Hydraulic Design of Highway Culverts - DOT On-Line Publications

APPENDIX B
HYDRAULIC RESISTANCE OF CULVERT BARRELS
NOTE: Since Appendix B is presented as a summary of a research report, it is only
presented in English Units.
A. General
In outlet control, the hydraulic resistance of the culvert barrel must be calculated using a friction
loss equation. Numerous equations, both theoretical and empirical, are available, including the
Darcy equation and the Manning equation. The Darcy equation, shown in Equation (33), is
theoretically correct, and is described in most hydraulic texts.
h
2
⎛ L ⎞ ⎛ V ⎞
= f ⎜ ⎟ ⎜
⎟
⎝ D ⎠ ⎝ 2g
⎠
f (33)
hf is the friction head loss, ft
f is the Darcy resistance factor
L is the conduit length, ft
D is the conduit diameter, ft
V is the mean velocity, ft/s
g is the acceleration due to gravity, 32.2 ft/s/s
The Darcy friction factor, f, is selected from a chart commonly referred to as the Moody diagram,
which relates f to Reynolds number (flow velocity, conduit size, and fluid viscosity) and relative
roughness (ratio of roughness element size to conduit size). To develop resistance coefficients
for new and untested wall roughness configurations, the Darcy f value can be derived
theoretically and then converted to a Manning’s n value through use of the relationship shown in
Equation (34).
1/
6 1/
2
n = 0.
0926 R f
(34)
R is the hydraulic radius, ft
A comprehensive discussion of the Darcy f, its derivation, and its relationship to other resistance
coefficients is given in reference (62).
The Manning equation, an empirical relationship, is commonly used to calculate the barrel
friction losses in culvert design. The usual form of the Manning equation is as follows:
1.
486
n
R
S
2 / 3 1/
2
V = (35)
V is the mean velocity of flow, ft/s
R is the hydraulic radius, ft
S is the slope of the conduit, ft/ft, equal to the slope of the water surface in uniform flow
201