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.
Fig. 3.—Apparatus Used for Measuring the Friction of Water in Sands.
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 = cd2(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 ANDCLEAN SANDS OF THE STATED GRAIN SIZES AND WITH VARIOUS HEADS AT ATEMPERATURE OF 50°. | ||||||||
|---|---|---|---|---|---|---|---|---|
| h l | Effective Size in Millimeters 10 per cent finer than: | |||||||
| 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 + 0.033679t + 0.000221t2.
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.