Many computer models have been developed for calculating rainfall runoff. Examples include the U. S. Army Corps of Engineers HEC-HMS model, the NRCS TR-20 model, and the FHWA-funded HYDRAIN system. As with all computer models, the accuracy and validity of the output can be only as accurate and valid as the input. The input and output data must be carefully inspected by a capable and practiced user to ensure valid results. (See D. R. Maidment, Handbook of Hydrology, McGraw-Hill, 1993; and Highway Drainage Guidelines, Vol. 2, AASHTO, 1999.)
Example: Time of Concentration, Rainfall Intensity, and Design Discharge. A grassy roadside channel runs 500 ft (152 m) from the crest of a hill. The area contributing to the flow is 324 ft (98 m) wide and is made up of 24 ft (7.3 m) of concrete pavement and 300 ft (91 m) of grassy backslope. The distance from the channel to the ridge of the drainage area is 200 ft (61 m). The channel has a grade of 0.4 percent, and the edge of the contributing area is 5 ft (1.5 m) above the channel. Determine the time of concentration, rainfall intensity, and design discharge based on a 10-year-frequency rainfall.
Assume the grassy backslope is similar to the watershed described by the example in Table 5.1 with C = 0.32. From Table 5.2, assume for the pavement C = 0.90. Then, from Eq. (5.3), the weighted average value of the runoff coefficient is
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Separate the flow into overland flow and concentrated flow components for determining the time of concentration. For the overland flow time, proceed as follows.
The length of travel is 200 ft (61 m). The difference in elevation between the channel and the ridge of the drainage area is 5 ft (1.5 m). The slope is
U. S. Customary units: S = — = —— = 0.025 or 2.5%
3 L 200
SI units: S = 22 = 22 = 0.025 or 2.5%
L 61
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The overland flow is computed using Eq. (5.4):
SI units: Same calculation, using L = 61 X 3.28 = 200 ft
For the concentrated flow time, Manning’s equation [Eq. (5.11) below] is used to determine the concentrated flow velocity. Manning’s n value is taken from Table 5.6 and a hydraulic radius must be assumed.
U. S. Customary units: V = 227 (0.50)2/3 (0.004)1/2 = 2.2 ft/s
SI units: V = (0.15)2/3 (0.004)1/2/0.027 = 0.66 m/s
Then the concentrated flow time is computed using Eq. (5.7):
U. S. Customary units: T = —222— = 3.8 min 60 (2.2)
SI units: T = ————- = 3.8 min
60 (0.66)
Therefore the total time of concentration is 14.6 min + 3.8 min or 18.4 min.
Now use Fig. 5.1 to get a 10-year rainfall intensity of 3.8 in/h (96 m/h). Using the rational method Eq. (5.2), the design discharge for the 3.7 acres (0.015 km2) area is
U. S. Customary units: Q = 1 X 0.36 X 3.8 X 3.7 = 5.1 ft3/s
SI units: Q = 0.278 X 0.36 X 96 X 0.015 = 0.14 m3/s
The assumed hydraulic radius used in Manning’s equation must be verified by using Eq. (5.11). Through trial and success, the depth of flow is determined to be 0.71 ft (0.22 m), and therefore the hydraulic radius is 0.48. The assumed value is close to this so the convergence is acceptable.
