The following examples only cover open channel flow problems using the Gauckler-Manning-Strickler equation to calculate the missing parameters and the determination of the critical depth.
library(install.load)
load_package("iemisc", "iemiscdata", "rivr") # load needed packages using the load_package function from the install.load package (it is assumed that you have already installed these packages)## Loading required package: data.table# 1) Practice Problem 14.10 from Mott (page 391-392)
# What is the Q (discharge) for this cross-section?
# See nchannel in iemiscdata for the Manning's n table that the following example uses
# Use the normal Manning's n value for Natural streams - minor streams (top width at floodstage < 100 ft), Lined or Constructed Channels, Concrete, and unfinished.
# The 1st heading is "Manning's n for Channels"
# The 2nd heading is "Natural streams - minor streams (top width at floodstage < 100 ft)"
# The 3rd heading is "Lined or Constructed Channels,"
# The 4th heading is "Concrete"
# The 5th heading is "unfinished"
data(nchannel)
# load the data set nchannel from iemiscdata
nlocation <- grep("unfinished", nchannel$"Type of Channel and Description")
# search for the term "unfinished" in the "Type of Channel and Description" column in the nchannel data set
nlocation## [1] 72n <- nchannel[nlocation, 3] # 3 for column 3 - Normal n
# the value of n will be found in column 3 at the location specified by nlocation
n## [1] 0.017Q <- Manningrect(b = 3.5, y = 2, Sf = 0.1/100, n = n, units = "SI")##
## Flow is NOT in the rough turbulent zone so the Gauckler-Manning-Strickler equation is not acceptable to use.
##
##
## This is subcritical flow.# b = 3.5 m, y = 2 m, Sf = 0.1 percent m/m, n = 0.017, units = SI units
# This will solve for Q since it is missing and Q will be in m^3/s
Q## $Q
## [1] 12.4358
##
## $V
## [1] 1.776542
##
## $A
## [1] 7
##
## $P
## [1] 7.5
##
## $R
## [1] 0.9333333
##
## $Re
## [1] 1651.825
##
## $Fr
## [1] 0.401144# What is the critical depth for this given discharge?
critical_depth(Q$Q, 2, 9.80665, 3.5, 0)## [1] 1.087836# 2) Problem 1 from Hauser (page 88)
# What is the Sf (slope) for this cross-section?
Sf <- Manningrect(Q = 6.25 * 8 * 14.9, b = 8, y = 6.25, n = 0.01, units = "Eng")##
## Flow IS in the rough turbulent zone so the Gauckler-Manning-Strickler equation is acceptable to use.
##
##
## This is supercritical flow.# Q = 6.25 ft * 8 ft * 14.9 ft/sec, b = 8 ft, y = 6.25 ft, n = 0.01, units = Eng units
# This will solve for Sf since it is missing and Sf will be in ft/ft
Sf## $Sf
## [1] 0.003062629
##
## $V
## [1] 14.9
##
## $A
## [1] 50
##
## $P
## [1] 20.5
##
## $R
## [1] 2.439024
##
## $Re
## [1] 3233750
##
## $Fr
## [1] 1.050737# What is the critical depth for this given discharge?
critical_depth(6.25 * 8 * 14.9, 6.25, 9.80665 * (3937 / 1200), 8, 0)## [1] 6.459654
library(install.load)
load_package("iemisc", "iemiscdata", "rivr") # load needed packages using the load_package function from the install.load package (it is assumed that you have already installed these packages)
# 3) Practice Problem 14.17 from Mott (page 392)
# What is the y (flow depth) for this cross-section?
# See nchannel in iemiscdata for the Manning's n table that the following example uses
# Use the normal Manning's n value for Natural streams - minor streams (top width at floodstage < 100 ft), Lined or Constructed Channels, Concrete, and unfinished.
# The 1st heading is "Manning's n for Channels"
# The 2nd heading is "Natural streams - minor streams (top width at floodstage < 100 ft)"
# The 3rd heading is "Lined or Constructed Channels,"
# The 4th heading is "Concrete"
# The 5th heading is "unfinished"
data(nchannel)
# load the data set nchannel from iemiscdata
nlocation <- grep("unfinished", nchannel$"Type of Channel and Description")
# search for the term "unfinished" in the "Type of Channel and Description" column in the nchannel data set
nlocation## [1] 72n <- nchannel[nlocation, 3] # 3 for column 3 - Normal n
# the value of n will be found in column 3 at the location specified by nlocation
n## [1] 0.017y <- Manningtrap(Q = 15, b = 3, m = 1 / tan(40 * pi / 180), Sf = 0.1/100, n = n, units = "SI")##
## Flow is NOT in the rough turbulent zone so the Gauckler-Manning-Strickler equation is not acceptable to use.
##
##
## This is subcritical flow.# Q = 15, b = 3 m, m = 1 / tan(40 * pi / 180), Sf = 0.1 percent m/m, n = 0.017, units = SI units
# This will solve for y since it is missing and y will be in m
y## $y
## [1] 1.631874
##
## $V
## [1] 1.858903
##
## $A
## [1] 8.069276
##
## $P
## [1] 8.07749
##
## $R
## [1] 0.9989831
##
## $Re
## [1] 1849.978
##
## $Fr
## [1] 0.5484986# What is the critical depth for this given discharge?
critical_depth(15, y$y, 9.80665, 3, 1 / tan(40 * pi / 180))## [1] 1.16226# 4) Example 2 from FHWA
# What is the y (flow depth) for this cross-section?
y <- Manningtrap(Q = 150, b = 4, m = 2, Sf = 2/100, n = 0.030, units = "Eng")##
## Flow IS in the rough turbulent zone so the Gauckler-Manning-Strickler equation is acceptable to use.
##
##
## This is supercritical flow.# Q = 150 cfs, b = 4 ft, m = 2, Sf = 2/100 ft/ft, n = 0.030, units = Eng units
# This will solve for y since it is missing and y will be in ft
y## $y
## [1] 2.152071
##
## $V
## [1] 8.393437
##
## $A
## [1] 17.87111
##
## $P
## [1] 13.62436
##
## $R
## [1] 1.311703
##
## $Re
## [1] 979668.9
##
## $Fr
## [1] 1.24291# What is the critical depth for this given discharge?
critical_depth(150, y$y, 9.80665 * (3937 / 1200), 4, 2)## [1] 2.40582
library(install.load)
load_package("iemisc", "rivr") # load needed packages using the load_package function from the install.load package (it is assumed that you have already installed these packages)
# 5) Problem 17 from Hauser (page 89)
# What is the Q (discharge) for this cross-section?
Q <- Manningtri(y = 6, m = 4, Sf = 0.006, n = 0.025, units = "Eng")##
## Flow IS in the rough turbulent zone so the Gauckler-Manning-Strickler equation is acceptable to use.
##
##
## This is subcritical flow.# y = 6 ft, m = 4 ft/ft, Sf = 0.006 ft/ft, n = 0.025, units = Eng units
# This will solve for Q since it is missing and Q will be in ft^3/s
Q## $Q
## [1] 1351.443
##
## $V
## [1] 9.385019
##
## $A
## [1] 144
##
## $P
## [1] 49.47727
##
## $R
## [1] 2.910428
##
## $Re
## [1] 2430502
##
## $Fr
## [1] 0.9552611# What is the critical depth for this given discharge?
critical_depth(Q$Q, 6, 9.80665 * (3937 / 1200), 0, 4)## [1] 5.89115# 6) Example 2 from FHWA
# What is the y (flow depth) for this cross-section?
y <- Manningtri(Q = 150, m = 2, Sf = 2/100, n = 0.030, units = "Eng")##
## Flow IS in the rough turbulent zone so the Gauckler-Manning-Strickler equation is acceptable to use.
##
##
## This is supercritical flow.# Q = 150 cfs, m = 2, Sf = 2/100 ft/ft, n = 0.030, units = Eng units
# This will solve for y since it is missing and y will be in ft
y## $y
## [1] 2.975079
##
## $V
## [1] 8.473527
##
## $A
## [1] 17.70219
##
## $P
## [1] 13.30496
##
## $R
## [1] 1.330496
##
## $Re
## [1] 1003187
##
## $Fr
## [1] 1.224835# What is the critical depth for this given discharge?
critical_depth(150, y$y, 9.80665 * (3937 / 1200), 4, 2)## [1] 2.40582
library(iemisc)
# 7) Modified Practice Problem 14.32/14.34 from Mott (page 393)
# What is the Q (discharge) for this cross-section?
Q <- Manningcirc(d = 375/1000, y = 225/1000, Sf = 0.12/100, n = 0.015, units = "SI")##
## Flow is NOT in the rough turbulent zone so the Gauckler-Manning-Strickler equation is not acceptable to use.
##
##
## This is subcritical flow.# d = 375/1000 m, y = 225/1000 m, Sf = 0.12/100 m/m, n = 0.015, units = SI units
# This will solve for Q since it is missing and Q will be in m^3/s
Q## $Q
## [1] 0.03536432
##
## $V
## [1] 0.5111079
##
## $A
## [1] 0.06919149
##
## $P
## [1] 0.6645578
##
## $R
## [1] 0.1041166
##
## $Re
## [1] 53.01321
##
## $Fr
## [1] 0.3761052# 8) Problem 18 from Hauser (page 89)
# What is the Q (discharge) for this cross-section?
Q <- Manningcirc(d = 10/12, y = 3/12, Sf = 2/100, n = 0.025, units = "Eng")##
## Flow IS in the rough turbulent zone so the Gauckler-Manning-Strickler equation is acceptable to use.
##
##
## This is subcritical flow.# d = 10/12 ft, y = 3/12 ft, Sf = 2/100 ft/ft, n = 0.025, units = Eng units
# This will solve for Q since it is missing and Q will be in ft
Q## $Q
## [1] 0.3155138
##
## $V
## [1] 2.292697
##
## $A
## [1] 0.1376169
##
## $P
## [1] 0.9660662
##
## $R
## [1] 0.1424508
##
## $Re
## [1] 29061.33
##
## $Fr
## [1] 0.9522204
library(iemisc)
# 9) Modified Exercise 4.3 from Sturm (page 153)
# What is the B1 ("bank-full width") for this cross-section?
B1 <- Manningpara(Q = 32.2, y = 8, y1 = 5.1, Sf = 0.0092, n = 0.025, units = "SI")##
## Flow is NOT in the rough turbulent zone so the Gauckler-Manning-Strickler equation is not acceptable to use.
##
##
## This is subcritical flow.# Q = 32.2 m^3/s, y = 8 m, y1 = 5.1 m, Sf = 0.0092 m/m, n = 0.025, units = SI units
# This will solve for B1 since it is missing and B1 will be in m
B1## $B1
## [1] 0.982228
##
## $V
## [1] 4.907778
##
## $A
## [1] 6.561014
##
## $P
## [1] 16.10527
##
## $R
## [1] 0.407383
##
## $Re
## [1] 1991.771
##
## $Fr
## [1] 0.6786177
Barbara A. Hauser, Practical Hydraulics Handbook, Second Edition, Boca Raton, Florida: CRC Press, Inc., 1996, page 88-89.
Robert L. Mott and Joseph A. Untener, Applied Fluid Mechanics, Seventh Edition, New York City, New York: Pearson, 2015, page 392-393.
Terry W. Sturm, Open Channel Hydraulics, 2nd Edition, New York City, New York: The McGraw-Hill Companies, Inc., 2010, page 153.
U.S. Department of Transportation Federal Highway Administration (FHWA), “Design Charts for Open-Channel Flow HDS 3”, August 1961, http://www.fhwa.dot.gov/engineering/hydraulics/pubs/hds3.pdf.
Wikimedia Foundation, Inc. Wikipedia, 5 May 2016, “Gravitational acceleration”, https://en.wikipedia.org/wiki/Gravitational_acceleration.
Wikimedia Foundation, Inc. Wikipedia, 26 November 2015, “Manning formula”, https://en.wikipedia.org/wiki/Manning_formula.