38 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 



The line representing equation 22 is shown in figure 1 of Plate X. 

 The mean hydraulic radii in the above computations were obtained 

 by averaging the hydraulic radii for the selected tests in Table 4 for 



each size of tile, and not by using -g } because these radii are for 



tests varying from 95 per cent full to full. The mean hydraulic radii 

 have been plotted as abscissae with their respective revised intercept 

 values as ordinates. These points are designated in the figure by 

 stars. The centers of gravity as computed above havo also been 

 plotted, and a line drawn through them. Substituting in equation 22 

 transposing, and using the center of gravity just computed, 



Log e = \ogm'-{- 1.3128) log R (23) 



= 6.874896 + 1 .3128 X9.20479 

 and 6 = 0.00006775 

 Thus 



m ' = 0.00006775 R-^™ (24) 



where 0.00006775 is the intercept on the line R=l, and - 1.3128 is the 

 inclination of the line to the horizontal axis. The logarithmic 

 diagram showing the development of the line for equation 24 is shown 

 in figure 1 of Plate X. A similar line for clay tile is shown in figure 1 

 of Plate XL 



Substituting equation 24 and the mean value of z (p. 40) in the 

 general formula 17, this general equation is now obtained for concrete 

 tile: 



8 = 0.00006775 £-1-3128^1.96433 



0.00006775 F- 96433 , OK , 



— £1.3128 W°) 



From this, solving for V, we get 



V= 132.5 i? - 668 s - 509 (26) 



which is the formula derived analytically, using the mean hydraulic 

 radii for the selected experiments for each size of concrete tile in 

 Table 4. 



In a like manner, the formula as derived analytically for clay tile 

 was found to be 



F= 134.7 R°- c '™ s - 508 (27) 



The data used in deriving equation 27 for clay tile are shown on figure 

 1 of Plato XL This diagram has been prepared similarly to the 

 diagram in figure 1 of Plate X, except that the values used are from 

 the selected tests in Table 3, for clay tile. 



Formulae 26 and 27 were derived by the analytical method, using 

 only experiments with the tile flowing from 95 per cent full to full, 



