THE FLOW OF WATER IN DRAIN TILE. 39 



but not under pressure. In order to derive a formula graphically, 

 using the same data as those from which equation 26 was derived 

 analytically, a separate diagram was necessary. This diagram 

 (PI. X, fig. 2) was obtained by plotting the velocities used in figure 1 

 of Plate X as abscissae, against their respective slopes as ordinates, 

 just as in figure 1. Straight lines were drawn through each set of 

 symbols, averaging the points by eye. Although these lines were not 

 intentionally drawn parallel, it will be seen that they are practically 

 so. The slopes of these lines were determined by scale, and the 

 intercepts of the various lines with the unity vertical axis were read 

 from the diagram. The inclination and location of the line involving 

 the mean hydraulic radii and the intercepts were determined analyti- 

 cally. The formula as derived graphically for concrete tile is 



V= 138.5 R°' 6S0 s - 510 (28) 



It should be noted that the exponents of s are the same in equations 

 26 and 28, while the exponents of R and the coefficients preceding R 

 vary slightly. 



In a similar manner, the formula for the flow of water in clay tile 

 was derived graphically from the selected experiments in Table 3, 

 this diagram being shown in figure 2 of Plate XL In this case the 

 inclination and location of the line involving the mean hydraulic 

 radii and the intercepts were also determined analytically. The 

 formula as derived for clay tile is 



7=121.4i?°- 635 s - 5 (29) 



Comparing this formula with equation 27, it will be noted that the 

 exponents of s are i^ractically the same, while the exponents of R as 

 well as the coefficients preceding R vary somewhat. This difference 

 is probably due to the fact that the observations on the 6-inch tile 

 are slightly inconsistent with those on the other sizes, and this dis- 

 crepancy is treated somewhat differently in the analytical and graphi- 

 cal methods. In the latter method, greater weight was given to the 

 higher velocities than to the lower ones. The diagrams (PL XI, 

 figs. 1 and 2) show the variation in the inclination of the lines for the 

 6-inch tile. 



It will be noted that the formula for flow in clay tile, equation 27, 

 was derived analytically. In order to determine the variation in the 

 coefficient, the velocities for the selected experiments (column 8, 

 Table 3), together with their respective hydraulic radii and slopes, 

 were substituted in equation 27 and new coefficients computed. 

 The mean of the coefficients obtained for clay tile was 137.6. Thus 

 the formula for clay tile, using the same exponents for R and s as 

 in equation 27, was found to be 



V= 137.6 R -™ s - 508 (30) 



