10 BUI.LETI:N" 854, U. S. DEPARTMENT OF AGEICULTUEE. 
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 formulae 
recommended for tile drainage. Some formulae 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 formulae distinguish between the retardation influ- 
ences in concrete and those in clay drain tile, while many treat both 
kinds of tile the same. 
One formula used by drainage engineers is the well-known Chezy 
formula, 
V=C'yjRs=CR'''s'-' (1) 
This was introduced by Chezy, a French engineer, in 1775. In this 
formulae, 6^ is a coefl&cient, originally considered a constant but since 
discovered to vary with the retardation factors as well as with the 
mean hydraulic radius and the slope. 
The Kutter modification of the Chezy formula. 
1:811+41.66 + 5:^^5281 
n s 
1 + 
(„.„.M5-)|, 
^/Rs (2) 
is the equation probabl}^ most widely used by drainage engineers. To 
obtain this formula, the coeflicient C has been replaced by an ex- 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,^ or Eytelwein ^ formula 
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,"^ the mean velocity in 
drain tile is 
V= 44 2^ / —^^ - (4) 
. The Vincent formula is 
' Sullivan's New Hydraulics, p. 9. 
2 Hamilton Smith's Hydraulics, p. 272. 
3 L. Faure, Drainage et Assainissement Agricole des Terres, Paris, 1903, p. 9C. 
