WATERSHED OR PROJECT E x ~ f l P L E L 6
STATEP
STRUCTURE SITE OR SUBAREA
DR. AREA 23.0 SQ. MI. STRUCTU RECL SSC
TcHR. STORM DURATION
POINT RAINFALL 2 5 5 IN.
ADJUSTED RAINFALL:
AREAL : FACTOR
DURATION: FACTOR
RUNOFF CURVE NO. 77
Q Z 7 IN.
HYDROGRAPH FAMILY NO.
CDMPUTEDTp .56 HR.
To 10.26 HR.
Table 21.14.--Rainfall prior to excess rainfall.
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inches) inches) inches) inches) inches)
Table 21.15.--Wnfall and time ratios for determining To when the stormduration is greater than 6 hours.
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Rain- Time Rain- Time Rain- Time Rain- Timefall ratio fall ratio fall ratio fall ratio
ratio ratio ratio ratio
Change intabulation
increment.
Table 21.16. Hydrograph families and T o / ~ p atios for which dimensionless hydrograph ratios are given in table 21 17
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Asterisks signify that dimensionless hydrograph tabulations are given
in table 21.17.
Table 21 17 --Time discharge and accmmlated runoff ratios
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Line t/Tp qc/qpNo.
for dimensionless hydrographs
Hydrograph Family 1
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Table 21.17 continued)
Line
No.
5
6
78
910
12
131 4
1 5
16
1 718
1 920
Eydrograph Family
T / T ~ 4 To/TP 6
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Table 2l. .17 continued)
No.
2
3
45
6
789
10
ll12
1 314
15
16
171 8
1 9X
Hydrograph Family
1.22
2.44
3.664.88
6 .lo
7 728.54
9 76lo . 98
12 2013.4214.64
1517.08
18.30
19 5220.74
u 9623.18
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Table 21 17 Continued)
To/Tp 6
Line t/Tp qc/qp Q ~ / QNo.
Hydrograph Family 1
Table 21 17 continued)
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T ~ T ~1
Line t T p qc/qp Q ~ QNo.
Hydrograph amily 2
To/Tp 1.5
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Table 21.17 continued)
/TI, 3
Line t / ~ ~
No
1
2
3
45
678910
1112
1314
15
16
1718
1920
Eydrograph Family
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Table 21.17 con tinu ed) Hydrograph Family
Line t / ~ ~c/qp t / ~ p qc/qp t/
No
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Table 2l 17 (continued) Hydrograph Family 2
To/Tp 36 To/ 5 To/Tp 75
21.68
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Table 21.17 continued)
Line
No.
4
6
78
910
ll
121314
15
16718
1920
Hydrograph Family 3
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Table 21.17 continued)
TO/rp 3
Line t / ~ ~No
1 02 343 .684 1 02
5 1.36
6 1.707 2.048 2.389 2-7210 3.06
11 3.4012 3.7413 4.0814 4.4215 4.76
16 5.1017 5 4418 5.78
19 6.12X 6.46
Hydrograph Family 3
u.70
Table 21.17 ~ontinued) Hydrograph Family 3
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LineNo
1
2
345
6
7
910
U
12
1314
15
16
1718
19
20
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Table 21 17 Continued)
Line t/Tp qc qpNo.
Hydrograph Family 3
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Table 21 17 Continued)
LineNo.
1
4
6
78
910
ll
12
13
14
15
1617
iiydrograph Family
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Table 2 l 7 continued) Hydrograph Family
u.74
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Table 21.17 continued) EIydrograph amily 4
Line t ~ ~
No.
1 0
2 .50
3 1.00
4 1.505 2.00
6 2.50
7 3.00
8 3 504.00
10 4.50
ll 5.0012 5.50
13 6.00
14 6.50
115 7.00
6 7.50
17 8.00
8 8.50
19 9.002 9.50
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Table 21.17 continu ed)
Hydrograph amily
Line t / T p qc/qp
No
Hydrograph amily
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Table 2 l 7 continued) Hydrograph Family
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Table 21 17 continued) Hydrograph Family 5
Line t/Tp
No
1 0
2 363 -724 1.085 1.44
6 1.807 2.16
8 2.52g 2.8810 3.24
3 60
1 2 3.9613 4.3214 4.6815 5.04
16 5.40
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Table 21.17 continued) Hydrograph Family
Line t/Tp q p Q ~ / QNo.
Table 21 17 concluded) Hydrograph Family 5
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Line t/TP qc/qP Q ~ / QNo.
TO/T, 5
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21.81-HYDROLOGY: CRITERIA FOR DESIGN STORMS USED IN DEVELOPING
EMERGENCY SPILLWAY DESIGN AND FREEBOARD HYDROGRAPHS
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DRAINAGE AREA HI SOUARE MILES
1) RAINFALL RATIOS FOR DRAINAGE AREAS OF10 TO 100 SQUARE MILES
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.
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T L N T I o C E N
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T L T I C C E
INCHES) W R DEVELOPING THE FREEWARD HYDROGRAPH f R CLASS l l STRUPURES
6s 30
T L T I C C E
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P _ _ __. .. . .
ES 1 23 Sheet di 5
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MIN IMU M SIX.HOUR PRfCIPITAl ION l incherl for de r e l op fnp lh. FREEeOARD HYDROGRAPH or
CLASS 1 1 STRUCTURES or Ih. EMERGENCY SPILLWAY HYDROGRAPH or CLASS b) STRUCTURES
..05
rC A R B B E A N S E A
I 105 I U S SOIL CONSERVATIO N SERVICE JUNE 1V6I
V S 64-d Bl S 6V.0 61.35 6 7
ES 1 24
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AS ISLAND
SK JOHN ISLAND
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SIX.HOUR PRECIQIIAIION linrh.sJ for d.r.lopinp the fREElOARD HYDROGnArH lo CLASS d SIRUCIURES
Frob. - ax 6-hour Pdp:n tlm ron U.S.W.B. I Pr q