Manningcirc: Circular Cross-section Using the Gauckler-Manning-Strickler...
In iemisc: Irucka Embry's Miscellaneous Functions
Manningcirc R Documentation
Circular Cross-section Using the Gauckler-Manning-Strickler Equation 1
Description
Manningcirc and Manningcircy solve for a missing variable for a circular
cross-section. The uniroot function is used to obtain the
missing parameters.
The Manningcirc function solves for one missing variable in the Gauckler-
Manning equation for a circular cross-section and uniform flow. The
possible inputs are Q, n, Sf, y, and d. If y or d are not initially known,
then Manningcircy can solve for y or d to use as input in the Manningcirc
function.
Usage
Manningcirc(
Q = NULL,
n = NULL,
Sf = NULL,
y = NULL,
d = NULL,
Temp = NULL,
units = c("SI", "Eng")
)
Arguments
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.
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.
d
numeric vector that contains the diameters value (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
SI for International System of Units or Eng for English units
(United States Customary System in the United States and Imperial Units in
the United Kingdom)
Details
Circular cross-section using the Gauckler-Manning-Strickler equation
Gauckler-Manning-Strickler equation is expressed as
V = \frac{K_n}{n}R^\frac{2}{3}\sqrt{S}
- V
the velocity (m/s or ft/s)
- n
Manning's roughness coefficient (dimensionless)
- R
the hydraulic radius (m or ft)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
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}}\sqrt{S}
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- n
Manning's roughness coefficient (dimensionless)
- P
the wetted perimeters of the channel (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
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 circular cross-section follow:
R = \frac{A}{P}
- R
the hydraulic radius (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- P
the wetted perimeters of the channel (m or ft)
A = \left(\\theta - \sin \\theta\right) \frac{d^2}{8}
- A
the cross-sectional area (m^2 or ft^2)
- d
the diameters of the cross-section (m or ft)
- \theta
see the equation defining this parameters
\\theta = 2 \arcsin\left[1 - 2\left(\frac{y}{d}\right)\right]
- \theta
see the equation defining this parameters
- y
the flow depth (normal depth in this function) [m or ft]
- d
the diameters of the cross-section (m or ft)
d = 1.56 \left[\frac{nQ}{K_n\sqrt{S}}\right]^\frac{3}{8}
- d
the initial diameters of the cross-section [m or ft]
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- n
Manning's roughness coefficient (dimensionless)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
the conversion constant – 1.0 for SI and
3.2808399 ^ (1 / 3) for English units – m^(1/3)/s or ft^(1/3)/s
Note: This will only provide the initial conduit diameters, check the design
considerations to determine your next steps.
P = \frac{\\theta d}{2}
- P
the wetted perimeters of the channel (m or ft)
- \theta
see the equation defining this parameters
- d
the diameters of the cross-section (m or ft)
B = d \sin\left(\frac{\\theta}{2}\right)
- B
the top width of the channel (m or ft)
- \theta
see the equation defining this parameters
- d
the diameters of the cross-section (m or ft)
D = \frac{A}{B}
- D
the hydraulic depth (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- B
the top width of the channel (m or ft)
Z = \frac{\sqrt{2}}{2}my^2.5
- Z
the Section factor (m or ft)
- y
the flow depth (normal depth in this function) [m or ft]
- m
the horizontal side slope
E = y + \frac{Q^2}{2gA^2}
- E
the Specific Energy (m or ft)
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- g
gravitational acceleration (m/s^2 or ft/sec^2)
- A
the cross-sectional area (m^2 or ft^2)
- y
the flow depth (normal depth in this function) [m or ft]
VH = \frac{V^2}{2g}
- VH
the Velocity Head (m or ft)
- V
the velocity (m/s or ft/s)
- g
gravitational acceleration (m/s^2 or ft/sec^2)
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}
- Re
Reynolds number (dimensionless)
- \rho
density (kg/m^3 or slug/ft^3)
- R
the hydraulic radius (m or ft)
- V
the velocity (m/s or ft/s)
- \mu
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)}
- Fr
the Froude number (dimensionless)
- V
the velocity (m/s or ft/s)
- g
gravitational acceleration (m/s^2 or ft/sec^2)
- D
the hydraulic depth (m or ft)
Value
the missing parameters (Q, n, or Sf) & theta, area (A), wetted
perimeters (P), velocity (V), top width (B), hydraulic depth (D), hydraulic radius (R), E (Specific Energy), Vel_Head (Velocity Head), Z (Section Factor), Reynolds number (Re), and Froude number (Fr) as a list. for the
Manningcirc function.
Note
Assumptions: uniform flow, prismatic channel, and surface water temperature
of 20 degrees Celsius (68 degrees Fahrenheit) at atmospheric pressure
Note: Units must be consistent
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
Author(s)
Irucka Embry
References
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, 123-125, 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, 377-378, 392.
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.
See Also
Manningtrap for a trapezoidal cross-section, Manningrect for a
rectangular cross-section, Manningtri for a triangular cross-section,
and Manningpara for a parabolic cross-section.
Manningcircy
iemisc documentation built on Sept. 25, 2023, 5:09 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| Manningcirc | R Documentation |
Circular Cross-section Using the Gauckler-Manning-Strickler Equation 1
Description
Manningcirc and Manningcircy solve for a missing variable for a circular
cross-section. The uniroot function is used to obtain the
missing parameters.
The Manningcirc function solves for one missing variable in the Gauckler- Manning equation for a circular cross-section and uniform flow. The possible inputs are Q, n, Sf, y, and d. If y or d are not initially known, then Manningcircy can solve for y or d to use as input in the Manningcirc function.
Usage
Manningcirc(
Q = NULL,
n = NULL,
Sf = NULL,
y = NULL,
d = NULL,
Temp = NULL,
units = c("SI", "Eng")
)
Arguments
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. |
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. |
d |
numeric vector that contains the diameters value (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
|
Details
Circular cross-section using the Gauckler-Manning-Strickler equation
Gauckler-Manning-Strickler equation is expressed as
V = \frac{K_n}{n}R^\frac{2}{3}\sqrt{S}
- V
the velocity (m/s or ft/s)
- n
Manning's roughness coefficient (dimensionless)
- R
the hydraulic radius (m or ft)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
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}}\sqrt{S}
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- n
Manning's roughness coefficient (dimensionless)
- P
the wetted perimeters of the channel (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
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 circular cross-section follow:
R = \frac{A}{P}
- R
the hydraulic radius (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- P
the wetted perimeters of the channel (m or ft)
A = \left(\\theta - \sin \\theta\right) \frac{d^2}{8}
- A
the cross-sectional area (m^2 or ft^2)
- d
the diameters of the cross-section (m or ft)
- \theta
see the equation defining this parameters
\\theta = 2 \arcsin\left[1 - 2\left(\frac{y}{d}\right)\right]
- \theta
see the equation defining this parameters
- y
the flow depth (normal depth in this function) [m or ft]
- d
the diameters of the cross-section (m or ft)
d = 1.56 \left[\frac{nQ}{K_n\sqrt{S}}\right]^\frac{3}{8}
- d
the initial diameters of the cross-section [m or ft]
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- n
Manning's roughness coefficient (dimensionless)
- S
the slope of the channel bed (m/m or ft/ft)
- K_n
the conversion constant – 1.0 for SI and 3.2808399 ^ (1 / 3) for English units – m^(1/3)/s or ft^(1/3)/s
Note: This will only provide the initial conduit diameters, check the design considerations to determine your next steps.
P = \frac{\\theta d}{2}
- P
the wetted perimeters of the channel (m or ft)
- \theta
see the equation defining this parameters
- d
the diameters of the cross-section (m or ft)
B = d \sin\left(\frac{\\theta}{2}\right)
- B
the top width of the channel (m or ft)
- \theta
see the equation defining this parameters
- d
the diameters of the cross-section (m or ft)
D = \frac{A}{B}
- D
the hydraulic depth (m or ft)
- A
the cross-sectional area (m^2 or ft^2)
- B
the top width of the channel (m or ft)
Z = \frac{\sqrt{2}}{2}my^2.5
- Z
the Section factor (m or ft)
- y
the flow depth (normal depth in this function) [m or ft]
- m
the horizontal side slope
E = y + \frac{Q^2}{2gA^2}
- E
the Specific Energy (m or ft)
- Q
the discharge m^3/s or ft^3/s (cfs) is VA
- g
gravitational acceleration (m/s^2 or ft/sec^2)
- A
the cross-sectional area (m^2 or ft^2)
- y
the flow depth (normal depth in this function) [m or ft]
VH = \frac{V^2}{2g}
- VH
the Velocity Head (m or ft)
- V
the velocity (m/s or ft/s)
- g
gravitational acceleration (m/s^2 or ft/sec^2)
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}
- Re
Reynolds number (dimensionless)
- \rho
density (kg/m^3 or slug/ft^3)
- R
the hydraulic radius (m or ft)
- V
the velocity (m/s or ft/s)
- \mu
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)}
- Fr
the Froude number (dimensionless)
- V
the velocity (m/s or ft/s)
- g
gravitational acceleration (m/s^2 or ft/sec^2)
- D
the hydraulic depth (m or ft)
Value
the missing parameters (Q, n, or Sf) & theta, area (A), wetted
perimeters (P), velocity (V), top width (B), hydraulic depth (D), hydraulic radius (R), E (Specific Energy), Vel_Head (Velocity Head), Z (Section Factor), Reynolds number (Re), and Froude number (Fr) as a list. for the
Manningcirc function.
Note
Assumptions: uniform flow, prismatic channel, and surface water temperature of 20 degrees Celsius (68 degrees Fahrenheit) at atmospheric pressure
Note: Units must be consistent
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
Author(s)
Irucka Embry
References
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, 123-125, 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, 377-378, 392.
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.
See Also
Manningtrap for a trapezoidal cross-section, Manningrect for a
rectangular cross-section, Manningtri for a triangular cross-section,
and Manningpara for a parabolic cross-section.
Manningcircy
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.