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Units:
cfs=cubic foot per second, cm=centimeter, ft=foot, gal=U.S. gallon, m=meter, min=minute, s=second, yr=year
Topics: Introduction
Variables Manning's n
coefficients Error messages References
Introduction
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). Because it is empirical, the Manning equation has
inconsistent units which are handled through the conversion factor k. Uniform means
that the water surface has the same slope as the channel bottom. Uniform flow is
actually only achieved in channels that are long and have an unchanging
crosssection. However, the Manning equation is used in other situations despite not
strictly achieving these conditions.
To model a channel that has sloped sides, rather than vertical sides,
please see our trapezoidal open channel calculator. We wrote the rectangular open channel hydraulics calculator
before we wrote the trapezoidal channel calculator. Even though the trapezoidal calculator solves the case of
a rectangular channel, we have kept the rectangular open channel flow calculator on the website.
In our rectangular open channel flow 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, y" and "Enter Q, n, S, b"). Our numerical
solutions utilize a cubic solver. All of our calculations utilize double precision.
Variables [L]=Length units, [T]=Time units.
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A = Flow crosssectional area, determined normal (perpendicular) to the bottom surface [L^{2}].
b = Channel bottom width [L].
F = Froude number. F is a nondimensional parameter indicating the relative effect
of inertial effects to gravity effects. Flows 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
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.
Required since the Manning equation is empirical and its units are inconsistent.
n = Manning coefficient. n is a function of the channel material, such as gravel, earthy, weedy,
concrete, etc. Values for n can be found in the table below of Manning's n coefficients.
P = Wetted perimeter [L]. P is the contact length (in the crosssection) between the
water and the channel.
Q = Discharge or flow rate [L^{3}/T].
R = Hydraulic radius of the flow crosssection [L].
S = Slope of channel bottom or water surface [L/L]. Vertical distance divided by
horizontal distance.
V = Average velocity of the water [L/T].
y = Water depth measured normal (perpendicular) to the bottom of the channel [L]. If
the channel has a small slope (S), then entering the vertical depth introduces only
minimal error.
Manning's n Coefficients
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The table shows the Manning n values for materials that might be used in open
channels. 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).
Material 
Manning n 
Material 
Manning n 
Natural Streams 
Excavated Earth Channels 
Clean and Straight 
0.030 
Clean 
0.022 
Major Rivers 
0.035 
Gravelly 
0.025 
Sluggish with Deep Pools 
0.040 
Weedy 
0.030 


Stony, Cobbles 
0.035 

Metals 
Floodplains 
Brass 
0.011 
Pasture, Farmland 
0.035 
Cast Iron 
0.013 
Light Brush 
0.050 
Smooth Steel 
0.012 
Heavy Brush 
0.075 
Corrugated Metal 
0.022 
Trees 
0.15 

NonMetals 
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 
Corrugated Polyethylene (PE) with smooth inner walls^{ a,b} 
0.0090.015 
Corrugated Polyethylene (PE) with corrugated inner walls^{
c} 
0.0180.025 
Polyvinyl Chloride (PVC) with smooth inner walls^{ d,e} 
0.0090.011 
Error Messages
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"An input is ≤ 0". All inputs must be positive.
"Infeasible input. Output < 0". One or more computed values
are negative, which is physically impossible.
References
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Footnotes refer to Manning n table above. All equations and other Manning n values
were obtained from the references listed in our Discussion and
References page.
^{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.
^{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.
© 20032022 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or questions about open channel flow.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 7072614
LMNO@LMNOeng.com https://www.LMNOeng.com

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