10 BULLETIN" 854, U. S. DEPARTMENT OF AGRICULTURE. 



One authority includes a third force caused by the head due to height 

 of the water table in the soil. 



It is interesting to note the variations between the different formulas 

 recommended for tile drainage. Some formulas take into account 

 only the grade or slope of the tile drain, while others include the 

 additional head caused by the weight of the water in the soil above 

 the drain. Few formulas distinguish between the retardation influ- 

 ences in concrete and those in clay drain tile, while many treat both 

 kinds of tile ihe same. 



One formula used by drainage engineers is the well-known Chezy 

 formula, 



V=C^Rs=CR°- 5 s^ (1) 



This was introduced by Chezy, a French engineer, in 1775. In this 

 formula?, C is a coefficient, originally considered a constant but since 

 discovered to vary with the retardation factors as well as with the 

 mean h}^draulic radius and the slope. 



The Kutter modification of the Chezy formula, 



V= 



1.811... aa , 0.00281 

 f- 41. 66 -I 



n s 



1+ („ee + -f^y 



^Rs (2) 



is the equation probably most widely used by drainage engineers. To 

 obtain this formula, the coefficient C has been replaced by an ex- 

 pression involving the hydraulic grade or slope and the mean hy- 

 draulic radius, as well as a quantity, n, to represent the influence of 

 the roughness of the walls of the channel or conduit. 

 The Poncelet, Hawkesley, 1 or Eytelwein 2 formula 



y - 48 V™ (3) 



applies to drains in which the velocity is due only to the hydraulic 

 grade or slope of the drain. It has been used to a great extent for 

 small tile systems in close soil and for determining the size of outlet 

 drains. 



According to Wollender, Wage, and John, 3 the mean velocity in 

 drain tile is 



F - 44 - 2 Vot25 (4) 



The Vincent formula is 



F = 45 - 95g Vg(b <« 



1 Sullivan's New Hydraulics, p. 9. 



2 Hamilton Smith's Hydraulics, p. 272. 



3 L. Faure, Drainage et Assainissemcnt Agricole des Terres, Taris, 1903, p. 90. 



