iemisc: Comparing Other Hydraulic Software Output to iemisc’s Manningtrap for Critical Conditions

In iemisc: Irucka Embry's Miscellaneous Functions

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Introduction

This document compares the results for 2 examples for a trapezoidal channel with a critical state for the FHWA Hydraulic Toolbox Version 4.4, Dr. Xing Fang’s open channel flow calculator, and Irucka Embry’s iemisc [https://CRAN.R-project.org/package=iemisc] Manningtrap_critical function.

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Replicate the R code without the images

Note: If you wish to replicate the R code below, then you will need to copy and paste the following commands in R first (to make sure you have all the of the required packages):

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install.packages(c("install.load", "iemisc", "pander", "data.table"))
# install the packages and their dependencies

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# load the required package
install.load::load_package("iemisc", "pander", "data.table")

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Critical State Description

“When F (Froude number) is equal to unity, ... the flow is said to be in a critical state. If F is less than unity, ... the flow is subcritical. If F is greater than unity, ... the flow is supercritical.

“... the critical state of flow through a channel section is characterized by several important conditions. Recapitulating, they are (1) the specific energy is a minimum for a given discharge; (2) the discharge is a maximum for a given specific energy; (3) the specific force is a minimum for a given discharge; (4) the velocity head is equal to half the hydraulic depth in a channel of small slope; (5) the Froude number is equal to unity; and (6) the velocity of flow in a channel of small slope with uniform velocity distribution is equal to the celerity of small gravity waves in shallow water caused by local disturbances.

“Discussions on critical state of flow have referred mainly to a particular section of a channel, known as the critical section. If the critical state of exists throughout the entire length of the channel or over a reach of the channel, the flow in the channel is a critical flow.”

–Ven Te Chow, Ph.D., Open-Channel Hydraulics, McGraw-Hill Classic Textbook Reissue, New York City, New York: McGraw-Hill Book Company, 1988, pages 13, 63.

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Example 1

Given a trapezoidal channel with 3 ft symmetric side slopes, a channel width of 4 ft, a longitudinal slope of 0.02 ft/ft, Manning’s roughness coefficient of 0.0550, and a depth of 1.454 ft, calculate the missing parameters for a critical state.

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FHWA Hydraulic Toolbox Example 1 (Image)

linguisticsdown::include_graphics2("compare.png")

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FHWA Hydraulic Toolbox Example 1 (Text Table)

fhwa_ex1 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), Value = c(44.001, 1.454, 12.161, 13.197, 0.921, 3.618, 12.725, 3.0, 3.0, 4.0, 0.02, 0.0550, 0.652, 1.163, 5.052, 0.04979, 10.978, 1.815, 1.150), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "",  "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))


pander(fhwa_ex1, missing = "")

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Dr. Xing Fang’s Open Channel Flow Calculator’s Solution of Example 1 (Image)

linguisticsdown::include_graphics2("trapezoid1.png")

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Dr. Xing Fang’s Open Channel Flow Calculator’s Solution of Example 1 (Text Table)

fang_ex1 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), Value = c(43.9882, 1.454, 12.16, 13.2, "", 3.6179, 12.72, 3.0, 3.0, 4.0, 0.02, 0.0550, 0.65, 1.17, "", 0.0492, "", "", ""), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "", "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))


pander(fang_ex1, missing = "")

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iemisc's Manningtrap Solution of Example 1

uuc1 <- Manningtrap_critical(y = 1.454, b = 4, m = 3, Sf = 0.02, n = 0.0550, units = "Eng", type = "symmetrical", critical = "accurate", output = "data.table")

pander(uuc1, missing = "")


uuc1a <- Manningtrap_critical(y = 1.454, b = 4, m = 3, Sf = 0.02, n = 0.0550, units = "Eng", type = "symmetrical", critical = "accurate", output = "list")

uuc1b <- Manningtrap_critical(y = 1.454, b = 4, m = 3, Sf = 0.02, n = 0.0550, units = "Eng", type = "symmetrical", critical = "approximate", output = "list")

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Comparing All 3 Solutions for Example 1

compare_ex1 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Normal Froude Number", "Critical Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), `FHWA Value` = c(44.001, 1.454, 12.161, 13.197, 0.921, 3.618, 12.725, 3.0, 3.0, 4.0, 0.02, 0.0550, 0.652, "", 1.163, 5.052, 0.04979, 10.978, 1.815, 1.150), `Wang Value` = c(43.9882, 1.454, 12.16, 13.2, "", 3.6179, 12.72, 3.0, 3.0, 4.0, 0.02, 0.0550, 0.65, "", 1.17, "", 0.0492, "", "", ""), `iemisc Value (Accurate Critical Froude)` = c(uuc1a$Q, uuc1a$y, uuc1a$A, uuc1a$P, uuc1a$R, uuc1a$V, uuc1a$B, uuc1a$m, uuc1a$m, uuc1a$b, uuc1a$Sf, uuc1a$n, uuc1a$Fr, uuc1a$Frc, uuc1a$yc, uuc1a$Vc, uuc1a$Sfc, uuc1a$Bc, uuc1a$taud, uuc1a$tau0), `iemisc Value (Approximate Critical Froude)` = c(uuc1b$Q, uuc1b$y, uuc1b$A, uuc1b$P, uuc1b$R, uuc1b$V, uuc1b$B, uuc1b$m, uuc1b$m, uuc1b$b, uuc1b$Sf, uuc1b$n, uuc1b$Fr, uuc1b$Frc, uuc1b$yc, uuc1b$Vc, uuc1b$Sfc, uuc1b$Bc, uuc1b$taud, uuc1b$tau0), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "", "", "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))


pander(compare_ex1, missing = "")

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Example 2

Given a trapezoidal channel with 2 ft and 1.5 ft non-symmetric side slopes, a channel width of 8 ft, a longitudinal slope of 0.01 ft/ft, Manning’s roughness coefficient of 0.0150, and a flow of 745 cfs, calculate the missing parameters for a critical state.

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FHWA Hydraulic Toolbox Example 2

linguisticsdown::include_graphics2("2019-05-22_08_24_13-ChannelAnalysis.png")

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FHWA Hydraulic Toolbox Example 2 (Text Table)

fhwa_ex2 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), Value = c(745.000, 3.298, 45.419, 21.320, 2.130, 16.408, 19.543, 2.0, 1.5, 8.0, 0.01, 0.0150, 1.896, 4.639, 9.965, 0.0257, 24.235, 2.058, 1.329), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "", "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))



pander(fhwa_ex2, missing = "")

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Dr. Xing Fang’s Open Channel Flow Calculator’s Solution of Example 2

linguisticsdown::include_graphics2("trapezoid2.png")

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Dr. Xing Fang’s Open Channel Flow Calculator’s Solution of Example 2 (Text Table)

fang_ex2 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), Value = c(745, 3.3, 45.51, 21.34, "", 16.371, 19.56, 2.0, 1.5, 8.0, 0.01, 0.0150, 1.89, 4.64, "", 0.0026, "",  "", ""), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "", "", "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))


pander(fang_ex1, missing = "")

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iemisc’s Manningtrap Solution of Example 2

uuc2 <- Manningtrap_critical(Q = 745, b = 8, m1 = 2, m2 = 1.5, Sf = 0.01, n = 0.0150, units = "Eng", type = "non-symmetrical", critical = "accurate", output = "data.table")

pander(uuc2, missing = "")



uuc2a <- Manningtrap_critical(Q = 745, b = 8, m1 = 2, m2 = 1.5, Sf = 0.01, n = 0.0150, units = "Eng", type = "non-symmetrical", critical = "accurate", output = "list")

uuc2b <- Manningtrap_critical(Q = 745, b = 8, m1 = 2, m2 = 1.5, Sf = 0.01, n = 0.0150, units = "Eng", type = "non-symmetrical", critical = "approximate", output = "list")

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Comparing All 3 Solutions for Example 2

compare_ex2 <- data.table(Parameter = c("Flow", "Depth", "Area of Flow", "Wetted Perimeter", "Hydraulic Radius", "Average Velocity", "Top Width (T)", "Side slope 1 (Z1)", "Side slope 2 (Z2)", "Channel width (B)", "Longitudinal slope", "Manning's roughness", "Normal Froude Number", "Critical Froude Number", "Critical Depth", "Critical Velocity", "Critical Slope", "Critical Top Width", "Max Shear Stress", "Avg. Shear Stress"), `FHWA Value` =  c(745.000, 3.298, 45.419, 21.320, 2.130, 16.408, 19.543, 2.0, 1.5, 8.0, 0.01, 0.0150, 1.896, "", 4.639, 9.965, 0.0257, 24.235, 2.058, 1.329), `Wang Value` = c(745, 3.3, 45.51, 21.34, "", 16.371, 19.56, 2.0, 1.5, 8.0, 0.01, 0.0150, 1.89, "", 4.64, "", 0.0026, "",  "", ""), `iemisc Value (Accurate Critical Froude)` = c(uuc2a$Q, uuc2a$y, uuc2a$A, uuc2a$P, uuc2a$R, uuc2a$V, uuc2a$B, uuc2a$m1, uuc2a$m2, uuc2a$b, uuc2a$Sf, uuc2a$n, uuc2a$Fr, uuc2a$Frc, uuc2a$yc, uuc2a$Vc, uuc2a$Sfc, uuc2a$Bc, uuc2a$taud, uuc2a$tau0), `iemisc Value (Approximate Critical Froude)` = c(uuc2b$Q, uuc2b$y, uuc2b$A, uuc2b$P, uuc2b$R, uuc2b$V, uuc2b$B, uuc2b$m1, uuc2b$m2, uuc2b$b, uuc2b$Sf, uuc2b$n, uuc2b$Fr, uuc2b$Frc, uuc2b$yc, uuc2b$Vc, uuc2b$Sfc, uuc2b$Bc, uuc2b$taud, uuc2b$tau0), Unit = c("cfs", "ft", "sq ft", "ft", "ft", "fps", "ft", "", "", "ft", "ft/ft", "", "", "", "ft", "fps", "ft/ft", "ft", "lb/ft^2", "lb/ft^2"))



pander(compare_ex2, missing = "")

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Works Cited

FHWA Hydraulic Toolbox Version 4.4. https://www.fhwa.dot.gov/engineering/hydraulics/software/toolbox404.cfm

The open channel flow calculator. Dr. Xing Fang, Department of Civil Engineering, Lamar University, 2000. https://eng.auburn.edu/~xzf0001/Handbook/Channels.html

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Copyright and License

All R code written by Irucka Embry is distributed under the GPL-3 (or later) license, see the GNU General Public License {GPL} page.

All written content originally created by Irucka Embry is copyrighted under the Creative Commons Attribution-ShareAlike 4.0 International License. All other written content retains the copyright of the original author(s).

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

iemisc documentation built on Sept. 25, 2023, 5:09 p.m.