Description Usage Arguments Details Value Note Source References See Also Examples
This function solves for one missing variable in the GaucklerManning
Strickler equation for a trapezoidal crosssection and uniform flow. The
uniroot
function is used to obtain the missing parameter.
1 2 3 4 5 6 7 8 9 10 11 12 13 
Q 
numeric vector that contains the discharge value [m^3/s or ft^3/s], if known. 
n 
numeric vector that contains the Manning's roughness coefficient n, if known. 
m 
numeric vector that contains the "crosssectional side slope of m:1 (horizontal:vertical)", if known. 
m1 
numeric vector that contains the "crosssectional side slope of m1:1 (horizontal:vertical)", if known. 
m2 
numeric vector that contains the "crosssectional side slope of m2:1 (horizontal:vertical)", if known. 
Sf 
numeric vector that contains the bed slope (m/m or ft/ft), if known. 
y 
numeric vector that contains the flow depth (m or ft), if known. 
b 
numeric vector that contains the bottom width, if known. 
T 
numeric vector that contains the temperature (degrees C or degrees Fahrenheit), if known. 
units 
character vector that contains the system of units [options are

type 
character vector that contains the type of trapezoid (symmetrical
or nonsymmetrical). The symmetrical trapezoid uses 
GaucklerManningStrickler equation is expressed as
V = \frac{K_n}{n}R^\frac{2}{3}S^\frac{1}{2}
the velocity (m/s or ft/s)
Manning's roughness coefficient (dimensionless)
the hydraulic radius (m or ft)
the slope of the channel bed (m/m or ft/ft)
the conversion constant – 1.0 for SI and 3.2808399 ^ (1 / 3) for English units – m^(1/3)/s or ft^(1/3)/s
This equation is also expressed as
Q = \frac{K_n}{n}\frac{A^\frac{5}{3}}{P^\frac{2}{3}}S^\frac{1}{2}
the discharge [m^3/s or ft^3/s (cfs)] is VA
Manning's roughness coefficient (dimensionless)
the wetted perimeter of the channel (m or ft)
the crosssectional area (m^2 or ft^2)
the slope of the channel bed (m/m or ft/ft)
the conversion constant – 1.0 for SI and 3.2808399 ^ (1 / 3) for English units – m^(1/3)/s or ft^(1/3)/s
Other important equations regarding the trapezoidal crosssection follow:
R = \frac{A}{P}
the hydraulic radius (m or ft)
the crosssectional area (m^2 or ft^2)
the wetted perimeter of the channel (m or ft)
A = y≤ft(b + my\right)
the crosssectional area (m^2 or ft^2)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
the bottom width (m or ft)
P = b + 2y√{≤ft(1 + m^2\right)}
the wetted perimeter of the channel (m or ft)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
the bottom width (m or ft)
B = b + 2my
the top width of the channel (m or ft)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
the bottom width (m or ft)
D = \frac{A}{B}
the hydraulic depth (m or ft)
the crosssectional area (m^2 or ft^2)
the top width of the channel (m or ft)
A rough turbulent zone check is performed on the water flowing in the channel using the Reynolds number (Re). The Re equation follows:
Re = \frac{ρ RV}{μ}
Reynolds number (dimensionless)
density (kg/m^3 or slug/ft^3)
the hydraulic radius (m or ft)
the velocity (m/s or ft/s)
dynamic viscosity (* 10^3 kg/m*s or * 10^5 lb*s/ft^2)
A critical flow check is performed on the water flowing in the channel using the Froude number (Fr). The Fr equation follows:
Fr = \frac{V}{≤ft(√{g * D}\right)}
the Froude number (dimensionless)
the velocity (m/s or ft/s)
gravitational acceleration (m/s^2 or ft/sec^2)
the hydraulic depth (m or ft)
the missing parameter (Q, n, b, m, Sf, or y) & area (A), wetted
perimeter (P), velocity (V), top width (B), hydraulic depth (D), hydraulic
radius (R), Reynolds number (Re), and Froude number (Fr) as a list
.
Assumptions: uniform flow, prismatic channel, and surface water temperature of 20 degrees Celsius (68 degrees Fahrenheit) at atmospheric pressure
Note: Units must be consistent
r  Better error message for stopifnot?  Stack Overflow answered by Andrie on Dec 1 2011. See https://stackoverflow.com/questions/8343509/bettererrormessageforstopifnot.
Terry W. Sturm, Open Channel Hydraulics, 2nd Edition, New York City, New York: The McGrawHill Companies, Inc., 2010, page 2, 8, 36, 102, 120, 153.
Dan Moore, P.E., NRCS Water Quality and Quantity Technology Development Team, Portland Oregon, "Using Mannings Equation with Natural Streams", August 2011, http://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/xsec/manningsNaturally.pdf.
Gilberto E. Urroz, Utah State University Civil and Environmental Engineering  OCW, CEE6510  Numerical Methods in Civil Engineering, Spring 2006 (2006). Course 3. "Solving selected equations and systems of equations in hydraulics using Matlab", August/September 2004, https://digitalcommons.usu.edu/ocw_cee/3.
Tyler G. Hicks, P.E., Civil Engineering Formulas: Pocket Guide, 2nd Edition, New York City, New York: The McGrawHill Companies, Inc., 2002, page 423, 425.
Andrew Chadwick, John Morfett, and Martin Borthwick, Hydraulics in Civil and Environmental Engineering, Fourth Edition, New York City, New York: Spon Press, 2004, pages 132133.
Wikimedia Foundation, Inc. Wikipedia, 26 November 2015, “Manning formula”, https://en.wikipedia.org/wiki/Manning_formula.
John C. Crittenden, R. Rhodes Trussell, David W. Hand, Kerry J. Howe, George Tchobanoglous, MWH's Water Treatment: Principles and Design, Third Edition, Hoboken, New Jersey: John Wiley & Sons, Inc., 2012, page 18611862.
Robert L. Mott and Joseph A. Untener, Applied Fluid Mechanics, Seventh Edition, New York City, New York: Pearson, 2015, page 376, 392.
Wikimedia Foundation, Inc. Wikipedia, 17 March 2017, “Gravitational acceleration”, https://en.wikipedia.org/wiki/Gravitational_acceleration.
Wikimedia Foundation, Inc. Wikipedia, 29 May 2016, “Conversion of units”, https://en.wikipedia.org/wiki/Conversion_of_units.
Manningrect
for a rectangular crosssection, Manningtri
for a triangular crosssection, Manningpara
for a parabolic
crosssection, and Manningcirc
for a circular crosssection.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  library("iemisc")
library(iemiscdata)
# Exercise 4.1 from Sturm (page 153)
Manningtrap(Q = 3000, b = 40, m = 3, Sf = 0.002, n = 0.025, units = "Eng")
# Q = 3000 cfs, b = 40 ft, m = 3, Sf = 0.002 ft/ft, n = 0.025,
# units = English units
# This will solve for y since it is missing and y will be in ft
# Practice Problem 14.19 from Mott (page 392)
# See nchannel in iemiscdata for the Manning's n table that the following
# example uses
# Use the minimum Manning's n value for 1) Natural streams  minor streams
# (top width at floodstage < 100 ft), 2) Lined or Constructed Channels,
# 3) Concrete and 4) float finish.
data(nchannel)
nlocation < grep("float finish",
nchannel$"Type of Channel and Description")
n < nchannel[nlocation, 3][1] # 3 for column 3  Normal n
Manningtrap(y = 1.5, b = 3, m = 3/2, Sf = 0.1/100, n = n, units = "SI")
# y = 1.5 m, b = 3 m, m = 3/2, Sf = 0.1/100 m/m, n = 0.023, units = SI
# units
# This will solve for Q since it is missing and Q will be in m^3/s

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