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 June 22, 2024, 9:45 a.m.
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| 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
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