6 BULLETIN 376, U. S. DEPABTMENT OF AGBICTJLTUBE. 
(6) The Kutter modification of the Chezy formula, 
V = 
i^iL + 41 . 66 + 0^0281 
(41.66,5^)^1 
^s (5) 
in which C is elaborated so that it takes into consideration the in- 
fluence of the hydraulic grade and of the mean hydraulic radius and 
introduces a new variable, n, which is supposed to represent all the 
retarding influences. 
(c) The Weisbach formula, 
LV 2 
h f =45- g (6) 
From the same field data comparison is made between the follow- 
ing formulas : 
(d) The Tutton 1 formula for flow in wood-stave pipes, 
V = QE - 6 ^ - 51 with C x = 129 (7) 
Cj in this formula is not to be confused with C in the Chezy formula. 
(e) The Williams-Hazen general formula 2 for many kinds of pipes 
Y = C w R - 63 s - 54 0.001-°- 04 (8) 
which may be arranged in the same form as formulas 9 and 12 for 
comparison, becoming, with C w = 120, 
.427 V 1 - 852 
H = — jyjv — (8a) 
For wood-stave pipe a value for C w of 120 is recommended by Wil- 
liams and Hazen. This recommendation is based on their study of 
pipes Nos. 20, 41, 44, 47, and 48, Tables 2 and 3. The exponents 
of the formula "were selected as representing as nearly as possible 
average conditions, as deduced from the best available records of 
experiments upon the flow of water in such pipes and channels as 
most frequently occur in waterworks practice." 
(f) The Moritz formulas : 3 
8.6 V'- 8 0.38 V'- 8 
X1 — Jl.26 ~~ J)1.26 W-J 
V=1.72D°- 7 H - 555 (10) 
Q = 1.35D 2 - 7 E d - 555 (11) 
These three formulas express the same values from different 
points of view. Unlike formulas 4, 5, and 6, they were developed 
i Tutton, C. H. Journal Assoc. Engin. Socs., 23 (1899), p. 151. 
2 Hydraulic Tables, Williams and Hazen, 2d ed. New York, 1909. 
8 Flow of water in pipes, E. A. Moritz, Eng. Rec., 68, No. 24, p. 667. 
