Runoff Calculation Manually

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A Method for EstimatingVolume andRate of Runoff in Small Watersheds

U.S. DEPARTMENT F AGRICULTURESOIL CONSERVATION ERVICE SCS-TP-149Revised April 1973


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ABSTRACTThe Soil Conservation Service (SCS) has developed charts ES-1026 and ES-1027 for estimating theinstantaneous peak discharge expected from small areas. They provide the peak discharge rate forestablishing conservation practices on individual farms and ranches and for the design of water-control measures in small watersheds. The graphs were prepared from computations made by automaticdata processing (ADP). Each graph relates peak discharge to drainage area and rainfall depths foreach of (1) a given set of watershed characteristics, (2) different rainfall time distributions and

(3) three categories of average watershed slopes. Peak discharges range from 5 to 2,000 cubic feetper second (cfs), drainage areas range from 5 to 2,000 acres, and 24-hour rainfall depths range from1 to 12 inches. Curve numbers (CN) are used to represent watershed characteristics that influencerunoff. Each chart represents one of seven curve numbers ranging from 60 to 90 in increments of 5.Each group of seven charts represents one of the three average watershed slope factors (FLAT, MODER-ATE, and STEEP) making a total of 21 charts for each of two rainfall time distributions. The pro-cedures for computation of peak discharges by ADP were based upon those in the SCS National Engi-neering Handbook, Section 4, Hydrology, August 1972. The logic and procedures used for the ADPcomputation are described.

CONTENTS PageIntroduction .................................Stormrainfall ................................Rainfall-runoff equation ...........................Watershed lag and time of concentration ...................Watershed shape factor ...........................Use of curve numbers to reflect overland retardance ............Average watershed slope ..........................Interpolation for intermediate slopes ...................Triangular hydrograph equation ........................Incremental hydrographs. ...........................Basic procedure for estimating peak discharge without developing a hydrographEquations and assumptions used in computer solutions for ES-1026 and ES-1027 .Storm rainfall ...............................Rainfall-runoff equations .........................Watershed lag ...............................Period of runoff affecting peak discharge .................Incremental peak discharge .........................Combined peak discharge ..........................Literature cited ...............................Appendix ...................................

....... 1....... 1

....... 4....... 7....... 8....... 8....... 11....... 11....... 11....... 12....... 12....... 17....... 17....... 17....... 17....... 17....... 17....... 18....... 19....... 20


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A Method for Estimating Volume andRate of Runoff in Small Watersheds

K. M. Kent (retired), Chief,.Hydro logy Branch,Soil Conservation Service

INTRODUCTIONVen Te Chow has described many methods which

have been used for determining waterway areasand the design of drainage control structures insmall watersheds (I), Some of these methodshave been used by the Soil Conservation Service(SCS) for estimating peak discharge rates.These include the rational method (Ramser curvesafter C. E. Ramser), the Cook method after H. L.Cook, the modified Cook or CW method by M. M.Culp and others, and the methoa by Victor Mockusand others described in the National EngineeringHandbook, Section 4, Hydrology (NEH-4) an in-service handbook of SCS (7). SCS has used thesemethods primarily for the-design of measures forindividual farms and ranches.The NEW-4 method provides for the developmentof a complete hydrograph and involves more de-tailed computations than the others. It is usedprimarily for planning and designing largermeasures--larger than those for farms andranches--in watersheds planned under the Water-shed Protection and Flood Prevention Act (PublicLaw 566, 83d Cong.; Stat. 666), as amended.Using different methods under similar condi-tions SCS, obtained wide differences in the peakrates. These differences were mainly due to thechoice of coefficients and factors inherent ineach method rather than to the method itself.The method adopted by SCS is shown in charts~~-1026 and ~~-1027 (appendix). Guidelines havebeen established for selecting nationally appli-cable values for this method's parameters. Thisset of parameters is expected to provide ade-quate and more uniform estimates of peak dis-charges between areas having similar watershedcharacteristics.A primary requirement was that the method besimple enough to be used by all grades of pro-fessional and subprofessiona l personnel inscs. They all need to make quick, on-the-spotestimates of peak discharge rates fo r planningand designing soil and water conservation mea-sures.It is further desirable for the method to beclosely allied with those in NEH-4. The peakdischarge for a small watershed with unusualcharacteristics can then be computed using themore detailed procedures in NEH-4 but with thesame parameters. Specific values are computedfor each parameter in contrast to the averagevalues used in the charts.The method described here is generally limitedto drainage areas of 2,000 acres or less and towatersheds that have average slopes of less than

30 percent. The NEH-4 method is generally usedfor-watersheds exceeding these limits or whenthe computed peak discharge exceeds 2,000 cfs.There are other circumstances where the methoddescribed here may not provide adequate esti-mates and the NEH-4 method should be used.These are described later under pertinentheadings.

STORM RAINFALLStream-gage measurements are rarely availablefor small watersheds . Generalized rainfall data,however, are available nationally. Therefore itis desirable that the national SCS method forcomputing peak discharge rates and runoff vol-umes in small areas use rainfall for their basic

input.The Weather Bureau's Rainfall-FrequencyAtlases covering the United States, Puerto Rico,and the Virgin Islands provide rainfall-frequen-cy data for areas less than 400 square miles,for durations to 24 hours, and for frequenciesfrom 1 to 100 years (5, 8; 9, 10, 11).-Adjustment of rainfall wiX7ZS$?Z-to area isnot necessary in the method described becausethe drainage areas are small. But the distribu-tion of storm rainfall with respect to tme isan important parameter. Two major regions wereidentified for this purpose. Time distributionsfor each are tabulated in table 1 and shown infigure 1. Qpe I represents regions with a mari-time climate. Type II represents regions in whichthe high rates of runoff from small areas areusually generated from summer thunderstorms.The type I and type II distributions are basedon generalized rainfall depth-dura tion relation-ships obta ined from Weather Bureau technicalpapers. The accumulative graphs in figure 2,which are the basis for type I and II distribu-tions, were established by (1) plotting a ratioof rainfall amount for any duration to the 24-hour amount against duration for a number of lo-cations and (2) selecting a curve of best fit.Selected curves a re shown as dashed lines infigure 2. Note that the type II distribution(fig. 2) underestimates the l-hour duration byabout 0.6 inch at Lincoln, Nebr., overestimatesit by about 0.5 inch at Mobile, Ala., and iswithin 0.1 inch on the northwest corner of Utah.The type I distribution underestimates the &hourduration by about 1 inch at Kahuka Point,Oahu, Hawaii. These variations are within theaccuracy of rainfall amounts read from theWeather Bureau references.


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TIME IN HOURS14 15 I6 17 IR 19 70 71 22-T-T

f1.0

Type 1 - Hawaii, coastal side of Sierra Nevada in southern::1 : :

: .:i:/_. ..,i. .,. .,. j_


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Table l.--Accumulation of rainfall to 24 hours

0 0 02.0 ,035 .0224.0 .076 .048 I- I I7 I I A/ /6.0 .125 ,080 ,2: .194156 -----120a.5 .219 -----9.0 .254 .1479.5 .303 .1.639.75 .362 -----10.0 .515 .18110.5 .583 .20411.0 .624 .23511.5 .654 .28311.75 ----- .38712.0 .682 .66312.5 ----- .735 OL I I13.0 .727 .772 1 2 3 6 !* -4

13.5 ----- a79914.0 .767 .820 DURATION (HOURS)16.0 .830 .88020.0 .926 .95224.0 1.000 1.000

Time Px/P21$(hours)Type 1 Tree II

.L/ Ratio accumulated rainfallto total.Average intensity-duration values used to de-velop the dashed lines in figure 2 are rear-ranged to form the type I and II distributionsin figure 1. The type I distribution is arrangedso that the greatest 30-minute depth occurs atabout the IO-hour point of the 24-hour period,

the second largest in the next 30 minutes, andthe third largest in the preceeding 30 minutes.This alternation continues with each decreasingorder of magnitude until the smallest incrementsfall at the beginning and end of the 24-hourrainfall (fig. 1). The type II distribution isarranged in a similar manner but the greatest30-minute depth occurs near the middle of the24-hour period. The selection of the period ofmaximum intensity for both distributions wasbased on design consideration rather than mete-orological factors.The effective storm period that contributes toan instantaneous peak rate of discharge varieswith the time of concentration (T,) of each 2 3 6 12 21small watershed. It is only a few minutes for avery short T, and up to 24 hours for a long T,. DURATION ( HOURS 1The effective period for most watersheds smallerthan 2,000 acres is less than 6 hours. Becauseof the "built-in" range of 30-minute intensities Figure 2 .--Generalized 25-year frequency rainfallthe 24-hour duration is equally appropriate for depth-duration relationships (U.S. Weathera 5-acre watershed with less than a 30-minute Bureau Rainfall Atlases).

3


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effective storm period as it is for a 2,OOOAacrewatershed where the effective periods may takeup the entire 24 hours.

RAINFALL-RUNOFF EQUATIONThe runoff equation used by SCS was developedby Victor Mockus and others about 1947(1, 2, I).A relationship between accumulated rainfall andaccumulated runoff was derived from experimentalplots for numerous soils and vegetative cover

conditions. Data for land-treatment measures,such as contouring and terracing, from experi-mental watersheds were included. The equationwas developed mainly for small watersheds forwhich only daily rainfall and watershed data areordinarily available. It was developed fromrecorded storm data that included total amountof rainfall in a calendar day but not its dis-tribution with respect to time. The SCS runoffequation is therefore a method of estimatingdirect runoff from storm rainfall of-1 dayor less.The equation

Where :& =P =

I, =

s =

accumulated direct runoff.accumulated rainfall (potentialmaximum runoff).initial abstraction includingsurface storage, interception, andinfiltration prior to runoff.potential maximum retention.

The inset in figure 3 shows the initialabstraction (I,) in a typical storm. The rela-tionship between I, and S was developed fromexperimental watershed data. It removes thenecessity for estimating I, for common usage.The empirical relationship used in the SCS run-off equation is:Ia = 0.2s (2)

Substituting 0.2s for I, in equation (l), theequation follows:& = (P - 0.2s)ZP + 0.8s (3)

To show the rainfall-runoff relationshipgraphically, S values are transformed into curve

numbers (CN) by the following equation (fig. 3):1000CN = 10 + s

The S values for CN's ranging from 0 to 100are tabulated in NEH-4, table 10.1. Researchdata provided the association of CN's with var-ious hydrologic soil-cover complexes as shown intable 2 for an average antecedent moisture con-dition. Soils are divided into four hydrologicsoil groups: A, B, C, and D. Group A soilshave a high infiltration rate even whenthoroughly wet. When thoroughly wet, group %soils have a moderate infiltration rate,group C soils a slow infiltration rate, andgroup D soils a very slow infiltration rate.Table 7.1 of NEH-4 lists more than 9,000 soilsand their hydrologic group.The rainfall-runoff chart (fig. 3) is usedmostly for estimating the runoff from watershedsfor which composite CN's are obtained fromlistings like those in table 2. The curves canin turn be used to estimate a composite CN foran unlisted watershed characteristic with rain-fall and runoff data for only a few years. Therainfall-runoff values for each storm in theshort period can be plotted on a facsimile offigure 3. The curve in figure 3 equally divid-ing the plotted points can be assumed to repre-sent the runoff CN for an average antecedentmoisture condition in the watershed. Theplotted points are usually widely sca ttered,representing a change in the value of S in equa-tion (3) and hence a corresponding change in CNfrom one storm to the next. Most of this dif-ference is the result of variations in soilmoisture preceding each storm. Mockus based theantecedent moisture condition (AMC) on the totalrainfall in the 5-day period preceding a stormand divided the AMC into three conditions (table3).Figure 4 demonstrates how the plotted pointsusually fall between the CN's representing AMCI and AMC III with AMC II equally dividingthem. This capability is an advantage toengineers working in foreign countries where,without experimental data on watershed charac-teristics unique to the local area, a minimumamount of measured data may suffice to establishCN's adequate for the design of small structures.Changes in plant cover between seasons alongwith changes in land use from year to year canalso affect the degree of scatter of plotted Pand Q points. Furthermore, if rain gages arenot spaced close enough to measure watershedprecipitation accurately, this will causeunrealistic scat.ter in the P and Q plotting.

The peak discharge computations in ~~-1026 andES-1027 are based on AMC-II.

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RAINFALL (PI IN INCHES

(P - 0.2s)ZFigure 3.--Solution of the runoff equation, Q = P + o 8s


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Table 2 .--Runoff curve numbers for hydrologic soil-cover complexes(Antecedent moisture condition II, and I, = 0.2 S)

Land use and treatment Hydrologic Hydrologic soil grouporpractice condition A B C DFallowStraight row ............Row cropsStraight row ............Straight row ............Contoured ...............Contoured ...............Contoured and terraced . .Contoured and terraced . .Small grainStraight row ............

Straight row ............Contoured ...............Contoured ...............Contoured and terraced . .Contoured and terraced . .Close-seeded legumes orrotation meadowStraight row ............Straight row ............Contoured ...............Contoured ...............Contoured and terraced . .Contoured and terraced . .Pasture or rangeNo mechanical treatmentNo mechanical treatmentNo mechanical treatmentContoured ...............Contoured ...............Contoured ...............Meadow ............. ..> ......Woods .......................

Farmst 7ads ..................Road&Dirt ....................Hard surface ............

---- 77 6 91 94Poor 72 81 88 91Good 67 78 85 89Poor 70 79 84 88Good 65 75 82 86Poor 66 74 80 82Good 62 71. 78 81PoorGoodPoorGoodPoorGood

656326159

76;;73727084 8883 8782 8581 8479 8278 81

PoorGoodPoorGoodPoorGood

77 85 8972 81 8575 83 8569 78 8373 80 8367 76 80

PoorFairGoodPoorFairGoodGoodPoorFairGood----

6849z;256z;362559

7969::59352:60:z

86797481757071777370a2

8984808883797883792

-------- 82 87 8984 90 92

L/ Including rights-of-way.6


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Table 3.--Curve numbers (CN) for wet (AMC III)and dry (AMC I) antecedent moistureconditions corresponding to an averageanteceden moisture condition(AMC fII)1 .

CN for Corresponding CN'sAMC II AMC I AMC III10095

ii;8075::6055z;403530252015105

1008778706357z:4035312622181512z42

10098969491888582787-L2:6055:337302213

11 AMC I. Lowest runoff potential,.Soils in the watershed aredry enough for satisfactoryplowing or cultivation.AMC II. The average condition.AMC III. Highest runoff potential.Soils in the watershed arepractically saturated fromantecedent rains.

WATERSHED AG AND TIME OF CONCENTRATIONThe average slope within the watershed to-gether with the overall length and retardance ofoverland f-low are major factors affecting therunoff rate through the watershed.Time of concentration (T,) is the time ittakes for water to travel from the most hydrau-lically distant point in a watershed to its out-let. Lag (L) can be considered as a weightedtime of concentration. When runoff from awatershed is nearly uniform it is usually suffi-cient to relate lag to time of concentration asfollows :

L = 0.6 T, (5)The lag for the runoff from an increment ofexcess rainfall can further be considered as thetime between the center of mass of the excess

STORM RAINFALL IN INCHES

Figure L.--Limited-gage data used to assigncurve numbers to new and unmeasuredwatershed characteristics.

INCREMENTOF EXCESSRAINFALLORINFLOW

OUTFLOWHYOROGRAPH

I- AD -I I I

A$ = = I" C.F.S.fi+L2Where:

A0 = INCREMENTOFSTORM PERIOD N HOURSA0 = RUNOFFINlNCHESDURlNGPERlOD 4DA = PEAK DISCHARGEN C.F.S.FURAN INCREMENTOF RUNOFFA = DRAINAGEAREAIN SQUAREMILESTp= TlMETOPEAK(=++L)INHOURSTL, = TlMEOFBASEf= 2.67 Tp ) IN HOURS

Figure 5.--Triangular hydrograph relationships.7


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rainfall increment and the peak of its incremen-tal outflow hydrograph (fig. 5). A graph forestimating lag is shown in figure 6. The equa-tion is:L = Q3*8 (s + 1) o-71900 Y.j

Where :L = lag in hours.i! = length of mainstream to farthestdivide in feet.Y = average slope of watershed inpercent.

1000S=CN-10CN' = A retardance factor approximated bythe curve number representing thewatershed's hydrologic soil-covercomplex.

Watershed Shape FactorThe length (1) of the mainstream to the far-thest divide was measured on ARS maps of thesmall experimental watersheds (2, 5; p. 2.2-7)The hydraulic length and area of these water-sheds are plotted in figure 7. The relationshipis represented by the equation:

R = 209 a"s6 (7)Where:

R = hydraulic length in feet.a = drainage area in acres.

The ratio of length (a) to average width (w)of a watershed may be referred to as a "shapefactor." It follows from equation (7) that theshape factor varies with drainage area.R = 43,560 a/w (8)

Where:w = average width of watershed in feet.

Substituting the value of R in equation (7) forR in equation (8):w = (43,560 a)/(209 a"s6)

and:w = 208.4 a"s4 (9)

Combining equations (7) and (9):

a/w = Ka0.2 (10)Where:

K = 209/208.4 (or 1 for practicalpurposes).a/w = watershed shape factor.

Variation in shape factor with respect todrainage area based on equation (10) is shown inthe following tabulation.

Drainage area(acres ) k/WJ Ratio

10 1.58100 2.511000 3.98l-1 w is average width of watershed, area/length.

There are small watersheds that do not conformto the shape factor in equation (10); some de-viate considerably. In the example shown infigure 8, the diversion terrace along one sidechanges the shape in reference to the hydrauliclength and average width relationship. Here thea/w factor is 3.75 as compared to a factor of1.69 based on the general equation (7) used for~~-1026 and ES-1027 solutions. Example 2 underthe heading tlBasic Procedure for Estimating PeakDischarge Without Developing a EIydrographn com-putes the peak discharge for this watershed tobe 43 cfs as compared to 46 cfs obtained fromthe solution in ES-1027. The ES-1026 andES-1027 solution provides a higher peak dis-charge estimate for all watersheds that havediversions or terraces and will result in agreater capacity requirement for the design ofa structure. This is generally acceptable andoften desirable for the installation of smallermeasures. Where the economy of a structurerequires close adherence to the lesser designcapacity, the peak discharge can be determinedmanually as shown later in example 2. Noattempt has been made to modify the precomputedestimates in ~~-1026 and ES-1027 for specialwatershed shape factors since those used changewith each change in drainage area as shown byequation (10) and the tabulation following it.Use of Curve Numbers to Reflect OverlandRetardance

The chart for estimating watershed lag infigure 6 uses Cii's to reflect the retardanceeffect of surface conditions on the rate atwhich runoff moves down the slope. A hay meadowor a thick mulch in a forest is associated with


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p. = GREATEST FLOW LENGTH IN FEET

Figure G.--Watershed lag (NEH-I-I- January 1971).


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(8) 133zl NI 03HS1131WM O H13N3-l

10


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Figure B.--Natural watershed shape factoraltered by a diversion terrace.

low CN's and high retardance. Conversely, abare surface is associated with high CN's andlow retardance. The CN's denoting retardanceare the same as those used for estimating thedepth of runoff from rainfall (table 2).The ADP solutions for charts ~~-1026 andES-1027 used the same CN' for computing water-shed lag in equation (6) as the CN for depthof runoff in equation (3).There are unusual situations for which a com-mon CN and CN' does not provide an adequate esti-mate of peak discharge. One example is a water-shed in which the soils have a high infiltrationrate (hydrologic soil group A or B) but no sur-face cover and are on rather steep slopes. Herethe CN for estimating depth of runoff is smallbecause of the hydrologic soil group class.Once the soil is saturated and runoff has com-menced, however, the overland retardance (CN')for the bare surface is greater than the CNrepresenting the hydrologic soil complex number.In special situations where it is believed thata closer approximation of lag or time of con-centration can be made and where a closer peak

discharge determination is warranted, the manualsolution described later should be made andcompared with the results in ~~-1326 or ES-1027.Average Watershed Slope

Slope as used in this method for computing

peak discharge means primarily average watershedslope in the direction of overland flow. Slopeis readily available at most locations fromexisting soil survey data. On larger watershedsthe gradient of the stream channel becomes anadditional considerat ion in estimating time ofconcentration. An estimate of one average slopefor all the land within watersheds of less than2,000 acres is adequate for the slope parameter(Y) in equation (6).Average slope is defined under three broadcategories for the peak discharge charts ~~-1026and ES-1027 (table 4). Peak discharges werecomputed for the slopes shown in the second col-umn and assigned to the broad categories of thefirst and third columns. Ordinarily the peakdischarge values given for one of the threeslope categories in ~~-1026 and ES-1027 are ade-quate for most uses without interpolatingbetween slope categories.

Table 4.--Slope factors for peak dischargecomputations in charts ~~-1026 andES-1027.

Slope for whichSlope factor computations Averagewere made slope range

FLAT1/MODERATESTEEP

Percent1416

Percent0 to 33 to 88 or more

lJ Level to nearly level.

Interpolation for Intermediate SlopesIf a closer estimate of peak discharge isneeded than that provided in ~~-1026 and ES-1327for the three slope categories, the value can bedetermined by interpolation between 1 percent(FLAT), 4 percent (MODERATE), and 16 percent(STEEP). The estimate is made simpler by in-terpolating along a straight-line plot of peakagainst slope on log-log paper (fig. 9). Thestraight-line plot on log-log paper can also beused to extrapolate peak discharge values forslopes steeper than 16 percent. But otherparameters than those in equation (6) may needto be considered for average watershed slopessteeper than 33 percent.

TRIANGULAR HYDROGRAPH QUATIONThe triangular hydrograph is a practical re-presentation of excess runoff with only onerise, one peak, and one recession. It has been


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L = drainage area lag.INCREMENTAL HYDROGRAPHS

AVERAGEWATERSHEDSLOPEIN EACENl

Figure Y.--Logarithmic interpolation of peakdischarge for intermediate slopes.

very useful in the design of soil and water con-servation measures. Its geometric makeup can beeasily described mathematically, which makes itvery useful in the processes of estimating dis-charge rates.SCS developed the following equation to esti-mate the peak rate of discharge for spillway andchannel capacities for conservation measures andwater-control structures:

Where:qp = (KAQ)/T~ (11) (2, 2, 1)

qp = peak rate of discharge.A = drainage area contributing to thepeak rate.Q = storm runoff.K = a constant.

Tp = time to peak.Time to peak (Tp) is expressed as:

Tp=$+LWhere:

D = storm duration.

Total storm rainfall rarely if ever occursuniformly with respect to time. Because rain-fall gage data and the variation of rainfallwith time are lacking in most small watersheds,it is desirable that variations in rainfall withrespect to time be standardized for the designof soil and water conservation measures. To useequation (11) for other than uniform storm rain-fall, it is necessary to divide the storm intoincrements of duration (AD) and compute corre-sponding increments of runoff (AQ)The peak discharge equation for anrunoff is:(fig. 5).increment of

(12)

Where :

A is in square miles.AQ is in inches.AD and L are in hours.

A% is in cfs.The constant, K, in equation (11) becomes 484when the peak discharge is computed in units ofcfs for the triangular hydrograph (fig. 5). Theordinates of the individual triangular hydro-graphs for each Aqpare added to develop a com-posite hydrograph (fig. lc)). Note how each in-cremental hydrograph is displaced one AD to theright for each succeeding time increment.

BASIC PROCEDUREFOR ESTIMATING PEAK DISCHARGEWITHOUT DEVELOPING A HYDROGRAPHThe plotting and summation of unit hydrographordinates (fig. 10) require more time thandesirable or necessary to obtain only the peakdischarge (qp) for a design storm. The peakdischarge, without the further development ofthe entire composite hydrograph, is all that isrequired for most SCS applications. For thesethe solution can be reduced to the period ofrunoff or of excess rainfall that directlyaffects the peak rate corresponding to a givenwatershed lag (L). A relationship between AD

and L can be chosen that enables the summationof only a single ordinate from each incrementalhydrograph within the effective runoff period tocompute the peak discharge. The usual choice isto make AD equal to one-third the time to peak(Tp) (fig. 11). If AD is taken to equal Tp/3then the equation for AD is:


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Figure lO.--Composite hydrograph from hydro-graphs for storm increments AD.

Where :AD = 0.4L (13)

Tp = (ADl2) + L (fig, 5)and

Tp = 3 ADThe effective peak-producing runoff period isTAD with the fifth increment AD, being the mostintense runoff increment (fig. 12). The peakdischarge for each increment (Aq,) can be com-puted by equation (12) using:

AQ., = Mass Q2 - Mass Q 1AQ2 = Mass Q, - Mass Q, etc. (14)

SELECTAD = l/3 Tp OR Tp = 3 ADSINCET = w@- +L AD = 0.4~p 2 '

Figure Il.--Making AD equal to one-third thetime to peak.

1

- 4AD -4 AD c- 2AD+

Figure 12.--Effective peak-producing period andmost effective increment.

The y values in figure 13 are the proportionalcontributing to thebeen obtained forThe product (y)Aq foreach of the seven increments of runoff ar8 addedto obtain the composite peak rate (qp). Thesummation equation is:

q = C 0.2Aq, + 0.4Aq, + o.6Aq3 + o.8Aq 4+ l.OAq, + $Aq6 'f yb, ( I51

Figure 13.--Proportional parts of incrementalhydrographs that contribute to thecomposite peak.


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The equations were solved by ADP to get thepeak-discharge rates for ~~-1026 and ES-1027.These equations can be solved manually by fol-lowing the examples given here.Example l.-- Given a loo-acre watershed withrunoff characteristics represented by CN 80 intable 2. The average slope of the watershed is1 percent. The peak discharge is required for alo-inch rain in 24 hours. The watershed islocated in the area covered by the type II curvein figure 1.

Step l.--Estimate the hydraulic length of thewatershed by equation (7):R = 209aos6R = 209(100)"'6R = 3,300 feet

Step 2.-- Read watkrshed lag from figure 6 forR = 3,300 feet; Y = 1 percent and CN 80:L = 0.83 hour

Step 3.--Compute AD from equation (13),assuming AD = Tp/3:AD = 0.4LAD = 0.4(0.83)

Step 6.--Prepare working curve. Plot mass Qversus time (fig. 14). Select midpoint of maxi-mum increment of runoff (11.88 hours). Thiswill be the same for most type II distributions,but it will occur later where initial abstrac-tion (I, = 0.2s) has not been satisfied prior to11.75 hours. Mark the curve with the 7AD begin-ning at10.39hours for the selected midpoin-tminus 4.5AD.

AD = 0.33 hour 11.88 - 4.5(0.33) = 10.39Step 4.--Compute the effective peak-producingrunoff period for TAD: Step T.--Prepare computations for instantane-ous peak discharge (table 5). The increment in

TAD = 7(0.33) hourTAD = 2.31 hoursStep T.--Prepare a tabulation based on a typeII distribution in table 1; P,, = 10 inches andrunoff (Q) for CN 80 from figure 3:

Time(hours)10.0LO.511.0Il.5II.7512.012.5l.3.0

PxjP240.181

.204.235.283.387.663.735.772

Mass P Mass Q(inches) (inches)1.81 0.442.04 .592.35 .782.83 1.123.87 1.946.63 4.367.35 5.027.72 5.36

TIME IN HOURSFigure lb.--Working curve for manual computation from type II storm distribution, table 1.

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Table 5.--Example 1, computations for instanta-neous peak discharge

(1) (2) (3) (4) (5) (6) (7)MassIncrement Time runoff AQ A& yd Y(Acl)Honrs Inches Inches Cfs Cfs---e -10.39 3.5510.72 .6711.05 .8011.38 .9811.71 1.7512.04 4.5312.37 4.9512.70 5.17

3.12 9.1 0.2.13 9.9 .4.18 13.7 .6.77 55.5 .8

2.78 211.3 1.0.42 31.9 213.22 16.7 113

1.84 08.2

46.8211.3

21.35.6

FEZ3111 FK~ equation (12) Aq = 76.0 (AQ)?J See figure 13ai qp = 300 (approx) from ES-1027, Rev. e-15-71sheet 5 of 21.

column 1 and the time in column 2 correspondwith the beginning and end of each incrementalperiod, AD, in figure 14. The runoff (Q) incolumn 3 is read from the curve in figure 14.Column 4 is the incremental runoff for each AD.Peak discharge for each increment of runoff iscomputed by equation (12) and tabulated in col-umn 5. Column 6 lists the proportion of incre-mental peak that contr ibutes to the total peakas shown in figure 13. Column 7 is the summa-tion of proportiona te parts of each incrementalpeak in equation (15).Example 2.--Given watershed W-II, 13.8 acreslocated at Cohocton, N. Y. The watershed is incultivation with good conservation treatment ineffect; its soils are predominantly in hydrologicsoil group C. The average watershed slope is 20percent and hydraulic length k is measured as1,500 feet following the course of the diversionterrace (fig. 8). The peak discharge for a 25-year frequency storm is desired for AMC II.Step I.--Select CN from table 2 based on thewatershed description: CN = 82Step 2.--Compute S from equation (4):

s=1ooo-10CN~~1ooo~1082

:. s = 2.2

Step T.--Prepare a tabulation from data insteps 1 and 4 for the period in step 6, solvingfor Q by using equation (3) o r by reading Q fromfigure 3:P = 4.3 inches; S = 2.2 inches.

Time Mass P Mass &(hours) (inches 1 (inches)11.5 0.283 1.22 0.2011.75 .387 1.66 .4412.0 .663 2.85 1.26

lfFrom table 1, type II distribution.

Step 3.--Read watershed lag (L) from figure 6or compute L from equation (6):L = 0.1 (approx.)Step li.--The 24-hour, 25-year frequency rain-fall for Cohocton, N. Y., in the Weather BureauAtlas is 4.3 inches. Use type II distribution.Step 5.--Compute AD from equation (13) assum-ing AD = Tp/3:

AD = 0.4LAD = 0.4(0.1) = 0.94 hour

Step 6.--Compute the effective peak-producingrunoff period for TAD:TAD = T(C.04) hourTAD = 9.28 hour

Step 8.--Prepare working curve (fig. 15) fromdata in step 7.Step 9.--Prepare computations for instantane-ous peak discharge (table 6).'Ihe peak discharge for this example is roundedto 43 cfs, as computed manually, and by estimat-ing lag (L) on the actual hydraulic length (a)along the diversion terrace. The peak dischargeobtained from ES-1027 (sheets 19 and 20), with Rbased on equation (7) and not the measuredlength along the diversion terrace, is:

9 for STEEP, CN 80, 13.8 acres,and P = 4.3 inches is 43 cfs.q for STEEP, CN 85, 13.8 acres,and P = 4.3 inches is 50 cfs.

By interpolation,q for STEEP, CN 82, 13.8 acres,and P = 4.3 inches is l+& cfs.

Converting from the 16-percen t slope for STEEPto a 20-percent slope would not add more than 1


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0.8

0.6

0.4

0.2

01.5 11.6 11.7 11.8 11.9 12.0TIME IN HOURS

Figure 15.--Working curve for example 2.

or 2 cfs by extrapolation on log-log paper aswas suggested for special cases (fig. 9).It may be concluded that the ES-1027 chartsoverestimate the peak discharge in this exampleby about 3 cfs or 7 percent. This is duemainly to the alteration of the watershed shapefactor by the diversion terrace.Example 3.--This example demonstrates the needfor making AD smaller -than 0.4L as used in theprevious two examples. To keep it less than 0.5hour and more commensurate with the increment ofmaximum storm intensity in table 1, it is setequal to l/6 Tp instead of l/3 Tp and it followsthat:AD = 0.182~ (16)

Given a 2,000-acre watershed with CN 60 and anaverage slope of 8 percent located on KahukaPoint, Oahua, Hawaii. An estimatedischarge for a 25-year frequencydesired.

of the peakrainstorm isStep l.--Estimate the hydraulic length of thewatershed by equation (7) or read from figure 7:

R = 20,000 feet

Table 6.--Example 2, computations for instanta-neous peak discharge(1) (2) (3) (4) (5) (6) (7)MassIncrement Time runoff AQ &'I Y Y(Aci)Hours Inches Inches CfS Cfs--- - -11.702/ 0.39

11.743' 0.4311.78 0.5411.82 0.6711.86 0.8011.90 0.9311.94 1.0611.98 1.19

0.04 3.5 0.2 .70.11 9.6 0.4 3.80.13 11.3 0.6 6.80.13 11.3 0.8 9.00.13 11.3 1.0 11.30.13 11.3 213 7.50.13 11.3 l/3 3.8

TOTAL = G

lag = 484 A (AQ) _ (484) (13.8) (AQ) =+j +L (0.02 + 0.1) 640 87.0 AQ

dli.88 - 4.5 AD = 11.88 - 4.5cO.4) = 11.70d11.70 + AD = il.70 + 0.04 = 11.7'4 hours (etc.)

Step 2.--Read watershed lag from figure 6 fora' = 2G,OOO feet; Y = 8 percent and CN' 60:L = 2.1 hours

Step 3.--Compute AD from equation (16), assum-ing AD = ~~16:AD '= 0.38 hour

Step 4.--Compute the effective peak-producingrunoff period for 15AD:15AD = 15(0.38) hour15AD ='5.7 hours

Step 5.--Prepare a tabulation based on a typeI distribution in table 1; P24 = 10 inches andCN 60:Time(hours) PxlP24 Mass P Mass Q(inches) (inches)6.00 0.125 1.25 0.007.00 .156 1.056 .oo8.00 .1g4 1.94 -058050 .219 2.l.9 .lO9.00 .254 2.54 .189.50 0303 3.03 .359.75 a362 3.62 .5910.00 .515 5.15 I.3910.50 .583 5.83 1.8211.00 .624 6.24 2.08IL.50 .654 6.54 2.2812.00 .682 6.82 2.47

16


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Step 6.--Prepare working curve (fig. 16) fromdata in step 5.Step 7.--Prepare computations for instantane-ous peak discharge (table 7).

EQUATIONS AND ASSUMPTIONS USED IM COMPUTERsommo~s FOR CMRTS ~~-1026 AND ~~-1027Storm Rainfall

Fifteen- and 30-minute increments of aceumula-ted-to-total ratios of rainfall were used withboth type I and II distributions shown in figureI. The 15-minute increments extended throughthe most intense l-hour period of each distribu-tion. Twenty-four-hour storms were generatedaccordingly for each distribution for thoserainfall depths shown in the ES charts.Rainfall-Runoff Equations

Runoff (Q) was computed accumulatively fromthe two accumulated rainfall distributions andtheir increments described. This solution wasmade for all rainfall depths and for each of theseven Cm's included in the ES charts by the fo l-lowing equations: & = (P - 0.2s):P + 0.8s (3)and

s=L!!!Z-,,CN (17)Watershed Lag

Lag time (L) was computed for I-, 4-, and 16-percent slopes (Y) for each of the seven Cm's inthe ES charts and for each of the followingdrainage areas (a):5 acres10 to 100 acres by IO-acre increments100 to 1,000 acres by 20-acre increments1,000 to 2,000 acres by 50-acre increments

The programmed equations were:L= ,o.e (s + 1) 0.71goo Y".hv. = 209 aJ-6 (7)

CN' for computing T, is approximated by theCN from table 2.

(17)

TIME IN HOURSFigure 16 .--Working curve for example 3.

Period of Runoff Affecting Peak DischargeThe computer program related the incrementedperiods (AD) of storm runoff to lag (L) asin (example 3):

AD = 0.182 L (16)The peak producing storm period for this rela-tionship is 15 AD (table 7, example 3).The computer solution determined the time atwhich the midperiod of the most intense 15-minute increment of accumulated runoff occurred.This was at 9.875 hours for the type I distribu-tion and 11.875 hours for the type II distribu-tion. It computed the time at the beginning ofthe effective period (15AD) as:

9.875 - 9.5 AD for type I11.875 - 9.5 AD for type IIIncremental Peak Discharge

The instantaneous peak discharge was computedfor each increment of runoff (AQ) within the

17


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Table 7.--Example 3, computations for instanta- effective period (IsAD) described according toneous peak discharge the following equation:Aq = q(AQ) (18)(1) (2) (3) (4) (5) (6) (7)MassIncrement Time runoff AQ A& Y Y(k)Hours Inches Inches Cfs Cfs---- -

6.27/6.65217.037.417.798.178.5:8.939.319.69

10.0710.45lo.8311.2111.5911.97

0.00 0.00 0.oo .oo 0.oo .oo 0.02 .02 13.04 .03 20.07 .04 26.ll .06 40.17 .09 59.26 .23 152.49 1.00 6601.49.31 205x.80 .20 1322.00 .17 1122.17 .15 992.32 .13 862.45TOTAL q =

0.1 0.2 0.3 0.4 5.5 10.6 16.7 28.a 47.9 137

1.0 660516 1714/6 88316 56216 33116 1.4

lzG- cfs1/ aq = 484 (AQ) = ,,,(P~f~i (AQ) = 660 (AQ)g+,

Combined Peak DischargeThe incremental peaks (As's) were combined inthe computer program in a manner similar to themanual solution shown in table 7, example 3.

zf 9.88 - 9.5AC 9.88 - 9.5c.38) = 6.27?f 6.27 + AD 6.27 + .38 6.65 hours(etc.)

18


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LITERATURE CITED(1) Chow, Ven te. 1962. Hydrologic determina-tions of waterway areas for the design ofdrainage structures in small drainage ba-sins. 111. Engr. Expt. Sta. Bull. 462,104 p.(2) Ogrosky, Harold O., and Victor Mockus. 1964.Hydrology of agricultural lands. In Hand-book of applied hydrology, Ven te ?%OFJ,

ed., (sec. 21), 97 p. McGraw-Hill Bookco. ) New York.(3) U.S. Agricultural Research Service. 1963.Hydrologic data for experimental agricul-tural watersheds in the United States1956,-59. Misc. Publ. 945. 611 n,(4) 1960. Selected runoff eventsfor small agricultural watersheds in theUnited States. 374 P.(5) U.S. Bureau of Reclamation. 1960. Designof small dams (appendix A). 611 p.(6) U.S. National Weather Service. 1973. Rre -cipitation-frequency atlas of westernUnited States. NOAA atlas No. 2, v. l-11.(7) U.S. Soil Conservation Service. 1972.Hydrology. Nat. Eng. Handb., sec. 4.547 p.

(8) U.S. Weather Bureau. 1963. Probable maxi-mum precipitation and rainfall-frequencydata for Alaska for areas to 400 squaremiles, durations to 24 hours, and returnperiods from 1 to 100 years. Tech. Paper47. 69 P.(9) 1962. Rainfall-frequency atlasfor the Hawaiian Islands for areas to 200square miles, durations to 24 hours, andreturn periods from 1 to 100 years. Tech.Paper 43.(10) - 1961. Generalized estimate ofprobable maximum precipitation and rain-fall-frequency data for Puerto Rico andVirgin Islands for areas to 400 squaremiles, durations to 24 hours, and returnperiods from 1 to 100 years. Tech. Paper42. 94 p.(11) 1961. Rainfall-frequency atlasof the United States for durations from30 minutes to 24 hours and return periodsfrom 1 to 100 years. Tech. Paper 40.115 P.

19


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-APPENDIXPEAK RATES OF DISCHARG

TYPE I STORM DISTRIBUTISLOPES - FLATCURVE NUMBER - 60

24 HOUR RAINFALL FROM US WB TP-43,TP-47, B (Revised) TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1026SHEET 1 OF 21DATE 6-1-71


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PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE I STORM DISTRIBUTION

SLOPES - FLATCURVE NUMBER - 65

24 HOUR RAINFALL FROM US WB TP-43,TP-47, 8. (Revised) TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG NO.ES- 1026SHEET 2-.-OF 21DATE 6-l-71 __


24/64

1 PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE I STORM DISTRIBUTION


24 HOUR RAINFALL FROM US WB TP-43,TP-47, & (Revised) TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG. ND.ES- 1026SHEET 3 OF 21DATE 6-I-71


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~~__r_l__-~j.~-SH

-SLOPES - FL/Al-


DRAINAGE AREA IN ACRESSTANDARD DWG NOES- !026SHEET 4 OF 2!--DATE 6-l-7,


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_--__S OF DISCHARGE F ALL WATERSHEDS

---SLOPES - FLATCURVE NUMBER - 80


DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1026SHEET 5 OF 21DATE 6-1-71


27/64


28/64

PEAK RATES OF DISCHARGE FOR SMALL W SHEDSTYPE I STORM DISTRIBUTION


24 HOUR RAINFALL FROM US WB TP-43,TP-47, 8 (Revised) TP-40

I DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1026SHEET 7 OF 21-DATE 6-1-71


29/64

PEAK RATES I= DISCHARGE FOR SMALL WATERSHEDSTYPE I ST

SLOPES - MODERATECURVE NUMBER - 60


DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1026SHEET 8 OF 21DATE 6-I-71


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6


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SLOPES - MCDERATE

24 HOUR RAINFALL FROM US WB V-43,TP-47, & (Revisedj TP-40


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DRAINAGE AREA IN ACRESSTANDARD DWG NO.ES- 1026SHEET 11 OF 21DATE 6-l-71


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24 HOUR WiNFALL FROM US WB V-43,7P-47, & (Revised) TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG NDES- 1026SHEET 12 OF 21DATE 6-1-71


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24 HOUR RAINFALL FROM US WB P-43,TP-47, 8, (Revised) TP-40


35/64


36/64

PEAK RATES OF DISCHARGE FOR SMALL WTORM DISTRIBUTI

SLOPES - STEEPCURVE NUMBER - 60


DRAINAGE AREA IN ACRESSTANDAKD DWG. ND.ES- 102fiSHEET 15 DF 21DATE 6-l-71


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/ PEAK RATES OF DISCHARGE FOR SMALL ~A~E~S~EDS



DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1026SHEET 16 OF 21DATE 6-l-71


38/64


39/64



10009008007006002 500Eii 400

-.m70 8:z- 80LL 702 604 5050 40E

DRAINAGE AREA iN ACRESSTANDARD DWG NO.ES- 1026SHEET &OF 21DATE 6-1-71


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SLOPES - STEEP

24 HO UR RAAINFALL FROM US A8 V-43,IP-47, 8 (Revised) TWO

BRAINAGE AREA IN ACRESSTANDARD DWG. ND. BES- 1026SHEET 9 OF 21


41/64

PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE I STORM DISTRIBUTIBN


24 HOUR RAINFALL FROM US WB TP-43,TP-47, 8, (Revised) TP-40

STANDARD DWG. NO.ES- 1026SHEET ZOF 21DATE 6-1-71


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PEA ATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE I STORM DISTRIBUTION

SLOPES - STEEPCURVE NUMBER - 90--


DRAINAGE AREA IN ACRESSTANDARD DWG NOES- 1026SHEET&OF 21__-DATE b-i-71

--


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PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE II STORM DISTRIBUTION

CURVE NUMBER 6024 HOUR RAINFALL FROM US WB TP 40

906 * ,,,.800700 I600

a 500Z

DRAINAGE AREA IN ACRESSTANDARD DWG NOES-1027SHEET 1 OF21DATE 2-15 -71


44/64



24 HOUR RAINFALL FROM US WB TP.40

[Lkt; 200t0m2 10090Z- 80

1000 * . ;,*,,900 * ..;800 , ,...700 _,, . .: 1I . ^ ,".

02 30wa 20

DRAINAGE AREA IN ACRESSTANDARD DWG. ND.ES- 1027SHEET - OF21DATE 2-15 -71


45/64



24 HOUR RAINFALL FROM US WB TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG. NO,ES-1027SHEET L-OF&DATE 2-15 -71


46/64



DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1027SHEET 2- OFADATE Z-15 -71


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SLOPES FLATCURVE NUMBER - 80

24 HOUR RAINFALL FROM US WB TP~40

a 8 8 ssss 8In uJhco& cl 00 8:: a $ 8 3i?s$E 8 me m ID r.COm- R2000 r . .I ,. _,_,

,. I .,a, .,.,,I I ., .I .,.600 * ^ ,,..a

_,.

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES-1027SHEET 2-e OF 21DATE 2-15 - 71


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PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE IT STORM DISTRIBUTION

SLOPES FLATCURVE NUMBER &5

24 HOUR RAINFALL FROM US WE! TP-40

STANDAKu DWG. NO,ES-1027SHEET a- OF 21DATE 2-15 -71


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1000 *900800700600

n 500g 400g 300@Lw *a+ 200iLL

SLOPES FLATCURVE NUMBER - 90

24 HOUR RAINFALL FROM US WE TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES-1027SHEET LOF&DATE Z-15-71

--


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SLOPES MODERATECURVE NUMBER - 60


700600, _, ,,

/p/y3oo/

c-lEiz 100Z- 7c8 6CccQ- 50$ 4c05 30

it 20

109a76

./ : /40

/

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES-1027SHEET 8OFL2.LDATE Z-15-71 _


51/64


SLOPES - MODERATECURVE NUMBER 65


1000 ." .;900 ::800 ,,_700 .e ,,,.600 ' "500 ~400 . " _..^,300

200,

700600/Y

/400

, I _I / 300

* I

/

40I , / 3o

STANDARD DWG. NO.ES- 1027SHEET -9 OF &DATE 2-15 -71


52/64

PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE It- STORM DISTRIBUTION

1000900KHI700600

n 500E 400YfJ7 300E+ 200zIL0m= 10090Z- 80?J 70lx 60z 50$ 40az 30iti! 20

109876s

SLOPES - MODERATECURVE ,NUMBER - 70


1. .* _., ., .I

,.. 300

, A.. ,. /60

/ . / 30

STANDARD DWG. NO.ES 1027SHEET & OF 21DATE Z-15-71


53/64


SLOPES MODERATECURVE NUMBER 7L


wa+ 200zLL0z" 10090Z- 802 7002 502 40E2 30k! 20

It8765

STANDARD DWG. NO.ES-1027SHEET 11 OF 21--DATE 2-15-71


54/64

PEAK RATES OF DISCHARGE FOR SMALL WATERSHETYPE III STORM

SLOPES - MODERATECURVE NUMBER 80

24 HOUR RAINFALL FROM L!S WB TP-40

, .A.,,,/ .! 400300

200

I I, ,,I, I . I,700

.^,,,.

+ 200 I Iw

\?/, /, 10

STANDARD DWG. ND.ES- 1027SHEET -i&. OF 21DATE 2-15-71 _


55/64


SLOPES MODERATECURVE NUMBER 85


800 ;;700600 .

n 500

STANDARD DWG. NO,ES-1027DATE 2-15 -71


56/64


1000900800700600n 500E 400I+ 300ccawF 200tiIL0iii3 10090Z- 80g 70s 60= 50v) 400z 30it 20

109a765



I,._ ' 50a.*I .I*,;I . . -, 40I ,II -,30.," .." ' 20

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1027DATE 2-15 -71


57/64

PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE II STORM DlSTiXlBUTlON

SLOPES STEEPCURVE NUMBER 60


09::800700600n 5005 400s 300cckL 200wLLc-lm= 10090z- 80

/

/300

200

/100: 90807060

/

506 40' 30' 20

/i> / ;O87

STANDARD DWG. rj0ES-1027DATE Z-15-71


58/64

PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPEII STORM DlSTRlBtJTlON



1000900800700600500400300

200

STANEARD DWG. NOES-1027DATE 2-15 -71


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PEAK RATES OF DkHARGE FOR SMALL WATERSHEDSTYPE II STORM DISTRIBUTION


. ..,l24 HOUR RAINFALL FROM US WB TP-40

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1027SHEET LOF&DATE 2-15 -71

..*


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SLOPES STEEPCURVE NUMBER - 75


DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES- 1027SHEET 18 OF 21DATE z-15-71


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PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE II STORM DISTRIBUTIOti



DRAINAGE AREA IN ACRESSTANDARD DWG. NO,ES-1027SHEET 19 OF 21DATE 2-15 -71

1


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SLOPES _ STEEPCURVE NUMBER - 85


8.76

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES-1027SHEET 2 OF a-DATE 2-15 -71


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c

7 PEAK RATES OF DISCHARGE FOR SMALL WATERSHEDSTYPE II STORM DISTRIBUTION



1%800700600n 500ci 4002* 300ElaL 200wL0z0 1;;z 80s 705 60$ 4005z 302 20

109876

DRAINAGE AREA IN ACRESSTANDARD DWG. NO.ES-1027SHEET 21 OF 21--DATE 2-15 -71

GP0/1973/726-779/493/1301


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Note: ES 1027, 21 of 21 is the last page of TP-149.

Documents

Runoff Calculation Manually