The measurements of the depth of the water above the notch should be taken by a hook-gauge, as when a rule or gauge-slate is used the velocity of the water causes the latter to rise as it comes in contact with the edge of the measuring instrument and an accurate reading is not easily obtainable, and, further, capillary attraction causes the water to rise up the rule above the actual surface, and thus to show a still greater depth. When using a hook-gauge the top of the weir, as well as the notch, should be fixed level and a peg or stake fixed as far back as possible on the upstream side of the weir, so that the top of the peg is level with the top of the weir, instead of with the notch, as is the case when a rule or gauge-slate is used. The hook-gauge consists of a square rod of, say, lin side, with a metal hook at the bottom, as shown in Fig. 15, and is so proportioned that the distance from the top of the hook to the top of the rod is equal to the difference in level of the top of the weir and the sill of the notch. In using it the rod of the hook-gauge is held against the side of the gauge-peg and lowered into the water until the point of the hook is submerged. The gauge is then gently raised until the point of the hook breaks the surface of the water, when the distance from the top of the gauge-peg to the top of the rod of the hook-gauge will correspond with the depth of the water flowing over the weir.

CHAPTER VII.

RAINFALL.

The next consideration is the amount of rain-water for which provision should be made. This depends on two factors: first, the amount of rain which may be expected to fall; and, secondly, the proportion of this rainfall which will reach the sewers. The maximum rate at which the rain-water will reach the outfall sewer will determine the size of the sewer and capacity of the pumping plant, if any, while if the sewage is to be stored during certain periods of the tide the capacity of the reservoir will depend upon the total quantity of rain-water entering it during such periods, irrespective of the rate of flow.

Some very complete and valuable investigations of the flow of rain-water in the Birmingham sewers were carried out between 1900 and 1904 by Mr. D. E. Lloyd-Davies, M.Inst.C. E., the results of which are published in Vol. CLXIV., Min Proc. Inst.C.E. He showed that the quantity reaching the sewer at any point was proportional to the time of concentration at that point and the percentage of impermeable area in the district. The time of concentration was arrived at by calculating the time which the rain-water would take to flow through the longest line of sewers from the extreme boundaries of the district to the point of observation, assuming the sewers to be flowing half full; and adding to the time so obtained the period required for the rain to get into the sewers, which varied from one minute where the roofs were connected directly with the sewers to three minutes where the rain had first to flow along the road gutters. With an average velocity of 3 ft per second the time of concentration will be thirty minutes for each mile of sewer. The total volume of rain-water passing into the sewers was found to bear the same relation to the total volume of rain falling as the maximum flow in the sewers bore to the maximum intensity of rainfall during a period equal to the time of concentration. He stated further that while the flow in the sewers was proportional to the aggregate rainfall during the time of concentration, it was also directly proportional to the impermeable area. Putting this into figures, we see that in a district where the whole area is impermeable, if a point is taken on the main sewers which is so placed that rain falling at the head of the branch sewer furthest removed takes ten minutes to reach it, then the maximum flow of storm water past that point will be approximately equal to the total quantity of rain falling over the whole drainage area during a period of ten minutes, and further, that the total quantity of rainfall reaching the sewers will approximately equal the total quantity falling. If, however, the impermeable area is 25 per cent. of the whole, then the maximum flow of storm water will be 25 per cent. of the rain falling during the time of concentration, viz., ten minutes, and the total quantity of storm water will be 25 per cent. of the total rainfall.

If the quantity of storm water is gauged throughout the year it will probably be found that, on the average, only from 70 per cent. to 80 per cent. of the rain falling on the impermeable areas will reach the sewers instead of 100 per cent., as suggested by Mr. Lloyd-Davies, the difference being accounted for by the rain which is required to wet the surfaces before any flow off can take place, in addition to the rain-water collected in tanks for domestic use, rain required to fill up gullies the water level of which has been lowered by evaporation, and rain-water absorbed in the joints of the paving.

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 quantity of rain which may have to be dealt with.

It is impracticable to provide sewers to deal with the maximum quantity 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 principally 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