Rectangular open channel for river or laboratory hydraulics - Discharge, water depth, slope, velocity, Froude
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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 semi-empirical
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
cross-section. 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 cross-sectional area, determined normal (perpendicular) to the bottom surface [L2].
b = Channel bottom width [L].
F = Froude number. F is a non-dimensional 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/s2 = 9.8066 m/s2.
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 cross-section) between the
water and the channel.
Q = Discharge or flow rate [L3/T].
R = Hydraulic radius of the flow cross-section [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 |
| Non-Metals | |||
| 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 | 0.009-0.015 | ||
| Corrugated Polyethylene (PE) with corrugated inner walls c | 0.018-0.025 | ||
| Polyvinyl Chloride (PVC) with smooth inner walls d,e | 0.009-0.011 | ||
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. 109-129. 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 25-27, 1990.
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