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



When j^ equals 1 (when the tile is flowing full) and assuming the 



exponent of s to be 0.5 for all depths of flow, 



7=51.26 Z> - 5581 s - 5 (55) 



The similarlity of this formula to Prony's formula in equation 7 

 should be noted. 



A formula for the clay tile using only the data on the 5, 6, and 8 inch 

 sizes (1-foot lengths) was derived, as well as a formula for the 10 and 

 12 inch clay tile (2-foot lengths). These, however, were not deemed 

 of great importance as indicating the effect of joints in the tile line, 

 since an insufficient number of tile sizes were available for considera- 

 tion. 



From a study of the data on the flow in tile running partly full, it 

 will be seen that the velocity does not vary in accordance with the 

 variation of the hydraulic radius. This fact suggested an attempt to 

 derive a formula that does not involve the hydraulic radius, but is of 

 the type, 



f= (pO s °' 5 (56) 



That is, instead of the hydraulic radius, or the area divided by the 

 wetted perimeter, it was recognized that the area might have one 

 exponent and the perimeter a different exponent. A careful study of 

 this type of formula revealed the fact that it would be impracticable. 

 Another type of formula which was considered was of the form 



V = &(p^)V 5 (57) 



where Tc, x, and are unknown constants. This type was also con- 

 sidered inadvisable. 



Still another formula considered was of the type 



f <ftW) Vs (58 > 



where Fand /3 are constants and B is the breadth of the water surface 

 in the tile exposed to the air. This type was investigated quite care- 

 fully with the data relating to the concrete tile, but was not consid- 

 ered applicable to the conditions. 



From a study of the velocity-depth of flow curves it will be seen 

 that the greatest velocity in a pipe is approximately at 0.8 depth. 

 Theoretically it would be at 0.81 depth. Below this the velocity 

 decreases rapidly with the depth of flow. Observations on the flow in 



