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Units in trapezoidal open channel calculation: cm=centimeter, cfs=cubic foot per second, ft=foot, gal=gallon (U.S.), hr=hour, km=kilometer, m=meter, min=minute, s=second, yr=year
Links on this page: Introduction Variables Manning n coefficients
Error Messages References
Introduction
Many natural and manmade channels are approximately trapezoidal. Our trapezoidal open channel calculation
uses the most commonly used equation for analyzing rivers and streams  the Manning equation.
It is the equation beginning with V=... above. The Manning
equation is best used for uniform steady state flows. Uniform means that the
crosssection geometry of the channel remains constant along the length of the channel,
and steady state means that the velocity, discharge, and depth do not change with
time. Though these assumptions are rarely ever strictly achieved in rivers and streams, the
Manning equation is still used to model most rivers and streams where conditions are
relatively steady and for reaches (portions of rivers) that have a reasonably constant
crosssection for a long enough distance that the depth remains fairly constant.
The Manning equation is a semiempirical equation. Thus, its units are
inconsistent. The factor, k, has units which allow the equation to be used
properly. Our calculation takes care of all the unit conversions for you, and
allows you to enter and compute variables in a wide variety of units.
In our trapezoidal open channel calculation, most of the combinations of inputs have analytic (closed form)
solutions to compute the unknown variables; however, some combinations of inputs require numerical
solution. Our numerical solutions utilize a cubic solver that finds roots of the
equations with the result accurate generally to at least 8 significant digits. All
of our calculations utilize double precision. Two depths and bottom widths are
possible for certain combinations of entered values when Q, T, n, and S
or V, T, n, and S are entered.
Since two solutions are possible for some input combinations, the text fields are extra wide to accommodate two numbers.
Variables [ ]
indicates dimensions. [L]=Length, [T]=Time.
To calculation
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. River 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.
n = Manning coefficient. n is a function of the channel material,
such as grass, concrete, earth, etc. Values for n can be found in the table
of Manning's n coefficients shown below.
P = Wetted perimeter [L]. P is the contact length between the
water and the channel bottom and sides.
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.
T = Top width of the flowing water [L].
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 using the vertical depth
introduces only minimal error.
z_{1}, z_{2} = Side slopes of each bank of the channel.
These slopes are computed as horizontal distance divided by vertical distance.
θ = Angle formed by S.
Manning's n Coefficients
To calculation
The Manning's n coefficients 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
To calculation
"Invalid boxes checked." This message is displayed if too many or
too few variables are selected to be entered. A problem cannot be overstated or
understated. In all, there are 30 combinations of inputs which are acceptable.
This message can be displayed to both registered and nonregistered users.
"Cannot be computed." This message is displayed in numeric fields
if enough variables are selected to compute some values but not others. For instance,
if only Q, y, and b are input, then n, S, and F cannot be computed but other values will be computed.
The following messages are displayed if an entered value lies outside the acceptable
range for the variable. These messages are only displayed when the
"Calculate" button is clicked  for registered users.
"b must be > 0", "b must be 1e9 to 10000 m", "n must be
1e9 to 100", "Q must be > 0", "Q must be 1e9 to 1e9 m^{3}/s",
"S must be 1e9 to 1e9", "T must be > 0", "T must be 1e9 to
10000 m", "V must be > 0", "V must be 1e9 to 1e9 m/s",
"y must be < 0", "y must be 1e9 to 1e9 m", "z_{1}, z_{2}
must be ≥ 0", "z_{1}, z_{2} cannot both be 0".
Note that the channel cannot have both z_{1}=0 and z_{2}=0. However,
if you wish to simulate a rectangular channel, you can set one of them to 0.0 and the
other to a very small positive number such as 0.00001. Or, you can use our rectangular open channel calculation. Triangular channels
can be modeled by setting the bottom width, b, to a very small positive number such as
0.001 m or as low as 10^{9} m.
The following messages are displayed if the values entered result in an infeasible
situation. For instance, entering certain combinations of values for T, Q, n,
and S can result in an impossible flow situation indicated by a negative bottom
width or negative depth. These messages are only displayed when the
"Calculate" button is clicked  for registered users.
"b will be < 0","T will be > 10000 m", "y will be
< 0", "y will be ≤ 0", "y or b will be < 0".
The calculation uses an upper limit of 10,000 m for top width.
References
To calculation
A further discussion of open channel flow, Manning's equation, and trapezoidal channel
geometry can be found in these references and on our discussion
page. The Manning's n coefficients shown above are compiled from the references
shown here. The footnotes refer to specific values shown in the Manning n table
above.
^{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.
Chaudhry, M. H. 1993. Open Channel Flow. PrenticeHall, Inc.
Chow, V. T. 1959. Open Channel Hydraulics. McGrawHill, Inc. (the
classic text)
French, R. H. 1985. Open Channel Hydraulics. McGrawHill Book Co.
Mays, L. W. editor. 1999. Hydraulic design handbook. McGrawHill Book
Co.
Munson, B.R., D. F. Young, and T. H. Okiishi. 1998. Fundamentals of Fluid
Mechanics. John Wiley and Sons, Inc. 3ed.
^{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.
Streeter, V. L., E. B. Wylie, and K. W. Bedford. 1998. WCB/McGrawHill.
9ed.
^{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.
© 20002022 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or questions about trapezoidal 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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