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Units in circular culvert design & analysis calculator:
cm=centimeter, cfs=cubic foot per second, ft=foot, gal=gallon (U.S.), m=meter, min=minute, s=second, yr=year
Circular Culvert Drawings and Equations
Links on this page: Introduction
Variables Manning's n
coefficients Error messages References
Introduction to Culvert Design and Analysis using Manning Equation
The equation beginning V=.... is called the Manning Equation. It is a semiempirical
equation and is the most commonly used equation for uniform steady state flow of water in
open channels (see Discussion and References for Open Channel
Flow for further discussion), including culverts that are not flowing full. Because it is empirical, the Manning equation has
inconsistent units which are handled through the conversion factor k. Uniform flow means
that the water surface in the culvert has the same slope as the culvert itself. Uniform flow is
actually only achieved in culverts that are long and have an unchanging
crosssection. However, the Manning equation is used in other situations despite not
strictly achieving these conditions. In situations where culvert inlet effects are important, please see our
Culvert Design Calculation using Inlet and Outlet Control.
In our circular culvert design and analysis calculation, most of the combinations of inputs have analytic (closed form)
solutions to compute the unknown variables; however, two require numerical solutions
("Enter Q, n, S, d" and "Enter V, n, S, d"). Our numerical
solutions utilize a cubic solver that finds roots of the equations with the result
accurate to at least eight significant digits. All of our software utilizes double
precision internally but output is to eight significant digits.
It is possible to get two answers in our culvert calculation using "Enter Q,n,S,d" or "Enter
V,n,S,d". This is because maximum Q and V do not occur when the pipe is full. Qmax
occurs when y/d=0.938. If y/d is more than that, Q actually decreases due to friction.
Given a pipe with diameter d, roughness n, and slope S, let Qo be the discharge when the
pipe is flowing full (y/d=1). As seen on the graph below for a circular culvert, discharge is also equal to Qo
when y/d=0.82. If the entered Q is greater than Qo (but less than Qmax), there will be two
solution values of y/d, one between 0.82 and 0.938, and the other between 0.938 and 1. The
same argument applies to V, except that Vo occurs at y/d=0.5, and Vmax occurs at y/d=0.81.
If the entered V is greater than Vo (but less than Vmax), there will be two solution
values of y/d, one between 0.5 and 0.81, and the other between 0.81 and 1. For
further information, see Chow (1959, p. 134).
The following graphs are valid for any circular culvert roughness (n) and slope (S):
Qo=full pipe discharge; Vo=full pipe velocity:
Variables in Culvert Equations [L] indicates length units. [T] indicates time units.
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A = Flow crosssectional area in culvert, determined normal (perpendicular) to the bottom surface [L^{2}].
d = Culvert diameter [L].
F = Froude number. F is a nondimensional parameter indicating the relative effect
of inertial effects to gravity effects. Flow with F<1 are low velocity flows
called subcritical. F>1 are high velocity flows called supercritical.
Subcritical flows are controlled by downstream obstructions while supercritical flows are
affected by upstream controls. F=1 flows are called critical.
g = acceleration due to gravity = 32.174 ft/s^{2} = 9.8066 m/s^{2}.
g is used in the equation for Froude number.
k = unit conversion factor = 1.49 if English units = 1.0 if metric units. Our
culvert software converts all inputs to SI units (meters and seconds), performs the computations
using k=1.0, then converts the computed quantities to units specified by the user.
n = Manning coefficient. n is a function of the culvert material, such as plastic,
concrete, brick, etc. Values for n can be found in the table below of Manning's n coefficients.
P = Wetted perimeter of culvert [L]. P is the contact length (in the crosssection) between the
water and the culvert.
Q = Discharge or flow rate through culvert [L^{3}/T].
R = Culvert hydraulic radius of the flow crosssection [L].
S = Slope of culvert bottom or water surface [L/L]. Vertical distance divided by
horizontal distance.
T = Top width of the flowing water in culvert [L].
V = Average velocity of the water in culvert [L/T].
y = Water depth in culvert measured normal (perpendicular) to the bottom of the culvert [L]. If
the culvert has a small slope (S), then entering the vertical depth introduces only
minimal error.
θ = Angle representing how full the culvert is [radians]. A culvert with θ=0
radians (0^{o}) contains no water, a culvert with θ=π radians (180^{o})
is half full, and a culvert with θ=2π radians (360^{o}) is completely full.
Manning's n Coefficients
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The table shows the Manning n values for materials most commonly used for
culverts. These values were compiled from the references listed under Discussion and References and in the references at the bottom of
this web page (note the footnotes which refer to specific references). A more
complete table of Manning n values can be found on our Manning n
page.
Culvert Material 
Manning n 
Culvert Material 
Manning n 
Metals: 
Brass 
0.011 
Smooth Steel 
0.012 
Cast Iron 
0.013 
Corrugated Metal 
0.022 

NonMetals: 
Corrugated Polyethylene (PE) culvert with smooth inner walls^{ a,b} 
0.0090.015 
Corrugated Polyethylene (PE) culvert with corrugated inner walls^{
c} 
0.0180.025 
Polyvinyl Chloride (PVC) culvert with smooth inner walls^{ d,e} 
0.0090.011 
Glass 
0.010 
Finished Concrete 
0.012 
Clay Tile 
0.014 
Unfinished Concrete 
0.014 
Brickwork 
0.015 
Gravel 
0.029 
Asphalt 
0.016 
Earth 
0.025 
Masonry 
0.025 
Planed Wood 
0.012 


Unplaned Wood 
0.013 
Error Messages for Circular Culvert Design and Analysis Calculation
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"Infeasible Input. T/d > 1",
"An input is ≤ 0",
"Infeasible Input. T ≤ 0",
"Infeasible Input. y/d ≥ 1".
"Invalid input". Usually appears when letters or unusual characters are entered.
"Infeasible Input". Combinations of input are unrealistic.
NaN in a numerical field means Not a Number and could be due to dividing by zero. Check input to make sure input values are reasonable.
References in Culvert Design and Analysis Calculation
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^{a} Barfuss, Steven and J. Paul Tullis. Friction factor test on high
density polyethylene pipe. Hydraulics Report No. 208. Utah Water Research
Laboratory, Utah State University. Logan, Utah. 1988.
^{c} Barfuss, Steven and J. Paul Tullis. Friction factor test on high
density polyethylene pipe. Hydraulics Report No. 208. Utah Water Research
Laboratory, Utah State University. Logan, Utah. 1994.
^{e} Bishop, R.R. and R.W. Jeppson. Hydraulic characteristics of PVC
sewer pipe in sanitary sewers. Utah State University. Logan, Utah.
September 1975.
Chow, V. T. 1959. OpenChannel Hydraulics. McGrawHill, Inc.
^{d} Neale, L.C. and R.E. Price. Flow characteristics of PVC sewer pipe.
Journal of the Sanitary Engineering Division, Div. Proc 90SA3, ASCE. pp.
109129. 1964.
^{b} Tullis, J. Paul, R.K. Watkins, and S. L. Barfuss. Innovative new
drainage pipe. Proceedings of the International Conference on Pipeline Design and
Installation, ASCE. March 2527, 1990.
© 19982014 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or other questions.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 5921890
LMNO@LMNOeng.com http://www.LMNOeng.com

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Culvert Design using Inlet and Outlet Conrol
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Circular culvert flow measurement using end depth in freeflow
Hydraulic jump in a circular culvert
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