91 by the McMath formula. Capt. R. L. Hoxie compared actual measured flows in Washington sewers with run-offs from the same areas calculated by three of the formulas, with the following results: The discrepancies are largely due to the causes already referred to that the formulas are empirical and that factors are taken as constants which are really variables. One of these errors is in using a fixed rate of rainfall, regardless of the section of the country under consideration, as is done by the Hawksley and Kirkwood. Also, the character of the majority of street surfaces has changed in imperviousness and smoothness since most of these formulas were devised. It seems certain that any formula that would represent by variable factors all the conditions that affect run-off would be so complicated that its use would probably be more difficult, and tedious than the solving of each problem by the rational method. The rational method is used by the cities of Baltimore, Boston, Cincinnati, Queens Borough (New York), Pawtucket, R. I., St. Louis, and many other cities. One of the first exponents of the rational method, the late Emil Kuichling, made extensive gaugings and studies of rainfall and sewer flow in Rochester, N. Y., from which he derived certain conclusions that would seem to be general in their application. These are as follows: 1. The percentage of the rainfall discharged from any given drainage area is nearly constant for rains of all considerable intensity and lasting equal periods of time. 2. The said percentage varies directly with the degree of urban development of the district, or, in other words, with the amount of impervious surface thereon. . . 3. The said percentage increases rapidly, and directly or uniformly with the duration of the maximum intensity of the rainfall, until a period is reached which is equal to the time required for the concentration of the drainage-waters from the entire tributary area at the point of observation; but if the rainfall continues at the same intensity for a long period, the said percentage will continue to increase for the additional interval of time at a much smaller rate than previously. This circumstance is manifestly attributable to the fact that the permeable surface is gradually becoming saturated and is beginning to shed some of the water falling upon it; or, in other words, the proportion of impervious surface slowly increases with the duration of the rainfall. 4. The said percentage becomes larger when a moderate rain has immediately preceded a heavy shower, thereby partially saturating the permeable territory and correspondingly increasing the extent of impervious surface. 5. The sewer discharge varies promptly with all appreciable fluctuations in the intensity of the rainfall. (Transactions Am. Soc. C. E., Vol. XX., page 37.) The maximum rate of rainfall seldom lasts more than a minute or two, and the longer the period considered, the lower is generally the maximum rate for the period. It follows, therefore, that an area that has a shorter run-off time than another will contribute a larger maximum run-off per unit of area. Storms seldom increase or decrease at a uniform rate, but by examining the records of excessive rainfalls in the locality in question, each represented by a curve as in Fig. 6, we may select for any given area the curve that will give the maximum run-off for such area; or such curve as would produce the run-off of the second or third greatest intensity, if we desire to reject rainfalls of infrequent occurrence in the calculation. The run-off calculated as resulting from a given rainfall will be a maximum when the sum of the products of rainfall rates during successive minutes as one factor, and the run-off areas used in succession (beginning with that furthest from the inlet) as the other factor, is a maximum. In the majority of rainfall records, the rates are given as the averages during successive five-minute periods. Consequently, five-minute contours will generally be used. As shown above, if the one-minute run-off areas can be assumed as equal, it is perfectly accurate to use as the maximum rainfall rate the average for the run-off time of the block in question. It is ordinarily assumed that such condition exists in city blocks, and the maximum average rainfall for five- or ten-minute periods is used. It is evident from the previous discussion that this does not give maximum run-off. It will appear later that this error does not greatly affect the calculation of capacity required for the main sewer; but it does affect that required for the inlet connections to the sewer and the inlet itself. CALCULATING RUN-OFF FROM A RESIDENTIAL CITY BLOCK This block (see Fig. 9) is 300 by 500 ft. measured on the property lines; sidewalks 15 feet wide, roadway 30 feet. Gutter grades are such as to give the estimated velocities of 10, 1.5, 1.2, and 1.6 feet per second as indicated. It is assumed that the conditions as to cross-slopes of sidewalk and roadway and grading of lawns will be such ultimately as to carry the run-off from property line to gutter and street center to gutter each in fifteen seconds, and across the yards to the sidewalk at the rate shown-1.6, 1.0, 0.4, and 0.6 feet per second, respectively; the grading of yards being such that the diagonals define the drainage slopes to the four sidewalks. Also that the imperviousness of sidewalks and road ways will be .90 and of yards .40. Also that at maximum flow ten seconds will be consumed in flowing from the inlet (in the lower right-hand corner of the block) to the sewer at C. The one-minute contour crosses the gutter on the bottom street (60-10) 1.0 or 50 feet from the inlet; and the right-hand street (60-10) 1.5 or 75 feet from the inlet. This contour crosses the right-hand property line at a point opposite a point in the gutter (60-10-15) 1.5 or 52.5 feet from the inlet; and the center of the street opposite the same point. The two-minute contour crosses the righthand gutter at a distance (60X1.5) or 90 feet beyond the one-minute contour, and is the same distance from such contour measured along both property line and center line of street. And each contour to the 6th is 90 feet beyond the previous one. From the point where the one-minute contour crosses the property line, measure at right angles to such line (60X1.0) = 60 feet, which will be a point on the two-minute contour (or such contour extended into the slope to the lower sidewalk, in this case). From the two-minute contour at the property measure 60 feet, which will give a point on the three-minute contour, etc. Draw straight lines through these points and those where the corresponding contours cross the property line,, extending the contours to the lot diagonals. Do the same for the lower street. The seventh contour will cross the gutter (7X60)—10— 500+30 or 56.7 seconds of flow along the top gutter, or56.7X1.2=68 feet from the 1.5 corner. The eight-, nine-, and ten-minute contours cross the top gutter at uniform intervals of (60X1.2) or 72 feet apart. And the intervals between them in the yard area, measured normal to the top gutter, is (60X0.4) or 24 feet. All the contours in each area of uniform slope are parallel. Those in the left-hand street and yard area are located in the same way. Then all the yard area between the inlet and contour 1 represents the area of such surface from which the run-off reaches the sewer in one minute, and the same of the street areas. The sum of all of the areas between contour I and contour 2 represents the surface from which the run-off reaches the sewer during the second minute after it fell. Up to area 13 there are two yard and two street areas to be added to give the successive minute run-off quantities; but beyond this there is but one area for each minute. Rain falling just above the intersection of the diagonals requires nineteen minutes to reach the sewer. We may now prepare a table like that shown herewith for calculating the run-off. It may be sufficiently accurate for practical purposes to plot the diagram, Fig. 9, on cross-section paper and determine each area by counting the squares it covers, estimating fractional squares; but generally a simple formula for calculating it will be apparent. For example, in area 7 at the left-hand corner, which is triangular in form, drop a perpendicular from the vertex D to the base, call it a and call the part of the base above this x, and that below it y. Then a y=300 500; a: x=0.6: 1.6; and x+y=96 feet. From which a is found to be 22.15 feet. Area 8 on this slope has three times the area of 7, area 9 has five times the area, etc. Each area within the property lines is then multiplied by 0.40, and each in the street is multiplied by 0.90, and the products placed in the proper columns, and the sum of such products for each minute taken and entered in the column "Total AI." CALCULATION OF RUN-OFF FROM SUBURBAN CITY BLOCK A in square feet. R in inches of actual rainfall * Equivalent to 3.6, 3.5 and 2.5 inches per hour, respectively. A rate of 3.1 inches per hour (see cumulative rainfall curve) would give a run-off of 458 cubic feet per minute, Total AI-2.443 acres. |