THE DESIGN OF WASH WATER TROUGHS FOR RAPID SAND FILTERS [with DISCUSSION]

Inspection of plans for rapid sand filter plants, and of the operation of completed plants, indicates considerable variation in the proportions of the wash water troughs. Quite often these are made too large, and therefore interfere with the distribution and functioning of the wash water to some extent. Sometimes they are too small to carry off the wash water. As one of the few visible evidences of the hydraulic design of the plant, it is a matter of satisfaction to the engineer when these are correctly proportioned, with neither excess nor deficiency of capacity. It is not difficult to write the differential equation2 of flow for a wash water trough, but the integration of the resulting equation in a practicable form seems to be impossible. This is due entirely to the friction term of the equation, and suggests that either the form in which these troughs are built is not in conformity with the theoretical requirements, or else that there are defects in our conceptions of fluid friction losses. While the exact solution of the problem is therefor of interest to the pure hydraulician, it is a fact that a sufficiently good practical solution can be obtained by approximating the refractory friction term, since for all ordinary sizes and proportions of troughs, this term is small as compared with the total losses which govern the equation of flow. Referring to figure 1, which represents a trough with parallel sides, but without restriction as to the shape of bottom, and wherein: