Chapter III: Filtering Materials

SAND.

The sand used for filtration may be obtained from the sea-shore, from river-beds or from sand-banks. It consists mainly of sharp quartz grains, but may also contain hard silicates. As it occurs in nature it is frequently mixed with clayey or other fine particles, which must be removed from it by washing before it is used. Some of the New England sands, however, as that used for the Lawrence City filter, are so clean that washing would be superfluous.

The grain size of the sand best adapted to filtration has been variously stated at from 1/8 to 1 mm., or from 0.013 to 0.040 inch. The variations in the figures, however, are due more to the way that the same sand appears to different observers than to actual variations in the size of sands used, which are but a small fraction of those indicated by these figures.

As a result of experiments made at the Lawrence Experiment Station[4] we have a standard by which we can definitely compare various sands. The size of a sand-grain is uniformly taken as the diameter of a sphere of equal volume, regardless of its shape. As a result of numerous measurements of grains of Lawrence sands, it is found that when the diameter, as given above, is 1, the three axes of the grain, selecting the longest possible and taking the other two at right angles to it, are, on an average, 1.38, 1.05, and 0.69, respectively and the mean diameter is equal to the cube root of their product.

It was also found that in mixed materials containing particles of various sizes the water is forced to go around the larger particles and through the finer portions which occupy the intervening spaces, so that it is the finest portion which mainly determines the character of the sand for filtration. As a provisional basis which best accounts for the known facts, the size of grain such that 10 per cent by weight of the particles are smaller and 90 per cent larger than itself, is considered to be the _effective size_. The size so calculated is uniformly referred to in speaking of the size of grain in this work.

Another important point in regard to a material is its degree of uniformity—whether the particles are mainly of the same size or whether there is a great range in their diameters. This is shown by the _uniformity coefficient_, a term used to designate the ratio of the size of the grain which has 60 per cent of the sample finer than itself to the size which has 10 per cent finer than itself.

The frictional resistance of sand to water when closely packed, with the pores completely filled with water and in the entire absence of clogging, was found to be expressed by the formula

_v_ = _cd_^2(_h_/_l_)(_t_ Fah. + 10°)/60,

where _v_ is the velocity of the water in meters daily in a solid column
of the same area as that of the sand, or approximately in
million gallons per acre daily;
_c_ is an approximately constant factor;
_d_ is the effective size of sand grain in millimeters;
_h_ is the loss of head (Fig. 3);
_l_ is the thickness of sand through which the water passes;
_t_ is the temperature (Fahr.).

TABLE SHOWING RATE AT WHICH WATER WILL PASS THROUGH EVEN-GRAINED AND CLEAN SANDS OF THE STATED GRAIN SIZES AND WITH VARIOUS HEADS AT A TEMPERATURE OF 50°.

-------+--------------------------------------------------------------
| Effective Size in Millimeters 10 per cent finer than:
_h_/_l_+------+------+-------+--------+--------+--------+-------+-----
| 0.10 | 0.20 | 0.30 | 0.35 | 0.40 | 0.50 | 1.00 | 3.00
-------+------+------+-------+--------+--------+--------+-------+-----
| | | Million Gallons per Acre daily. | |
.001 | .01 | .04 | .10 | .13 | .17 | .27 | 1.07 | 9.63
.005 | .05 | .21 | .48 | .65 | .85 | 1.34 | 5.35 |48.15
.010 | .11 | .43 | .96 | 1.31 | 1.71 | 2.67 | 10.70 |96.30
.050 | .54 | 2.14 | 4.82 | 6.55 | 8.55 | 13.40 | 53.50 |
.100 | 1.07 | 4.28 | 9.63 | 13.10 | 17.10 | 26.70 |107.00 |
1.000 |10.70 |42.80 | 96.30 | 131.00 | 171.00 | 267.00 | |
-------+------+------+-------+--------+--------+--------+-------+-----

The above table is computed with the value _c_ taken as 1000, this being approximately the values deduced from the earliest experiments. More recent and extended data have shown that the value of _c_ is not entirely constant, but depends upon the uniformity coefficient, upon the shape of the sand grains, upon their chemical composition, and upon the cleanliness and closeness of packing of the sand. The value may be as high as 1200 for very uniform, and perfectly clean sand, and maybe as low as 400 for very closely packed sands containing a good deal of alumina or iron, and especially if they are not quite clean. The friction is usually less in new sand than in sand which has been in use for some years. In making computations of the frictional resistance of filters, the average value of _c_ may be taken at from 700 to 1000 for new sand, and from 500 to 700 for sand which has been in use for a number of years.

The value of _c_ decreases as the uniformity coefficient increases. With ordinary filter sands with uniformity coefficients of 3 or less the differences are not great. With mixed sands having much higher uniformity coefficients, lower and less constant values of _c_ are obtained, and the arrangement of the particles becomes a controlling factor in the increase in friction.

The friction of the surface layer of a filter is often greater than that of all the sand below the surface. It must be separately computed and added to the resistances computed by the formula, as it depends largely upon other conditions than those controlling the resistance of the sand.

While the value of _c_ is thus not entirely constant, it can be estimated with approximate accuracy for various conditions, from a knowledge of the composition, condition, and cleanliness of the sand, and closeness of packing.

The following table shows the quantity of water passing sands at different temperatures. This table was computed with temperature factors as given above, which were based upon experiments upon the flow of water through sands, checked by the coefficients obtained from experiments with long capillary tubes entirely submerged in water of the required temperature.

RELATIVE QUANTITIES OF WATER PASSING AT DIFFERENT TEMPERATURES.

32° 0.70
35° 0.75
38° 0.80
41° 0.85
44° 0.90
47° 0.95
50° 1.00
53° 1.05
56° 1.10
59° 1.15
62° 1.20
65° 1.25
68° 1.30
71° 1.35
74° 1.40
77° 1.45

The effect of temperature upon the passage of water through sands and soils has been further discussed by Prof. L. G. Carpenter, _Engineering News_, Vol. XXXIX, p. 422. This article reviews briefly the literature of the subject, and refers at length to the formula of Poiseuille, published in the _Memoires des Savants Etrangers_, Vol. XI, p. 433 (1846). This formula, in which the quantity of water passing at 0.0° Cent., is taken as unity, is as follows:

Temperature factor = 1 + 0.033679_t_ + 0.000221_t_^2.

The results obtained by this formula agree very closely with those given in the above table throughout the temperature range for which computations are most frequently required. At the higher and lower temperatures the divergencies are greater, as is shown in a communication in the _Engineering News_, Vol. XL, p. 26.

The quantity of water passing at a temperature of 50° Fahr. is in many respects more convenient as a standard than the quantity passing at the freezing-point. Near the freezing-point, owing to molecular changes in the water, the changes in its action are rapid, and the results are less certain, and also 50° Fahr. is a much more convenient temperature for precise experiments than is the freezing point.

SANDS USED IN EUROPEAN FILTERS.

To secure definite information in regard to the qualities of the sands actually used in filtration, a large number of European works were visited in 1894, and samples of sand were collected for analysis. These samples were examined at the Lawrence Experiment Station by Mr. H. W. Clark, the author’s method of analysis described in Appendix III being used. In the following table, for the sake of compactness, only the leading points of the analyses, namely, effective size, uniformity coefficient, and albuminoid ammonia, are given. On page 28 full analyses of some samples from a few of the leading works are given.

ANALYSES OF SANDS USED IN WATER FILTRATION.

---------------------+---------+--------+--------+--------------------
|Effective| | Albu- |
|Size; 10%| Uni- | minoid |
| Finer |formity | Ammo- |
Source. | than | Coeffi-| nia. | Remarks.
|(Milli- | cient. |Parts in|
| meters).| |100,000.|
---------------------+---------+--------+--------+--------------------
London, E. London Co.| 0.44 | 1.8 | 0.45 |New sand, never
| | | | used or washed.
London, E. London Co.| 0.39 | 2.1 | 26.20 |Dirty sand, very
| | | | old.
London, E. London Co.| 0.37 | 2.0 | 8.60 |Same, washed by
| | | | hand.
London, Grand Junc. | 0.26 | 1.9 | 1.90 |Sand from rough
| | filter.
London, Grand Junc. | 0.40 | 3.5 | 10.00 |Old sand in final
| | | | filter.
London, Grand Junc. | 0.41 | 3.7 | 2.70 |Freshly washed old
| | | | sand.
London, Southw’k & V.| 0.38 | 3.5 | 5.00 |Freshly washed old
| | | | sand.
London, Southw’k & V.| 0.30 | 1.8 | 2.80 |Freshly washed new
| | | | sand.
London, Lambeth | 0.36 | 2.3 | 2.60 |Freshly washed old
| | | | sand.
London, Lambeth | 0.36 | 2.4 | 0.35 |New unused sand,
| | | washed.
London, Lambeth | 0.25 | 1.7 | 0.70 |New extremely fine
| | | | sand.
London, Chelsea | 0.36 | 2.4 | 2.10 |Freshly washed old
| | | | sand.
Middlesborough | 0.42 | 1.6 | 17.60 |Dirty sand, ordinary
| | | | scraping.
Middlesborough | 0.43 | 1.6 | 7.30 |Same, after washing.
Birmingham | 0.29 | 1.9 | 33.20 |Dirty sand.
Birmingham | 0.29 | 1.9 | 7.20 |Sand below surface
| | | | of filter.
Reading | 0.30 | 2.5 | 4.00 |Dirty sand.
Reading | 0.22 | 2.0 | 1.50 |Same, after washing.
Antwerp | 0.38 | 1.6 | 7.80 |Dirty sand.
Antwerp | 0.39 | 1.6 | 3.40 |Same, after washing.
Hamburg | 0.28 | 2.5 | 8.50 |Dirty sand.
Hamburg | 0.31 | 2.3 | 0.80 |Same, after washing.
Hamburg | 0.34 | 2.2 | 7.90 |Dirty sand, another
| | | | sample.
Hamburg | 0.30 | 2.0 | 0.90 |Same, after washing
| | | | drums.
Hamburg | 0.34 | 2.3 | 1.50 |Same, after washing
| | | | ejectors.
Altona | 0.32 | 2.0 | 9.00 |Dirty sand, old
| | | | filters.
Altona | 0.37 | 2.0 | 1.50 |Same, after washing.
Altona | 0.33 | 2.8 | 0.50 |Washed sand for new
| | | | filters.
Berlin, Stralau | 0.33 | 1.9 | 12.20 |Dirty sand-pile.
Berlin, Stralau | 0.35 | 1.7 | 4.50 |Filter No. 6,
| | | | 3″ below surface.
Berlin, Stralau | 0.34 | 1.7 | 6.30 |Filter No. 7,
| | | | 3″ below surface.
Berlin, Stralau | 0.35 | 1.7 | 4.00 |Filter No. 10,
| | | | 3″ below surface.
Berlin, Tegel | 0.38 | 1.6 | 11.00 |Dirty sand, old
| | | | filters.
Berlin, Tegel | 0.38 | 1.5 | 2.80 |Same, after washing,
| | | | old filters.
Berlin, Tegel | 0.35 | 1.6 | 3.20 |Same, after washing,
| | | | new filters.
Berlin, Müggel | 0.35 | 1.8 | 0.80 |Sand from filters
| | | | below surface.
Berlin, Müggel | 0.33 | 2.0 | 6.30 |Dirty sand, ordinary
| | | | scraping.
Berlin, Müggel | 0.34 | 2.0 | 15.30 |Dirty sand, another
| | | | sample.
Charlottenburg | 0.40 | 2.3 | 7.20 |Dirty sand.
Chemnitz | 0.35 | 2.6 | 0.20 |New sand not yet
| | | | used.
Magdeburg | 0.39 | 2.0 | 9.50 |Dirty sand.
Magdeburg | 0.40 | 2.0 | 2.80 |Same, after washing.
Breslau | 0.39 | 1.8 | 1.40 |Normal new sand.
Budapest | 0.20 | 2.0 | 0.80 |New washed Danube
| | | | sand.
Zürich | 0.28 | 3.2 | 6.20 |Dirty sand.
Zürich | 0.30 | 3.1 | 1.50 |Same, after washing.
Hague | 0.19 | 1.6 | 0.70 |Dune-sand used for
| | | | filtration.
Schiedam | 0.18 | 1.6 | 5.60 |Dune-sand used for
| | | | filtration; dirty.
Schiedam | 0.31 | 1.5 | 13.50 |River-sand; dirty.
Amsterdam | 0.17 | 1.6 | 2.40 |Dune-sand.
Rotterdam | 0.34 | 1.5 | 2.30 |River-sand; new.
Liverpool, Rivington | 0.43 | 2.0 | 0.76 |Sand from bottom of
| | | | filter.
Liverpool, Rivington | 0.32 | 2.5 | 1.00 |New sand unwashed
| | | | and unscreened.
Liverpool, Rivington | 0.43 | 2.7 | 4.10 |Washed sand which
| | | | has been in use
| | | | 30 to 40 years.
Liverpool, Oswestry | 0.30 | 2.6 | 9.40 |Dirty sand.
Liverpool, Oswestry | 0.31 | 4.7 | 2.20 |Same, after washing.
---------------------+---------+--------+--------+--------------------

NOTE.—It is obvious that in case the sands used at any place are not
always of the same character, as is shown to be the case by different
samples from some of the works, the examination of such a limited
number of samples as the above from each place is entirely inadequate
to establish accurately the sizes of sand used at that particular
place, or to allow close comparisons between the different works, and
for this reason no such comparisons will be made. The object of these
investigations was to determine the sizes of the sands commonly used
in Europe, and, considering the number and character of the different
works represented, it is believed that the results are ample for this
purpose.

The English and most of the German sands are washed, even when entirely new, before being used, to remove fine particles. At Breslau, however, sand dredged from the river Oder is used in its natural state, and new sand is used for replacing that removed by scraping. At Budapest, Danube sand is used in the same way, but with a very crude washing, and it is said that only new unwashed sand is used at Warsaw.

In Holland, so far as I learned, no sand is washed, but new sand is always used for refilling. At most of the works visited dune-sand with an effective size of only 0.17 to 0.19 mm. is used, and this is the finest sand which I have ever found used for water filtration on a large scale. It should be said, however, that the waters filtered through these fine sands are fairly clear before filtration, and are not comparable to the turbid river-waters often filtered elsewhere, and their tendency to choke the filters is consequently much less. At Rotterdam and Schiedam, where the raw water is drawn from the Maas, as the principal stream of the Rhine is called in Holland, river-sand of much larger grain size is employed. It is obtained by dredging in the river and is never washed, new sand always being employed for refilling.

The average results of the complete analyses of sands from ten leading works are shown in the table on page 28. These figures are the average of all the analyses for the respective places, except that one sample from the Lambeth Co., which was not a representative one, was omitted.

The London companies were selected for this comparison both on account of their long and favorable records in filtering the polluted waters of the Thames and Lea, and because they are subject to close inspection; and there is ample evidence that the filtration obtained is good—evidence which is often lacking in the smaller and less closely watched works. For the German works Altona was selected because of its escape from cholera in 1892, due to the efficient action of its filters, and Stralau because of its long and favorable record when filtering the much-polluted Spree water. These two works also have perhaps contributed more to the modern theories of filtration than all the other works in existence. The remaining works are included because they are comparatively new, and have been constructed with the greatest care and attention to details throughout, and the results obtained are most carefully recorded.

Some of the most interesting of these results are shown graphically on page 29. The method of plotting is that described in Appendix III.

TABLE SHOWING THE AVERAGE PER CENT OF THE GRAINS FINER THAN VARIOUS SIZES IN SANDS FROM LEADING WORKS.

--------------+----------------------------------------------------
| Per Cent by Weight Finer than
+------+------+------+-----+-----+-----+-----+-------
|0.106 |0.186 |0.316 |0.46 |0.93 |2.04 |3.89 |5.89
| mm. | mm. | mm. | mm. | mm. | mm. | mm. | mm.
--------------+------+------+------+-----+-----+-----+-----+-------
East London | 0.2 | 0.5 | 3.6 |22.2 |69.7 |89.8 |95.0 |99.0
Grand Junction| 0 | 0.2 | 3.1 |17.4 |47.1 |68.2 |84.7 |93.6
Southwark and | | | | | | | |
Vauxhall | | 0.7 | 8.0 |34.1 |69.7 |83.5 |90.0 |94.0
Lambeth | 0 | 0.5 | 5.5 |26.6 |63.0 |79.2 |88.0 |94.3
Chelsea | 0 | 0.1 | 5.0 |28.6 |63.0 |76.7 |86.0 |93.6
Hamburg | 0.2 | 1.5 |10.9 |33.2 |74.4 |95.7 |99.5 |
Altona | 0.1 | 1.1 | 7.8 |28.7 |72.1 |92.1 |95.8 |
Stralau | | 0.3 | 7.0 |37.3 |86.9 |95.4 |97.6 |
Tegel | | 0.2 | 4.5 |35.4 |94.3 |98.5 |99.1 |
Müggel | 0.1 | 0.5 | 7.9 |33.6 |79.7 |94.3 |98.5 |
+------+------+------+-----+-----+-----+-----+-------
Average of all| 0.06 | 0.56 | 6.33 |29.71|71.99|87.34|93.42|(97.45)
--------------+------+------+------+-----+-----+-----+-----+-------

AVERAGE EFFECTIVE SIZE, UNIFORMITY COEFFICIENT, AND ALBUMINOID AMMONIA IN SANDS FROM TEN LEADING WORKS.

I. LONDON FILTERS.
----------------------+--------------+------------+-------------------
| Effective | Uniformity |Albuminoid Ammonia.
| Size; 10% |Coefficient.+------------+------
| Finer than | | Dirty Sand.|Washed
|(Millimeters).| | | Sand.
----------------------+--------------+------------+------------+------
East London | 0.40 | 2.0 | 26.00 | 8.60
Grand Junction | 0.40 | 3.6 | 10.00 | 2.70
Southwark and Vauxhall| 0.34 | 2.5 | | 3.90
Lambeth | 0.36 | 2.4 | | 2.60
Chelsea | 0.36 | 2.4 | | 2.10
+--------------+------------+------------+------
Average | 0.37 | 2.6 | 18.00 | 3.98
----------------------+--------------+------------+------------+------

II. GERMAN WORKS.
----------------------+--------------+------------+------------+------
Stralau | 0.34 | 1.7 | 12.20 | 4.00
Tegel | 0.37 | 1.6 | 11.00 | 3.00
Müggel | 0.34 | 2.0 | 10.80 | 0.80
Altona | 0.34 | 2.3 | 9.00 | 1.50
Hamburg | 0.31 | 2.3 | 8.20 | 1.07
+--------------+------------+------------+------
Average | 0.34 | 2.0 | 10.25 | 2.07
----------------------+--------------+------------+------------+------

[_To face page 28._]]

The averages show the effective size of the English sands to be slightly greater than that of the German sands—0.37 instead of 0.34 mm.—but the difference is very small. The entire range for the ten works is only from 0.31 to 0.40 mm., and these may be taken as the ordinary limits of effective size of the sands employed in the best European works. The average for the other sixteen works given above, including dune-sands, is 0.31 mm., or, omitting the dune-sands, 0.34 mm.

It is important that filter sands should be free from lime. When water is filtered through such sands, no increase in hardness results. When, however, water is filtered through sand containing lime, some of it is usually dissolved and the water is made harder. The amount of lime taken up in this way depends both upon the character of the sand, and upon the solvent power of the water; and it does not necessarily follow that a sand containing lime cannot be used for filtration, but a sand nearly free from lime is to be preferred.

The presence of lime in sand can usually be detected by moistening it with hydrochloric acid. The evolution of gas shows the presence of lime. Some idea of the amount of lime can be obtained from the amount of gas given off, and the appearance of the sample after the treatment, but chemical analysis is necessary to determine correctly the amount.

Experiments with filters at Pittsburg were made with sand containing 1.3 per cent of lime, the result being that the hardness of the water was increased about one part in 100,000; but the amount of lime in the sand was so small that it would be washed out after a time, and then the hardening effect would cease. Larger amounts of lime would continue their action for a number of years and would be more objectionable.

Turning to the circumstances which influence the selection of the sand size, we find that both the quality of the effluent obtained by filtration and the cost of filtration depend upon the size of the sand-grains.

With a fine sand the sediment layer forms more quickly and the removal of bacteria is more complete, but, on the other hand, the filter clogs quicker and the dirty sand is more difficult to wash, so that the expense is increased.

EFFECT OF SIZE OF GRAIN UPON EFFICIENCY OF FILTRATION.

It is frequently stated that it is only the sediment layer which performs the work of filtration, and that the sand which supports it plays hardly a larger part than does the gravel which carries the sand, and under some circumstances this is undoubtedly the case. Nevertheless sand in itself, without any sediment layer, especially when not too coarse and not in too thin layers, has very great purifying powers, and, in addition, acts as a safeguard by positively preventing excessive rates of filtration on account of its frictional resistance. As an illustration take the case of a filter of sand with an effective size of 0.35 mm. and the minimum thickness of sand allowed by the German Board of Health, namely, one foot, and let us suppose that with clogging the loss of head has reached two feet to produce the desired velocity of 2.57 million gallons per acre daily. Suppose now that by some accident the sediment layer is suddenly broken or removed from a small area, the water will rush through this area, until a new sediment layer is formed, at a rate corresponding to the size, pressure, and depth of the sand, or 260 million gallons per acre daily—a hundred times the standard rate. Under these conditions the passing water will not be purified, but will pollute the entire effluent from the filter. Under corresponding conditions, with a deep filter of fine sand, say with an effective size of 0.20 mm. and 5 feet deep, the resulting rate would be only 17 million gallons per acre daily, or less than seven times the normal, and with the water passing through the full depth of fine sand, the resulting deterioration in the effluent before the sand again became so clogged as to reduce the rate to nearly the normal, would be hardly appreciable.

The results at Lawrence have shown that with very fine sands 0.09 and 0.14 mm., and 4 to 5 feet deep, with the quantity of water which can practically be made to pass through them, it is almost impossible to drive more than an insignificant fraction of the bacteria into the effluent. Even when the sands are entirely new, or have been scraped or disturbed in the most violent way, the first effluent passing, before the sediment layer could have been formed, is of good quality. Still finer materials, 0.04 to 0.06 mm., as far as could be determined, secured the absolute removal of all bacteria, but the rates of filtration which were possible were so low as to preclude their practical application.

With coarser sands, as long as the filter is kept at a steady rate of filtration, without interruptions of any kind, entirely satisfactory results are often obtained, although never quite so good as with the finer sands. Thus at Lawrence the percentages of bacteria (_B. prodigiosus_) appearing in the effluents under comparable conditions were as follows:

1892 1893
With effective grain size 0.38 mm .... 0.16
With effective grain size 0.29 mm .... 0.16
With effective grain size 0.26 mm .... 0.10
With effective grain size 0.20 mm 0.13 0.01
With effective grain size 0.14 mm 0.04 0.03
With effective grain size 0.09 mm 0.02 0.02

We may thus conclude that fine sands give normally somewhat better effluents than coarser ones, and that they are much more likely to give at least a tolerably good purification under unusual or improper conditions.

EFFECT OF GRAIN SIZE UPON FREQUENCY OF SCRAPING.

The practical objection to the use of fine sand is that it becomes rapidly clogged, so that filters require to be scraped at shorter intervals, and the sand washing is much more difficult and expensive. The quantities of water filtered between successive scrapings at Lawrence in millions of gallons per acre under comparable conditions have been as follows:

1892 1893
Effective size of sand grain 0.38 mm .... 79
Effective size of sand grain 0.29 mm .... 70
Effective size of sand grain 0.26 mm .... 57
Effective size of sand grain 0.20 mm 58 ....
Effective size of sand grain 0.14 mm 45 49
Effective size of sand grain 0.09 mm 24 14

The increase in the quantities passed between scrapings with increasing grain size is very marked.

With the fine sands, the depth to which the sand becomes dirty is much less than with the coarse sands, but as it is not generally practicable to remove a layer of sand less than about 0.6 inch thick, even when the actual clogged layer is thinner than this, the full quantity of sand has to be removed; and the quantities of sand to be removed and washed are inversely proportional to the quantities of water filtered between scrapings. On the other hand, with very coarse sands the sediment penetrates the sand to a greater depth than the 0.6 inch necessarily removed, so that a thicker layer of sand has to be removed, which may more than offset the longer interval. This happens occasionally in water-works, and a sand coarse enough to allow it occur is always disliked by superintendents, and is replaced with finer sand as soon as possible. It is obvious that the minimum expense for cleaning will be secured with a sand which just does not allow this deep penetration, and I am inclined to think that the sizes of the sands in use have actually been determined more often than otherwise in this way, and that the coarsest samples found, having effective sizes of about 0.40 mm., represent the practical limit to the coarseness of the sand, and that any increase above this size would be followed by increased expense for cleaning as well as by decreased efficiency.

SELECTION OF SAND.

In selecting a sand for filtration, when it is considered that repeated washings will remove some of the finest particles, and so increase slightly the effective size, a new sand coarser than 0.35 mm. would hardly be selected. Perhaps 0.20 might be given as a suitable lower limit. For comparatively clear lake- or reservoir-waters a finer sand could probably be used than would be the case with a turbid river-water. A mixed sand having a uniformity coefficient above 3.0 would be difficult to wash without separating it into portions of different sizes, and, in general, the lower the coefficient, that is, the more uniform the grain sizes, the better. Great pains should be taken to have the sand of the same quality throughout, especially in the same filter, as any variations in the grain sizes would lead to important variations in the velocity of filtration, the coarser sands passing more than their share of water (in proportion to the square of the effective sizes) and with reduced efficiency.

At Lawrence a sufficient quantity of natural sand was found of the grade required; but where suitable material cannot be so obtained it is necessary to use other methods. A mixed material can be screened from particles which are too large, and can be washed to free it from its finer portions, and in this way a good sand can be prepared, if necessary, from what might seem to be quite unpromising material. The methods of sand-washing will be described in Chapter V.

THICKNESS OF THE SAND LAYER.

The thickness of the sand layer is made so great that when it is repeatedly scraped in cleaning the sand will not become too thin for good filtration for a considerable time. When this occurs the removed sand must be replaced with clean sand. The original thickness of the sand in European filters is usually from 24 to 48 inches, thicknesses between 30 and 40 inches being extremely common, and this is reduced before refilling to from 12 to 24 inches. The Imperial Board of Health of Germany has fixed 12 inches as a limit below which the sand should never be scraped, and a higher limit is recommended wherever possible.

A thick sand layer has the same steadying action as a fine sand, and tends to prevent irregularities in the rate of filtration in proportion to its frictional resistance, and that without increasing the frequency of cleaning; but, on the other hand, it increases the necessary height of the filter, throughout, and consequently the cost of construction.

In addition to the steadying effect of a deep sand layer, some purification takes place in the lower part of the sand even with a good sediment layer on the surface, and the efficiency of deep filters is greater than that of shallow ones.

Layers of finer materials, as fine sand or loam, in the lower part of a filter, which would otherwise give increased efficiency without increasing the operating expenses, cannot be used. Their presence invariably gives rise sooner or later to sub-surface clogging at the point of junction with the coarser sand, as has been found by repeated tests at Lawrence as well as in some of the Dutch filters where such layers were tried; and as there is no object in putting a coarser sand under a finer, the filter sand is best all of the same size and quality from top to bottom.

UNDERDRAINING.

The underdrains of a filter are simply useful for collecting the filtered water; they play no part in the purification. One of the first requirements of successful filtration is that the rate of filtration shall be practically the same in all parts of the filter. This is most difficult to secure when the filter has just been cleaned and the friction of the sand layer is at a minimum. If the friction of the water in entering and passing through the underdrains is considerable, the more remote parts of the filters will work under less pressure, and will thus do less than their share of the work, while the parts near the outlet will be overtaxed, and filtering at too high rates will yield poor effluents.

To avoid this condition the underdrains must have such a capacity that their frictional resistance will be only a small fraction of the friction in the sand itself just after cleaning.

GRAVEL LAYERS.

The early filters contained an enormous quantity of gravel, but the quantity has been steadily reduced in successive plants. Thus in 1866 Kirkwood, as a result of his observations, recommended the use of a layer four feet thick, and in addition a foot of coarse sand, while at the present time new filters rarely have more than two feet of gravel. Even this quantity seems quite superfluous, when calculations of its frictional resistance are made. Thus a layer of gravel with an effective size of 20 mm.[5] (which is much finer than that generally employed) only 6 inches thick will carry the effluent from a filter working at a rate of 2.57 million gallons per acre daily for a distance of 8 feet (that is, with underdrains 16 feet apart), with a loss of head of only 0.001 foot, and for longer distances tile drains are cheaper than gravel. To prevent the sand from sinking into the coarse gravel, intermediate sizes of gravel must be placed between, each grade being coarse enough so that there is no possibility of its sinking into the layer below. The necessary thickness of these intermediate layers is very small, the principal point being to have a layer of each grade at every point. Thus on the 6 inches of 20 mm. gravel mentioned above, three layers of two inches each, of 8 and 3 mm. gravel and coarse sand, with a total height of six inches, or other corresponding and convenient depths and sizes, would, if carefully placed, as effectually prevent the sinking of the filter sand into the coarse gravel as the much thicker layers used in the older plants.

The gravel around the drains should receive special attention. Larger stones can be here used with advantage, taking care that adequate spaces are left for the entrance of the water into the drains at a low velocity, and to make everything so solid in this neighborhood that there will be no chance for the stones to settle which might allow the sand to reach the drains.

[_To face page 36._]]

At the Lawrence filter, at Königsberg in Prussia, at Amsterdam and other places, the quantity of gravel is reduced by putting the drains in trenches, so that the gravel is reduced from a maximum thickness at the drain to nothing half way between drains. The economy of the arrangement, however, as far as friction is concerned is not so great as would appear at first sight, and the cost of the bottom may be increased; but on the other hand it gives a greater depth of gravel for covering the drains with a small total amount of gravel.

As even a very small percentage of fine material is capable of getting in the narrow places and reducing the carrying power of the gravel, it is important that all such matters should be carefully removed by washing before putting the gravel in place. In England and Germany gravel is commonly screened for use in revolving cylinders of wire-cloth of the desired sizes, on which water is freely played from numerous jets, thus securing perfectly clean gravel. In getting gravel for the Lawrence filter, an apparatus was used, in which advantage was taken of the natural slope of the gravel bank to do the work, and the use of power was avoided. The respective grades of gravel obtained were even in size, and reasonably free from fine material, but it was deemed best to wash them with a hose before putting them in the filter.

To calculate the frictional resistance of water in passing gravel, we may assume that for the very low velocities which are actually found in filters the quantity of water passing varies directly with the head, which for these velocities is substantially correct, although it would not be true for higher rates, especially with the coarser gravels.[6] In the case of parallel underdrains the friction from the middle point between drains to the drains may be calculated by the formula:

Total head = (1/2)[(Rate of filtration × (1/2 distance between drains)^2)/(Average depth of gravel × discharge coefficient)].

The discharge coefficient for any gravel is 1000 times the quantity

of water which will pass when _h_/_l_ is 1/1000 expressed in million gallons per acre daily. The approximate values of this coefficient for different-sized gravels are as follows:

VALUES OF DISCHARGE COEFFICIENT.

For gravel with effective size 5 mm _c_ = 23,000
For gravel with effective size10 mm _c_ = 65,000
For gravel with effective size15 mm _c_ = 110,000
For gravel with effective size20 mm _c_ = 160,000
For gravel with effective size25 mm _c_ = 230,000
For gravel with effective size30 mm _c_ = 300,000
For gravel with effective size35 mm _c_ = 390,000
For gravel with effective size40 mm _c_ = 480,000

Example: What is the loss of head in the gravel at a rate of filtration of 2 million gallons per acre daily, with underdrains 20 feet apart, where the supporting gravel has an effective size of 35 millimeters, and is uniformly 1 ft. deep?

Total head = (1/2)[(2 × 10^2)/(1 × 390,000)] = .000256 ft.

The total friction would be the same with the same average depth of gravel whether it was uniformly 1 foot deep, or decreasing from 1.5 at the drains to 0.5 in the middle, or from 2.0 to 0. The reverse case with the gravel layer thicker in the middle than at the drains does not occur and need not be discussed.

The depth of gravel likely to be adopted as a result of this calculation, when the drains are not too far apart, will be much less than that actually used in most European works, but as the two feet or more there employed are, I believe, simply the result of speculation, there is no reason for following the precedent where calculations show that a smaller quantity is adequate.

The reason for recommending a thin lower layer of coarse gravel, which alone is assumed to provide for the lateral movement of the water, is that if more than about six inches of gravel is required to give a satisfactory resistance, it will almost always be cheaper to use more drains instead of more gravel; and the reason for recommending thinner upper layers for preventing the sand from settling into the coarse gravel is that no failures of this portion of filters are on record, and in the few instances where really thin layers have been used the results have been entirely satisfactory. In Königsberg filters were built by Frühling,[7] in which the sand was supported by five layers of gravel of increasing sizes, respectively 1.2, 1.2, 1.6, 2.0, 3.2, or, together, 9.2 inches thick, below which there were an average of five inches of coarse gravel. These were examined after eight years of operation and found to be in perfect order.

At the Lawrence Experiment Station filters have been repeatedly constructed with a total depth of supporting gravel layers not exceeding six inches, and among the scores of such filters there has not been a single failure, and so far as they have been dug up there has never been found to have been any movement whatever of the sand into the gravel. The Lawrence city filter, built with corresponding layers, has shown no signs of being inadequately supported. In arranging the Lawrence gravel layers care has always been taken that no material should rest on another material more than three or four times as coarse as itself, and that each layer should be complete at every point, so that by no possibility could two layers of greater difference in size come together. And it is believed that if this is carefully attended to, no trouble need be anticipated, however thin the single layers may be.

UNDERDRAINS.

The most common arrangement, in other than very small filters, is to have a main drain through the middle of the filter, with lateral drains at regular intervals from it to the sides. The sides of the main drain are of brick, laid with open joints to admit water freely, and the top is usually covered with stone slabs. The lateral drains may be built in the same way, but tile drains are also used and are cheaper. Care must be taken with the latter that ample openings are left for the admission of water at very low velocities. It is considered desirable to have these drains go no higher than the top of the coarsest gravel; and this will often control the depth of gravel used. If they go higher, the top must be made tight to prevent the entrance of the fine gravels or sand. Sometimes they are sunk in part or wholly (especially the main drain) below the floor of the filter. With gravel placed in waves, that is, thicker over the drains than elsewhere, as mentioned above, the drains are covered more easily than with an entirely horizontal arrangement. When this is done, the floor of the filter is trenched to meet the varying thickness of gravel, so that the top of the latter is level, and the sand has a uniform thickness.

Many filters (Lambeth, Brunswick, etc.) are built with a double bottom of brick, the upper layer of which, with open joints, supports the gravel and sand, and is itself supported by numerous small arches or other arrangements of brick, which serve to carry the water to the outlet without other drains. This arrangement allows the use of a minimum quantity of gravel, but is undoubtedly more expensive than the usual form, with only the necessary quantity of gravel; and I am unable to find that it has any corresponding advantages.

The frictional resistance of underdrains requires to be carefully calculated; and in doing this quite different standards must be followed from those usually employed in determining the sizes of water-pipes, as a total frictional resistance of only a few hundredths of a foot, including the velocity head, may cause serious irregularities in the rate of filtration in different parts of the filter.

The sizes of the underdrains differ very widely in proportion to the sizes of the filters in European works, some of them being excessively large, while in other cases they are so small as to suggest a doubt as to their allowing uniform rates of filtration, especially just after cleaning.

I would suggest the following rules as reasonably sure to lead to satisfactory results without making an altogether too lavish provision: In the absence of a definite determination to run filters at some other rate, calculate the drains for the German standard rate of a daily column of 2.40 meters, equal to 2.57 million gallons per acre daily. This will insure satisfactory work at all lower rates, and no difficulty on account of the capacity of the underdrains need be then anticipated if the rate is somewhat exceeded. The area for a certain distance from the main drain depending upon the gravel may be calculated as draining directly into it, provided there are suitable openings, and the rest of the area is supposed to drain to the nearest lateral drain.

In case the laterals are round-tile drains I would suggest the following limits to the areas which they should be allowed to drain:

Diameter of Drain. To Drain an Area not Corresponding Velocity of
Exceeding Water in Drain.
4 inches 290 square feet. 0.30 foot.
6 inches 750 square feet. 0.35 foot.
8 inches 1530 square feet. 0.40 foot.
10 inches 2780 square feet. 0.46 foot.
12 inches 4400 square feet. 0.51 foot.

And for larger drains, including the main drains, their cross-sections at any point should be at least 1/6000 of the area drained, giving a velocity of 0.55 foot per second with the rate of filtration mentioned above.

The total friction of the underdrains from the most remote points to the outlet will be friction in the gravel, plus friction in the lateral drains, plus the friction in main drain, plus the velocity head.

I have calculated in this way the friction of one of the Hamburg filters for the rate of 1,600,000 gallons per acre daily at which it is used. The friction was calculated for each section of the drains separately, so that the friction from intermediate points was also known. Kutter’s formula was used throughout with _n_ = 0.013. On the accompanying plan of the filter I have drawn the lines of equal frictional resistance from the junction of the main drain with the last laterals. My information was incomplete in regard to one or two points, so that the calculation may not be strictly accurate, but it is nearly so and will illustrate the principles involved.

[_To face page 42._]
]

The extreme friction of the underdrains is 11 millimeters = 0.036 foot.

The frictional resistance of the sand 39 inches thick, effective size 0.32 mm. and rate 1.60 million gallons per acre daily, when absolutely free from clogging, is by the formula, page 21, 15mm., or .0490 foot, when the temperature is 50°. Practically there is some matter deposited upon the surface of the sand before filtration starts, and further, after the first scraping, there is some slight clogging in the sand below the layer removed by scraping. We can thus safely take the minimum frictional resistance of the sand including the surface layer at .07 foot. The average friction of the underdrains for all points is about .023 foot and the friction at starting will be .07 + .023 = .093 foot (including the friction in the last section to the effluent well where the head is measured, .100 foot, but the friction beyond the last lateral does not affect the uniformity of filtration). The actual head on the sand close to the outlet will be .093 and the rate of filtration .093/.070 · 1.60 = 2.12. The actual head at the most remote point will be .093 - .036 = .057, and the rate of filtration will there be .057/.070 · 160 = 1.30 million gallons per acre daily. The extreme rates of filtration are thus 2.12 and 1.30, instead of the average rate of 1.60. As can be seen from the diagram, only very small areas work at these extreme rates, the great bulk of the area working at rates much nearer the average. Actually the filter is started at a rate below 1.60, and the nearest portion never filters so rapidly as 2.12, for when the rate is increased to the standard, the sand has become so far clogged that the loss of head is more than the .07 foot assumed, and the differences in the rates are correspondingly reduced. Taking this into account, it would not seem that the irregularities in the rate of filtration are sufficient to affect seriously the action of the filter. They could evidently have been largely reduced by moderately increasing the sizes of the lower ends of the underdrains, where most of the friction occurs with the high velocities (up to .97 foot) which there result.

The underdrains of the Warsaw filters were designed by Lindley to have a maximum loss of head of only .0164 foot when filtering at a rate of 2.57, which gives a variation of only 10 per cent in the rates with the minimum loss of head of .169 foot in the entire filter assumed by him. The underdrains of the Berlin filters, according to my calculations, have .020 to .030 foot friction, of which an unusually large proportion is in the gravel, owing to the excessive distances, in some cases over 80 feet, which the gravel is required to carry the water. In this case, using less or finer gravel would obviously have been fatal, but the friction as well as the expense of construction would be much reduced by using more drains and less gravel.

The underdrains might appropriately be made slightly smaller, with a deep layer of fine sand, than under opposite conditions, as in this case the increased friction in the drains would be no greater in proportion to the increased friction in the sand itself.

The underdrains of a majority of European filters have water-tight pipes connecting with them at intervals, and going up through the sand and above the water, where they are open to the air. These pipes were intended to ventilate the underdrains and allow the escape of air when the filter is filled with water introduced from below. It may be said, however, that in case the drains are surrounded by gravel and there is an opportunity for the air to pass from the top of the drain into the gravel, it will so escape without special provision being made for it, and go up through the sand with the much larger quantity of air in the upper part of the gravel which is incapable of being removed by pipes connecting with the drains.

These ventilator pipes where they are used are a source of much trouble, as unfiltered water is apt to run down through cracks in the sand beside them, and, under bad management, unfiltered water may even go down through the pipes themselves. I am unable to find that they are necessary, except with underdrains so constructed that there is no other chance for the escape of air from the tops of them, or that they serve any useful purpose, while there are positive objections to their use. In some of the newer filters they have been omitted with satisfactory results.

DEPTH OF WATER ON THE FILTERS.

In the older works with but crude appliances for regulating the rate of filtration and admission of raw water, a considerable depth of water was necessary upon the filter to balance irregularities in the rates of filtration; the filter was made to be, to a certain extent, its own storage reservoir. When, however, appliances of the character to be described in Chapter IV are used for the regulation of the incoming water, and with a steady rate of filtration, this provision becomes quite superfluous.

With open filters a depth of water in excess of the thickness of any ice likely to be formed is required to prevent disturbance or freezing of the sand in winter. It is also frequently urged that with a deep water layer on the filter the water does not become so much heated in summer, but this point is not believed to be well taken, for in any given case the total amount of heat coming from the sun to a given area is constant, and the quantity of water heated in the whole day—that is, the amount filtered—is constant, and variations in the quantity exposed at one time will not affect the average resulting increase in temperature. If the same water remained upon the filter without change it would of course be true that a thin layer would be heated more than a deep one, but this is not the case.

It is also sometimes recommended that the depth of water should be sufficient to form a sediment layer before filtration starts, but this point would seem to be of doubtful value, especially where the filter is not allowed to stand a considerable time with the raw water upon it before starting filtration.

It is also customary to have a depth of water on the filter in excess of the maximum loss of head, so that there can never be a suction in the sand just below the sediment layer. It may be said in regard to this, however, that a suction below is just as effective in making the water pass the sand as an equal head above. At the Lawrence Experiment Station filters have been repeatedly used with a water depth of only from 6 to 12 inches, with losses of head reaching 6 feet, without the slightest inconvenience. The suction only commences to exist as the increasing head becomes greater than the depth of water, and there is no way in which air from outside can get in to relieve it. In these experimental filters in winter, when the water is completely saturated with air, a small part of the air comes out of the water just as it passes the sediment layer and gets into reduced pressure, and this air prevents the satisfactory operation of the filters. But this is believed to be due more to the warming and consequent supersaturation of the water in the comparatively warm places in which the filters stand than to the lack of pressure, and as not the slightest trouble is experienced at other seasons of the year, it may be questioned whether there would be any disadvantage at any time in a corresponding arrangement on a large scale where warming could not occur.

The depths of water actually used in European filters with the full depth of sand are usually from 36 to 52 inches. In only a very few unimportant cases is less than the above used, and only a few of the older works use a greater depth, which is not followed in any of the modern plants. As the sand becomes reduced in thickness by scraping, the depth of water is correspondingly increased above the figures given until the sand is replaced. The depth of water on the German covered filters is quite as great as upon corresponding open filters. Thus the Berlin covered filters have 51, while the new open filters at Hamburg have only 43 inches.