The time of concentration for a watershed is defined as the time required for water to flow from the most remote point of the watershed to the outlet. The peak rate will occur when the entire watershed contributes to the runoff.

The peak runoff flow is influenced by many factors. For the purposes of this text, the only factors that will be considered are slope and length of the drainage way. Obviously, if the drainage way is short and steep, the water will arrive at the outlet quickly and the time of concentration will be short. A flat drainage way gradient has the opposite effect. The time of concentration for small watersheds with various lengths and drainage way gradients is shown in Table 17.2.

Table 17.2. Time of concentration for small watersheds (min).

Drainage way gradient (slope), %

Table 17.2. Time of concentration for small watersheds (min).

Drainage way gradient (slope), %

Maximum length of flow (ft) |
0.05 |
0.10 |
0.50 |
1.00 |
2.00 |
5.00 |

500 |
18 |
13 |
7 |
6 |
4 |
3 |

1,000 |
30 |
23 |
11 |
9 |
7 |
5 |

2,000 |
51 |
39 |
20 |
16 |
12 |
9 |

4,000 |
86 |
66 |
33 |
27 |
21 |
15 |

6,000 |
119 |
91 |
46 |
37 |
29 |
20 |

8,000 |
149 |
114 |
57 |
47 |
36 |
25 |

10,000 |
175 |
134 |
67 |
55 |
42 |
30 |

The Rational method equation has three variables, C, I, and A. A value must be determined for each one before the equation can be used. The value of C is determined using Table 17.1. The value of I is more complex. To determine I the rainfall intensity-duration-recurrence interval, Figure 16.10, is used. To find rainfall intensity from this graph the duration and recurrence interval must be known. In the Rational method the duration is determined from the time of concentration. The time of concentration is the amount of time that occurs from when the rainfall starts until the peak rate or runoff occurs, Figure 17.4.

Once the time of concentration is determine from Table 17.1, and the desired recurrence interval is known, Figure 16.10 can be used to determine the rainfall intensity.

Problem: Determine the peak runoff for a watershed consisting of 90.0 acres of pasture with tight clay soil and an average slope of 4.0%. The drainage way for the watershed is approximately 4,000 ft with a gradient of 0.50%. Assume a recurrence interval of 10 years.

Table 17.3. "C" value for sample problem.

Soil texture

Topography, vegetation and slope Sandy loam Clay and silt loam Tight clay

Table 17.3. "C" value for sample problem.

Soil texture

Topography, vegetation and slope Sandy loam Clay and silt loam Tight clay

Woodland | ||||

Flat 0-5% |
0.10 |
0.30 |
0.40 | |

Rolling 5-10% |
0.25 |
0.35 |
0.50 | |

Hilly 10-30% |
0.30 |
0.50 |
0.60 | |

Pasture | ||||

Flat 0-5% |
0.10 |
0.30 |
0.40 | |

Rolling 5-10% |
0.16 |
0.36 |
0.55 | |

Hilly 10-30% |
0.22 |
0.42 |
0.60 | |

Cultivated | ||||

Flat 0-5% |
0.30 |
0.50 |
0.60 | |

Rolling 5-10% |
0.40 |
0.60 |
0.70 | |

Hilly 10-30% |
0.52 |
0.72 |
0.82 |

The correct value for "C " is 0.40.

The correct value for "C " is 0.40.

Rational Method of Calculating Peak Rate of Runoff 239 Table 17.4. Time of concentration for sample problem.

Drainage way gradient (slope), %

Rational Method of Calculating Peak Rate of Runoff 239 Table 17.4. Time of concentration for sample problem.

Drainage way gradient (slope), %

Maximum length of flow (ft) |
0.05 |
0.10 |
0.50 1.00 |
2.00 |
5.00 | |

500 |
18 |
13 |
7 |
6 |
4 |
3 |

1,000 |
30 |
23 |
11 |
9 |
7 |
5 |

2,000 |
51 |
39 |
20 |
16 |
12 |
9 |

4,000 |
86 |
66 |
33 |
27 |
21 |
15 |

6,000 |
119 |
91 |
46 |
37 |
29 |
20 |

8,000 |
149 |
114 |
57 |
47 |
36 |
25 |

10,000 |
175 |
134 |
67 |
55 |
42 |
30 |

The time of concentration is 33 min.

Solution: To determine the solution a value must be determined for each on the three variables in the rational equation using Table 17.1, Table 17.2, and Figure 16.10. The correct numbers to use for this example problem are shown in Table 17.3, Table 17.4, and Figure 17.5. The rainfall intensity (I) is 4.4 in/hr.

15.0

15.0

Duration (minutes & hours)

FIGURE 17.5. Rainfalll intensity for sample problem.

Duration (minutes & hours)

FIGURE 17.5. Rainfalll intensity for sample problem.

With C = 0.40,1 = 4.5 in/hr, and A = 90 ac the peak rate of runoff is:

in ft3

In this example the best estimate of the peak runoff rate is 162 cfs. Note that the units do not cancel in the equation. This is because the C value is determined so that the answer is in cubic feet per second.

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