30. Time of Concentration.—By the time of concentration is meant the longest time without unreasonable delay that will be required for a drop of water[[24]] to flow from the upper limit of a drainage area to the outlet. Assuming a rainfall to start suddenly and to continue at a constant rate and to be evenly distributed over a drainage area of 100 per cent imperviousness and even slope towards one point, the rate of run-off would increase constantly until the drop of water from the upper limit of the area reached the outlet, after which the rate of run-off would remain constant. In nature the rate of rainfall is not constant. The shorter the duration of a storm the greater the intensity of rainfall. Therefore the maximum run-off during a storm will occur at the moment when the upper limit of the area has commenced to contribute. From that time on the rate of run-off will decrease.
The time of concentration can be measured fairly well by observing the moment of the commencement of a rainfall, and the time of maximum run-off from an area on which the rain is falling. A prediction of the time of concentration is more or less guess work. As the result of measurements some engineers assume the time of concentration on a city block built up with impervious roofs and walks, and on a moderate slope, is about 5 to 10 minutes. This is used as a basis for the judgment of the time of concentration on other areas. For relatively large drainage areas such a method cannot be used. The procedure is to measure the length of flow through the drainage channels of the area, to assume the velocity of the flood crest through these channels and thus to determine the time of concentration. Table 14 shows the flood crest velocities in various streams of the Ohio River Basin under flood conditions. The velocity over the surface of the ground may be approximated by the use of the formula[[25]]
V = 2,000I√S,
in which V = the velocity of flow over the surface of the ground in feet per minute; I = the percentage imperviousness of the ground; S = the slope of the ground.
For areas up to 100 acres where natural drainage channels are not existent this formula will give more satisfactory results than guesses based on the time of concentration of certain known areas.
Having determined the time of concentration, the rate of rainfall R to be used in the Rational Method is found by substitution in some one of the rainfall formulas given in Table 13.
| TABLE 14 | |||||||
|---|---|---|---|---|---|---|---|
| Flood Crest Velocities in Ohio River Basin in March, 1913 | |||||||
| From Table 12. U. S. G. S., Water Supply Paper. No. 334 | |||||||
| River | Stations | Distance between Stations in Miles | Distance to Mouth of River, Miles | Distance of Lower Station below Starting-point, Miles | Velocity between Stations, Miles per Hour | Velocity from Pittsburgh, Miles per Hour | Time between Stations in Hours |
| Ohio | Pittsburgh, Pa., to Wheeling, W. Va. | 90 | 967 | 90 | 9.0 | 9.0 | 10.0 |
| Ohio | Wheeling, W. Va., to Marietta, Ohio | 82 | 877 | 172 | 5.9 | 7.2 | 14 |
| Ohio | Marietta, Ohio, to Parkersburg, W. Va. | 12 | 795 | 184 | 0.9 | 4.8 | 14 |
| Ohio | Parkersburg to Point Pleasant, W. Va. | 80 | 783 | 264 | 6.7 | 5.3 | 12 |
| Ohio | Point Pleasant to Huntington, W. Va. | 44 | 703 | 308 | 11.0 | 5.7 | 4 |
| Ohio | Huntington to Catlettsburg, W. Va. | 9 | 659 | 317 | 0.8 | 4.1 | 11 |
| Ohio | Catlettsburg, W. Va., to Portsmouth, Ohio | 38 | 650 | 355 | 5.0 | ||
| Ohio | Portsmouth Ohio, to Maysville, Ky. | 52 | 612 | 407 | 5.2 | 5.0 | 10 |
| Ohio | Maysville, Ky., to Cincinnati, Ohio | 61 | 560 | 468 | 6.8 | 5.2 | 9 |
| Ohio | Cincinnati, Ohio, to Louisville, Ky. | 136 | 499 | 604 | 11.4 | 5.9 | 12 |
| Ohio | Louisville, Ky., to Evansville, Ind. | 183 | 363 | 787 | 1.9 | 5.3 | 96 |
| Ohio | Evansville, Ind., to Mt. Vernon Ind. | 36 | 180 | 823 | 9.0 | 5.3 | 4 |
| Ohio | Mt. Vernon, Ind., to Paducah, Ky. | 101 | 144 | 924 | 2.1 | 4.6 | 48 |
| Ohio | Paducah, Ky. to Cairo, Ill. | 43 | 43 | 967 | 2.9 | 4.2 | 15 |
| Monongahela | Fairmont, W. Va., to Lock No. 2 Pa. (Upper) | 107 | 119 | 107 | 6.7 | 16 | |
| Little Kanawha | Creston, W. Va., to Dam. No. 4 W. Va. (Upper) | 16 | 48 | 16 | 16.0 | 1 | |
| New | Radford, W. Va., to Hinton, W. Va. | 78 | 139 | 78 | 3.0 | 26 | |
| Kanawha | Kanawha Falls, W. Va. to Charleston, W. Va. | 37 | 95 | 37 | 2.6 | 14 | |
| Scioto | Columbus, Ohio, to Chillicothe, Ohio | 52 | 110 | 52 | 4.7 | 11 | |
| Miami | Dayton, Ohio, to Hamilton, Ohio | 44 | 77 | 44 | 14.7 | 3 | |
| Kentucky | Highbridge, Ky., to Frankfort, Ky. | 52 | 117 | 52 | 5.2 | 10 | |
| Cumberland | Celina, Tenn. to Nashville, Tenn. | 190 | 383 | 190 | 2.9 | 64.5 | |
| Tennessee | Knoxville to Chattanooga, Tenn. | 183 | 635 | 183 | 3.2 | 57 | |
| Note.—The velocities shown are the velocities of the crest of the flood wave and are not the average velocity of the flow of the river. The velocity of the crest of the flood wave should be used in determining the time of concentration. The flood crest velocity is slower then that of the river because of the storage in the river basin. | |||||||
31. Character of Surface.—The proportion of total rainfall which will reach the sewers depends on the relative porosity, or imperviousness, and the slope of the surface. Absolutely impervious surfaces such as asphalt pavements or roofs of buildings will give nearly 100 per cent run-off regardless of the slope, after the surfaces have become thoroughly wet. For unpaved streets, lawns, and gardens the steeper the slope the greater the per cent of run-off. When the ground is already water soaked or is frozen the per cent of run-off is high, and in the event of a warm rain on snow covered or frozen ground, the run-off may be greater than the rainfall. The run-off during the flood of March, 1913, at Columbus, Ohio, was over 100 per cent of the rainfall. Table 15[[26]] shows the relative imperviousness of various types of surfaces when dry and on low slopes. The estimates for relative imperviousness used in the design of the Cincinnati intercepter are given in Table 16.
| TABLE 15 | ||
|---|---|---|
| Values of Relative Imperviousness | ||
| Roof surfaces assumed to be water-tight | 0.70– | 0.95 |
| Asphalt pavements in good order | .85– | .90 |
| Stone, brick, and wood-block pavements with tightly cemented joints | .75– | .85 |
| The same with open or uncemented joints | .50– | .70 |
| Inferior block pavements with open joints | .40– | .50 |
| Macadamized roadways | .25– | .60 |
| Gravel roadways and walks | .15– | .30 |
| Unpaved surfaces, railroad yards, and vacant lots | .10– | .30 |
| Parks, gardens, lawns, and meadows, depending on surface slope and character of subsoil | .05– | .25 |
| Wooded areas or forest land, depending on surface slope and character of subsoil | .01– | .20 |
| Most densely populated or built up portion of a city | .70– | .90 |
| TABLE 16 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Coefficients of Imperviousness Used in the Design of the Cincinnati Sewers | ||||||||||
| Character of Improvement | Typical Commercial Area, 30.4 A. None Undeveloped. Sand and Gravel | Combined Tenement and Industrial. 35.6 A., 55 per Acre. Clay, Sand and Gravel | Residential, 291.1 A. 20 per Acre, Middle Class, Detached Dwellings, Yellow and Blue Clay Overlying Beds of Shale and Sandstone | |||||||
| Area in 1000’s Square Feet | Per Cent Total Area | I, Estimated | Equivalent Imp. Area, 1000’s Square Feet | Area in 1000’s Square Feet | Per Cent Total Area | I, Estimated | Per Cent of Total Area | I, Estimated | ||
| Roofs: | ||||||||||
| Public and commercial | 881.2 | 66.5 | 0.90 | 793.0 | 66.8 | 4.3 | 0.40 | 4.8 | 0.40 | |
| Residences | 289.2 | 18.6 | .90 | 13.1 | .90 | |||||
| Barns and sheds | 79.2 | 5.1 | .75 | 1.4 | .75 | |||||
| Interior Walks: | ||||||||||
| Brick | 7.5 | 0.6 | .40 | 3.0 | 35.6 | 2.3 | .40 | 0.6 | .40 | |
| Cement | 10.0 | 0.7 | .75 | 7.5 | 22.6 | 1.5 | .75 | 2.6 | .75 | |
| Street Walks: | ||||||||||
| Brick | 6.1 | 0.5 | .40 | 2.4 | 48.2 | 3.1 | .40 | 1.0 | .40 | |
| Cement | 139.3 | 10.5 | .75 | 104.5 | 78.1 | 5.0 | .75 | 3.4 | .75 | |
| Street Pavements: | ||||||||||
| Asphalt, brick, wood block | 145.5 | 11.0 | .85 | 123.7 | 5.0 | .85 | ||||
| Granite block | 111.4 | 8.4 | .75 | 83.6 | 1.0 | .75 | ||||
| Macadam and cobble | 23.2 | 1.8 | .40 | 9.3 | 238.6 | 15.4 | .40 | 4.8 | .40 | |
| Granite and poor macadam | 0.4 | .20 | ||||||||
| Unimproved yards and lawns: | 692.4 | 44.7 | .15 | |||||||
| Tributary to paved gutters | 57.1 | .15 | ||||||||
| Not tributary to paved gutters | 7.9 | .10 | ||||||||
| Total | 1324.2 | 100.0 | 1127.0 | 1550.7 | 100.0 | 100.0 | ||||
| Impervious coefficient for the district | 85.1 | 44.4 | 35.9 | |||||||