40 BULLETIN 854, IT. S. DEPARTMENT OF AGRICULTURE. 



In a like manner, the data for the experimental velocities for the 

 selected experiments (Table 4) were substituted in equation 26, and 

 the formula for concrete tile became 



7=131 i?°-668 S 0.500 (31) 



Noting how close the exponents of R and s were to f and J, it was 

 deemed advisable to determine what the coefficient would be when 

 using these latter values. For the clay tile, using all the various sizes 

 and lengths of tile, the formula became, 



F=136 7#s* (32) 



In the case of concrete tile, the data for the 4-inch size show that 

 greater resistance to flow is offered in this size than in the larger 

 sizes. This is clearly shown in the diagram in Plate X as well as in 

 column 10 of Table 4. Therefore, it was decided to eliminate the 

 4-inch size and use the remainder of the sizes in the derivation of the 

 formula. The formula for concrete tile, then, is 



F = 138.2i2'si (33) 



None of the previous formulae were derived from the combined data 

 for both clay and concrete tile. Therefore, it was decided to derive 

 a formula by using the velocities for both clay and concrete tile flow- 

 ing full as obtained from Plate IX. These velocities were plotted as 

 abscissae against their respective slopes as ordinates (PI. XII). 

 The formula derived graphically for both clay and concrete tile is 



F=137.96 J R°- 67 s - 5 (34) 



This formula is practically the same as that derived for concrete 

 tile as given in equation 33. Since it was derived from the data for 

 both clay and concrete tile, equation 34 is recommended as the general 

 formula for computing the capacity of tile, merely eliminating the 

 decimal in the coefficient and making the exponents § and \, respec- 

 tively, thus, 



V = 13$B$sl (13) 



FORMULAE FOR TILE FLOWING PARTLY FULL 



A great many experiments were made at other depths of flow as 

 shown in Tables 3 and 4. These have been plotted and mean curves 

 drawn through the points (see PL IX, figs. 1 to 12). The velocities 

 at 0.5, 0.6, 0.7, 0.8, and 0.9 depths and for the tile flowing full were 

 read from these curves and plotted on logarithmic charts as abscissae, 

 against their respective slopes as ordinates, to determine the equa- 

 tions for flow at these different depths. 



Figures 3 to 8, Plate XI, show the studies made of clay tile at 

 various depths of flow. With the exception of the 0.5 and 0.6 depths 

 of flow (figs. 7 and 8), the lines were drawn through the various points 

 by eve > the centers of gravity not being determined analytically. 



