These conditions are well illustrated by a few data upon the turbidity of three Pennsylvania streams, recently collected by the author. One of these streams is a small brook having a drainage area of less than three square miles. The observations extended over a period of 47 days. During this time there were five floods, or an average of one flood in ten days. The duration of floods was less than twenty-four hours in each case. Selecting the days when the turbidity was the highest, to the number of one tenth of the whole number of days, the sum of the turbidities for these days was 67 per cent of the aggregate turbidities for the whole period. That is to say, 67 per cent of the whole amount of mud was in the water of only a tenth of the days; the water of the other nine tenths of the days contained only 33 per cent of the whole amount of turbidity. The average turbidity of the water for the flood days was eighteen times as great as the average turbidity for the remaining days.
The next stream is a considerable creek having a drainage area of 350 square miles. The observations extended over 117 days, during which time there were seven floods, or an average of one flood in 19 days. The floods lasted in each case one or two days, and the sum of the turbidities for the one tenth of the whole number of days when the water was muddiest was 55 per cent of the aggregate of all the turbidities for the period.
The last case is that of a large river, with a drainage area of over 11,000 square miles. The observations extended over a full year. In this period there were sixteen floods, each lasting from one to six days, and the sum of the turbidities for the one tenth of the whole number of days when the water was muddiest is 45 per cent of the aggregate turbidities for the year. The floods occurred on an average of once in 22 days, and the average duration was two and one half days.
The results are very striking as showing that a very large proportion of the mud is carried by the water in flood flows of comparatively short duration. They also show that in small streams the proportion of mud in the flood-flows is greater, and the average duration of floods is shorter, than in larger streams. In other words, the differences between flood- and low-water flows are greatest in small streams, and gradually become less as the size of the stream increases.
When a stream is used for water-works purposes in the usual way, a certain quantity of water is taken from the stream each day, which quantity is nearly constant, and is not dependent upon the condition of the stream, or the volume of its flow. The proportions of the total flows taken at high- and low-water stages are very different, and it thus happens that the average quality of the water taken for water-works purposes is different from the average quality of all the water flowing in the stream.
Let us assume, for example, a stream having a watershed of such a size that in times of moderate floods water from the most distant points reaches the water-works intake in twenty-four hours. Let us assume further that rainfalls of sufficient intensity to cause floods and muddy water occur, on an average, once in ten days, and that the turbidity of the water at these times reaches 1.00, and that for the rest of the time the turbidity averages 0.10. Let us assume further that at times of storms the average flow of the stream is 100 units of volume, and for the nine days between storms the average flow is 10 units of volume. We shall then have in a ten days’ period, for one day, 100 volumes of water with a turbidity of 1.00, and nine days with 10 volumes each, or a total of 90 volumes of water with a turbidity of 0.10. The total discharge of the stream will then be 190 volumes, and the average turbidity 0.57. The turbidity of 0.57 represents the average turbidity all the water flowing in the stream, or, in other words, the turbidity which would be found in a lake if all the water for ten days should flow into it and become thoroughly mixed without other change.
Now let us compute the average turbidity of the water taken from the stream for water-works purposes. The water-works require, let us say, one volume each day, and we have for the first day water with a turbidity of 1.00, and then for nine days water with a turbidity of 0.10. The average turbidity of the water taken by the water-works for the period is thus only 0.19 in place of 0.57, the average turbidity of the whole run-off.
The average turbidity of all the water flowing in the stream is thus three times as great as that of the water taken from the stream for water-works purposes.
It is often noted that with long streams the water becomes muddier farther down, and it may naturally be thought that it is because of the added erosion of the stream upon its bed in its longer course. This, of course, may be a cause, or the lower tributaries may be muddier than the upper ones, but the fact that the water taken at the lower point is more muddy than farther up is not an indication of this.
Let us take, for example, a watershed of twice the size of that assumed above, that is, so long that 48 hours will be required for the water from the most remote feeders to reach the water-works intake. Let us divide this shed into two parts, which we will assume to be equal, one of which furnishes water reaching the intake within 24 hours, and the other water reaching the intake between 24 and 48 hours. Now suppose a storm upon the watershed producing turbidities equal to those just assumed for the smaller stream. On the first day the water from the lower half of the shed, namely, 100 volumes having a turbidity of 1.00, passes the intake, but this is mixed with 10 volumes of water from the upper half of the watershed, having a turbidity of 0.10, and the total flow is thus 110 volumes of water having a turbidity of 0.92. On the second day the water from the lower half of the watershed has returned to its normal condition, and the flood-flow of the upper half of the watershed, 100 volumes with a turbidity of 1.00, is passing, and mingles with the 10 volumes from the lower half with a turbidity of 0.10, and the total flow is again 110 volumes having a turbidity of 0.92. The following eight days, until the next rain, will have flows of 20 volumes each, with turbidities of 0.10. The average turbidity of all of the water flowing off is 0.57 as before, but the water taken for water-works purposes will consist of 2 volumes of water with turbidities of 0.92, and 8 volumes with turbidities of 0.10 making 10 volumes with an average turbidity of 0.26.