12 BULLETIN" 851, U. S. DEPARTMENT OF AGRICULTURE. 



A new formula based on tests actually made on drain tile, derived 

 as hereinafter explained, is tentatively offered for tile flowing full. 

 This formula is 



F=138#M (13) 



It may seem that the exponential type of formula is inconvenient 

 because logarithms must be used to calculate results from it. How- 

 ever, it is comparatively simple in the case of such a formula to 

 prepare a diagram or chart, composed of parallel, straight lines if on 

 logarithmic scale, from which the required velocity or the required 

 discharge for any size of tile at any grade can be obtained at a glance, 

 the accuracy of the reading depending entirely upon the scale of the 

 diagram. Plate XIII is a diagram prepared by using the formula as 

 derived from the actual tests made, but applied to commercial or 

 nominal sizes of tile. 



It should be noted that Elliott's modifications of Poncelet's or 

 Hawkesley's formula are the only ones which take into consideration 

 the head caused by the water table in the soil, while the Chezy-Kutter 

 formula is the only one in which the different retardation influences 

 in clay and concrete drain tile may be considered. 



NECESSARY DATA FOR COMPARING VELOCITY FORMULA. 



In order to test the relative accuracy of the various formula? which 

 have been recommended for use in determining the discharge of tile 

 drains, the effect of each hydraulic element involved in the formulae 

 must be determined by experiment. However, in the tests made at 

 the experimental plant it was impossible to determine the effect of 

 the additional head caused by the water table in the soil. The ele- 

 ments to be determined are as follows: (1) the mean velocity of the 

 water in the tile drain; (2) the grade or slope of the drain, or the 

 water slope if it is different from that of the drain; (3) the internal 

 size of the tile; (4) the actual depth of flow in the tile drain. 



MEAN VELOCITY. 



The mean velocity of the water flowing in the drain can be deter- 

 mined by various methods. However, only the following two methods 

 were used: (1) by actually measuring the quantity of water entering 

 or discharging from the tile drain per second, and then solving the 



equation V=—) (2) by timing a given volume of water through a 

 previously measured distance. 



HYDRAULIC GRADE OR SLOPE. 



The slope of the line of tile tested at the experimental plant was 

 always known, since the tile were laid in an adjustable flume which 

 could be changed to the desired grade, the grade always being checked 

 by a level. 



