42 



BULLETIN 854, U. S. DEPARTMENT OE AGRICULTURE. 



In a like manner, plotting values of the exponent of D as ordinates 

 against their respective depths of flow as abscissa?, the equation for 

 the exponent of D for any depth of flow was found to be (see text- 

 fig. 2) 



a = 0.6284(jy (43) 



Then writing the equation to cover every depth of flow in clay tile, 

 we have 



0.6284 



V 



55.57 



: UU - U ' T) 



//7\ 0.3067 1J 



\d) L . 



d \o-s 



(5) 



(44) 



.5. 



Depth ofF/ow% 

 .6 .7 .8 



i.O 



1.0 



V* 

 $ 



' 6 AA~ 633 



Equation of Line & =. 62841q\ 



Fig. 2.— Relation of exponent of D to depth of flow in formulae 35-40. 



When j. equals 1 — in other words when the tile is flowing full- 

 and assuming the exponent "of s to be 0.5 for all depths of flow, 



^ 



i 































^ 





) 



c^W 











CL 



.AY T 



ILE 



) 



^s 



>w ; 



c 





F = 5 



57 D°- 



(45) 



A study of figures 3 to 8, Plate X, shows that the 4-inch concrete 



tile appears to have a greater coefficient of roughness than do the 



larger sizes. This is also indicated in Table 4. Therefore it was 



decided to eliminate the 4-inch tile and consider only the remaining 



sizes in deriving a new formula. The formuke for the concrete tile 



for the 5, 6, 8, 1 0, and 1 2 inch sizes for all depths of flow then become: 



For I ile flowing full, F=51.15 D°- m s°- m (46) 



for tile flowing 0.9 depth, F=50.80 -D ""' 89 s°~ m (47) 



for tile flowing 0.8 depth, F=51.49 D°- m fi ' 498 (48) 



for tile flowing 0.7 depth, 7=51.93 J> 0fi25 s"- 501 (49) 



for tile flowing 0.G depth, F=51.37 -D " 723 s°- 504 (50) 



for tile flowing 0.5 depth, F=49.22 Z> 0,789 s 0,510 (51) 



