Synthetic Unit Hydrograph Formulas

Peak flows draining from urban and small catchment areas can be estimated from critical or design storm information using the synthetic unit hydrograph technique. One technique employed by the US Corps of Engineers [19] uses Snyder's method of synthesizing unit hydrographs, according to which a storm with a duration given by

Table 3 Runoff Coefficients, C

Description of area of surface C factor

Table 3 Runoff Coefficients, C

Business

Downtown

0.70-

-0.95

Neighborhood

0.50-

0.70

Residential

Single-family

0.30-

0.50

Multiunits, detached

0.40-

0.60

Multiunits, attached

0.60-

0.75

Residential (suburban)

0.50-

0.70

Apartment

0.50

0.70

Industrial

Light

0.50

0.80

Heavy

0.60

0.90

Parks, cemeteries

0.10-

0.25

Playgrounds

0.20-

0.35

Railroad yard

0.20-

0.35

Unimproved

0.10-

0.30

Pavement

Asphaltic and concrete

0.70

0.95

Brick

0.70

0.85

Roofs

0.75

0.95

Lawns, sandy soil

Flat, 2%

0.05

0.10

Average, 2-7%

0.10

0.15

Steep, 7%

0.15

0.20

Lawns, heavy soil

Flat, 2%

0.13

0.17

Average, 2-7%

0.18-

0.22

Steep, 7%

0.25

0.35

and a lag time given by to=Ct(LLcaf3

produces a peak flow for 1 in. of excess rain given by ^ tAGCpA

where ir=duration of the unit rainfall excess (hour), Zb=lag time (hour) from the centroid of unit rainfall excess to the peak of the synthetic unit hydrograph, Ci=coefficient representing variations of watershed slopes and storage, Z,=length (miles) of the main stream channel from the outlet to the farthest point (1 mile=16b9 m), Z,ca=length (miles) along the main channel to the point opposite the watershed centroid, Qp=peak flow of synthetic unit hydrograph (cfs) (1 cfs=b.02832 m3/s), Cp=coefficient of peak flow accounting for watershed retention or storage capacity, and ^watershed area (mile2) (1 mile2=2.59 km2).

According to another similar method developed by the Soil Conservation Service [2b] for constructing synthetic unit hydrographs, the peak flow produced from a storm event with a

Figure 5 Peak discharge vs. time of concentration tb for 24 hour Type II storm distribution (from Ref. 16).

duration D is equal to

where tp=time (hour) from the beginning of the effective rain to the time of the peak runoff flow, which by definition is tp=t0+D/2, where D=duration (hour) of rainfall, equal to 0.133tc, where tc is the time of concentration.

Both of the above empirical equations apply for a certain duration D of 1 in. net rain. The Qp from either formula can be multiplied by the actual net p (peak flow) for other storm events with equal D but different depths. Peak flows for storm events with longer or shorter durations D have to be estimated using unit hydrograph methods.

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