Manningtri | R Documentation |
This function solves for one missing variable in the Gauckler-Manning-
Strickler equation for a triangular cross-section and uniform flow. The
uniroot
function is used to obtain the missing parameters.
Manningtri(
Q = NULL,
n = NULL,
m = NULL,
Sf = NULL,
y = NULL,
Temp = NULL,
units = c("SI", "Eng")
)
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 "cross-sectional side slope of m: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. |
Temp |
numeric vector that contains the temperature (degrees C or degrees Fahrenheit), if known. |
units |
character vector that contains the system of units [options are
|
Gauckler-Manning-Strickler 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 perimeters of the channel (m or ft)
the cross-sectional 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 triangular cross-section follow:
R = \frac{A}{P}
the hydraulic radius (m or ft)
the cross-sectional area (m^2 or ft^2)
the wetted perimeters of the channel (m or ft)
A = my^2
the cross-sectional area (m^2 or ft^2)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
P = 2y\sqrt{\left(1 + m^2\right)}
the wetted perimeters of the channel (m or ft)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
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
D = \frac{A}{B}
the hydraulic depth (m or ft)
the cross-sectional area (m^2 or ft^2)
the top width of the channel (m or ft)
Z = \frac{\sqrt{2}}{2}my^2.5
the Section factor (m or ft)
the flow depth (normal depth in this function) [m or ft]
the horizontal side slope
E = y + \frac{Q^2}{2gA^2}
the Specific Energy (m or ft)
the discharge [m^3/s or ft^3/s (cfs)] is VA
gravitational acceleration (m/s^2 or ft/sec^2)
the cross-sectional area (m^2 or ft^2)
the flow depth (normal depth in this function) [m or ft]
VH = \frac{V^2}{2g}
the Velocity Head (m or ft)
the velocity (m/s or ft/s)
gravitational acceleration (m/s^2 or ft/sec^2)
w = \sqrt{y^2 + (y*m)^2}
the Wetted Length (m or ft)
the horizontal side slope
the flow depth (normal depth in this function) [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{\\rho RV}{\\mu}
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}{\left(\sqrt{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, m, Sf, or y) & area (A), wetted
perimeter (P), velocity (V), top width (B), 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
Irucka Embry
Terry W. Sturm, Open Channel Hydraulics, 2nd Edition, New York City, New York: The McGraw-Hill Companies, Inc., 2010, page 2, 8, 36, 102, 120, 153-154.
Dan Moore, P.E., NRCS Water Quality and Quantity Technology Development Team, Portland Oregon, "Using Mannings Equation with Natural Streams", August 2011, https://web.archive.org/web/20210416091858/https://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/xsec/manningsNaturally.pdf. Retrieved thanks to the Internet Archive: Wayback Machine
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 McGraw-Hill Companies, Inc., 2002, page 423, 425.
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 1861-1862.
Andrew Chadwick, John Morfett and Martin Borthwick, Hydraulics in Civil and Environmental Engineering, Fourth Edition, New York City, New York: Spon Press, Inc., 2004, page 133.
Robert L. Mott and Joseph A. Untener, Applied Fluid Mechanics, Seventh Edition, New York City, New York: Pearson, 2015, page 376, 393.
Ven Te Chow, Ph.D., Open-Channel Hydraulics, McGraw-Hill Classic Textbook Reissue, New York City, New York: McGraw-Hill Book Company, 1988, pages 21, 40-41.
Gary P. Merkley, "BIE6300 - Irrigation & Conveyance Control Systems, Spring 2004", 2004, Biological and Irrigation Engineering - OCW. Course 2, https://digitalcommons.usu.edu/ocw_bie/2/.
The NIST Reference on Constants, Units, and Uncertainty, Fundamental Constants Data Center of the NIST Physical Measurement Laboratory, "standard acceleration of gravity g_n", https://physics.nist.gov/cgi-bin/cuu/Value?gn.
Wikimedia Foundation, Inc. Wikipedia, 15 May 2019, "Conversion of units", https://en.wikipedia.org/wiki/Conversion_of_units.
Manningtrap
for a triangleal cross-section, Manningrect
for a
rectangular cross-section, Manningpara
for a parabolic cross-section,
and Manningcirc
for a circular cross-section.
# Please refer to the iemisc: Manning... Examples using iemiscdata
# [https://www.ecoccs.com/R_Examples/Manning_iemiscdata_Examples.pdf] and iemisc:
# Open Channel Flow Examples involving Geometric Shapes with the
# Gauckler-Manning-Strickler Equation
# [https://www.ecoccs.com/R_Examples/Open-Channel-Flow_Examples_Geometric_Shapes.pdf]
# for the cross-section examples using iemiscdata
library(iemisc)
# Modified Exercise 4.1 from Sturm (page 153)
Manningtri(Q = 3000, m = 3, Sf = 0.002, n = 0.025, units = "Eng")
# Q = 3000 cfs, 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
# Modified Exercise 4.5 from Sturm (page 154)
Manningtri(Q = 950, m = 2, Sf = 0.022, n = 0.023, units = "SI")
# Q = 950 m^3/s, m = 2, Sf = 0.022 m/m, n = 0.023, units = SI units
# This will solve for y since it is missing and y will be in m
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