The intensity of the rainfall decreases as the period over which the rainfall is taken is increased. For instance, a rainfall of lin may occur in a period of twenty minutes, being at the rate of 3 in per hour, but if a period of one hour is taken the fall during such lengthened time will be considerably less than 3 in In towns where automatic rain gauges are installed and records kept, the required data can be abstracted, but in other cases it is necessary to estimate the quant.i.ty of rain which may have to be dealt with.
It is impracticable to provide sewers to deal with the maximum quant.i.ty of rain which may possibly fall either in the form of waterspouts or abnormally heavy torrential rains, and the amount of risk which it is desirable to run must be settled after consideration of the details of each particular case. The following table, based princ.i.p.ally upon observations taken at the Birmingham Observatory, shows the approximate rainfall which may be taken according to the time of concentration.
TABLE No. 7.
INTENSITY OF RAINFALL DURING LIMITED PERIODS.
Equivalent rate in inches per hour of aggregate rainfall during Time of Concentration, period of concentration A B C D E 5 minutes ............... 1.75 2.00 3.00 -- -- 10 " ............... 1.25 1.50 2.00 -- -- 15 " ............... 1.05 1.25 1.50 -- -- 20 " ............... 0.95 1.05 1.30 1.20 3.00 25 " ............... 0.85 0.95 1.15 -- -- 30 " ............... 0.80 0.90 1.05 1.00 2.50 35 " ............... 0.75 0.85 0.95 -- -- 40 " ............... 0.70 0.80 0.90 -- -- 45 " ............... 0.65 0.75 0.85 -- -- 1 hour .................. 0.50 0.60 0.70 0.75 1.80 1-1/2 " .................. 0.40 0.50 0.60 -- 1.40 2 " .................. 0.30 0.40 0.50 0.50 1.10
The figures in column A will not probably be exceeded more than once in each year, those in column B will not probably be exceeded more than once in three years, while those in column C will rarely be exceeded at all. Columns D and E refer to the records tabulated by the Meteorological Office, the rainfall given in column D being described in their publication as "falls too numerous to require insertion," and those in column E as "extreme falls rarely exceeded." It must, however, be borne in mind that the Meteorological Office figures relate to records derived from all parts of the country, and although the falls mentioned may occur at several towns in any one year it may be many years before the same towns are again visited by storms of equal magnitude.
While it is convenient to consider the quant.i.ty of rainfall for which provision is to be made in terms of the rate of fall in inches per hour, it will be useful for the practical application of the figures to know the actual rate of flow of the storm water in the sewers at the point of concentration in cubic feet per minute per acre. This information is given in the following Table No. 8, which is prepared from the figures given in Table No. 7, and is applicable in the same manner.
TABLE No. 8.
MAXIMUM FLOWS OF STORM WATER.
--------------------------+---------------------------------- | Maximum storm water flow in | cubic feet per min per acre | of impervious area.
Time of Concentration. +------+------+------+------+------ | A | B | C | D | E --------------------------+------+------+------+------+------ 5 minutes | 106 | 121 | 181 | -- | -- 10 " | 75 | 91 | 121 | -- | -- 15 " | 64 | 75 | 91 | -- | -- 20 " | 57 | 64 | 79 | 73 | 181 25 " | 51 | 57 | 70 | -- | -- 30 " | 48 | 54 | 64 | 61 | 151 35 " | 45 | 51 | 57 | -- | -- 40 " | 42 | 48 | 54 | -- | -- 45 " | 39 | 45 | 51 | -- | -- 1 hour | 30 | 36 | 42 | 45 | 109 1-1/2 " | 24 | 30 | 36 | -- | 85 2 " | 18 | 24 | 30 | 30 | 67 --------------------------+------+------+------+------+------- l inch of rain = 3,630 cub. feet per acre.
The amount of rainfall for which storage has to be provided is a difficult matter to determine; it depends on the frequency and efficiency of the overflows and the length of time during which the storm water has to be held up for tidal reasons. It is found that on the average the whole of the rain on a rainy day falls within a period of 2-1/2 hours; therefore, ignoring the relief which may be afforded by overflows, if the sewers are tide-locked for a period of 2-1/2 hours or over it would appear to be necessary to provide storage for the rainfall of a whole day; but in this case again it is permissible to run a certain amount of risk, varying with the length of time the sewers are tide-locked, because, first of all, it only rains on the average on about 160 days in the year, and, secondly, when it does rain, it may not be at the time when the sewers are tide-locked, although it is frequently found that the heaviest storms occur just at the most inconvenient time, namely, about high water. Table No. 9 shows the frequency of heavy rain recorded during a period of ten years at the Birmingham Observatory, which, being in the centre of England, may be taken as an approximate average of the country.
TABLE No. 9.
FREQUENCY OF HEAVY RAIN -------------------------------------------------------
Total Daily Rainfall. Average Frequency of Rainfall
0.4 inches and over 155 times each year 0.5 " 93 "
0.6 " 68 "
0.7 " 50 "
0.8 " 33 "
0.9 " 22 "
1.0 " 17 "
1.1 " Once each year 1.2 " Once in 17 months 1.25 " " 2 years 1.3 " " 2-1/2 1.4 " " 3-1/3 1.5 " " 5 years 1.6 " " 5 years 1.7 " " 5 years 1.8 " " 10 years 1.9 " " 10 years 2.0 " " 10 years
It will be interesting and useful to consider the records for the year 1903, which was one of the wettest years on record, and to compare those taken in Birmingham with the mean of those given in "Symons" Rainfall," taken at thirty-seven different stations distributed over the rest of the country.
TABLE No. 10.
RAINFALL FOR 1903.
Mean of 37 stations in Birmingham England and Wales.
Daily Rainfall of 2 in and over ...... None 1 day Daily Rainfall of 1 in and over ...... 3 days 6 days Daily Rainfall of 1/2 in and over .... 17 days 25 days Number of rainy days.................. 177 days 211 days Total rainfall ...................... 33.86 in 44.89 in Amount per rainy day ................ 0.19 in 0.21 in
The year 1903 was an exceptional one, but the difference existing between the figures in the above table and the average figures in Table 9 are very marked, and serve to emphasise the necessity for close investigation in each individual case. It must be further remembered that the wettest year is not necessarily the year of the heaviest rainfalls, and it is the heavy rainfalls only which affect the design of sewerage works.
CHAPTER VIII.
STORM WATER IN SEWERS.
If the whole area of the district is not impermeable the percentage which is so must be carefully estimated, and will naturally vary in each case. The means of arriving at an estimate will also probably vary considerably according to circ.u.mstances, but the following figures, which relate to investigations recently made by the writer, may be of interest.
In the town, which has a population of 10,000 and an area of 2,037 acres, the total length of roads constructed was 74,550 lineal feet, and their average width was 36 ft, including two footpaths. The average density of the population was 4.9 people per acre. Houses were erected adjoining a length of 43,784 lineal feet of roads, leaving 30,766 lineal feet, which for distinction may be called "undeveloped"--that is, the land adjoining them was not built over. Dividing the length of road occupied by houses by the total number of the inhabitants of the town, the average length of road per head was 4.37 ft, and a.s.suming five people per house and one house on each side of the road we get ten people per two houses opposite each other.
Then 10 x 4.37 = 43.7 lineal feet of road frontage to each pair of opposite houses. After a very careful inspection of the whole town, the average area of the impermeable surfaces appertaining to each house was estimated at 675 sq. ft, of which 300 sq. ft was apportioned to the front roof and garden paths and 375 sq. ft to the back roof and paved yards. Dividing these figures by 43.71 in ft of road frontage per house, we find that the effective width of the impermeable roadway is increased by 6 ft 10 in for the front portions of each house, and by a width of 8 ft 7 in, for the back portions, making a total width of 36 ft + 2(6 ft 10 in) + 2(8 ft 7 in) = 66 ft 10 in, say 67 ft On this basis the impermeable area in the town therefore equals: 43,7841 in ft x 67 ft =2,933,528; and 30,766 lin ft x 36 ft = 1,107,576.
Total, 4,041,104 sq. ft, or 92.77 acres. As the population is 10,000 the impermeable area equals 404, say, 400 sq. ft per head, or ~ (92.77 x 100) / 2037 = 4.5 per cent, of the whole area of the town.
It must be remembered that when rain continues for long periods, ground which in the ordinary way would generally be considered permeable becomes soaked and eventually becomes more or less impermeable. Mr. D. E. Lloyd-Davies, M.Inst.C.E., gives two very interesting diagrams in the paper previously referred to, which show the average percentage of effective impermeable area according to the population per acre. This information, which is applicable more to large towns, has been embodied in Fig. 16, from which it will be seen that, for storms of short duration, the proportion of impervious areas equals 5 per cent.
with a population of 4.9 per acre, which is a very close approximation to the 4.5 per cent. obtained in the example just described.
Where the houses are scattered at long intervals along a road the better way to arrive at an estimate of the quant.i.ty of storm water which may be expected is to ascertain the average impervious area of, or appertaining to, each house, and divide it by five, so as to get the area per head. Then the flow off from any section of road is directly obtained from the sum of the impervious area due to the length of the road, and that due to the population distributed along it.
[Ill.u.s.tration: FIG. 16.--VARIATION IN AVERAGE PERCENTAGE OF EFFECTIVE IMPERMEABLE AREA ACCORDING TO DENSITY OF POPULATION.]
In addition to being undesirable from a sanitary point of view, it is rarely economical to construct special storm water drains, but in all cases where they exist, allowance must be made for any rain that may be intercepted by them. Short branch sewers constructed for the conveyance of foul water alone are usually 9in or 12 in in diameter, not because those sizes are necessary to convey the quant.i.ty of liquid which may be expected, but because it is frequently undesirable to provide smaller public sewers, and there is generally sufficient room for the storm water without increasing the size of the sewer.
If this storm water were conveyed in separate sewers the cost would be double, as two sewers would be required in the place of one. In the main sewers the difference is not so great, but generally one large sewer will be more economical than two smaller ones. Where duplicate sewers are provided and arranged, so that the storm water sewer takes the rain-water from the roads, front roofs and gardens of the houses, and the foul water sewer takes the rain-water from the back roofs and paved yards,
it was found in the case previously worked out in detail that in built-up roads a width of 36 ft + 2 (8 ft 7 in) = 53 ft 2 in, or, say, 160 sq. ft per lineal yard of road would drain to the storm water sewer, and a width of 2 (6 ft 10 in) = 13 ft 8 in, or, say, 41 sq. ft per lineal yard of road to the foul water sewer. This shows that even if the whole of the rain which falls on the impervious areas flows off, only just under 80 per cent. of it would be intercepted by the special storm water sewers. Taking an average annual rainfall of 30 in, of which 75 per cent. flows off, the quant.i.ty reaching the storm water sewer in the course of a year from each lineal
30 75 yard of road would be --- x 160 x --- = 300 cubic 12 100 feet = 1,875 gallons.
[Ill.u.s.tration: FIG. 17.--SECTION OF "LEAP WEIR" OVERFLOW]
The cost of constructing a separate surface water system will vary, but may be taken at an average of, approximately, l5s.
0d. per lineal yard of road. To repay this amount in thirty years at 4 per cent, would require a sum of 10.42d., say 10-1/2d. per annum; that is to say, the cost of taking the surface water into special
10-1/2 d. x 1000 sewers is ---------------- = 5.6, say 6d. per 1,000 1875 gallons.
If the sewage has to be pumped, the extra cost of pumping by reason of the increased quant.i.ty of surface water can be looked at from two different points of view:--
1. The net cost of the gas or other fuel or electric current consumed in lifting the water.
2. The cost of the fuel consumed plus wages, stores, etc., and a proportion of the sum required to repay the capital cost of the pumping station and machinery.