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.
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.