Manningtrap_critical: Trapezoidal cross-section for the Gauckler-Manning-Strickler...

In iemisc: Irucka Embry's Miscellaneous Functions

Trapezoidal cross-section for the Gauckler-Manning-Strickler equation (critical parameters)

Description

This function solves for one missing variable in the Gauckler-Manning- Strickler equation for a trapezoidal cross-section and uniform flow. The uniroot function is used to obtain the missing parameters. This function provides both normal and critical parameters values.

Usage

Manningtrap_critical(
  Q = NULL,
  n = NULL,
  m = NULL,
  m1 = NULL,
  m2 = NULL,
  Sf = NULL,
  y = NULL,
  b = NULL,
  Temp = NULL,
  units = c("SI", "Eng"),
  type = c("symmetrical", "non-symmetrical"),
  critical = c("approximate", "accurate"),
  output = c("list", "data.table")
)

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.
m	numeric vector that contains the symmetric "cross-sectional side slope of m:V (horizontal:vertical)", if known.
m1	numeric vector that contains the non-symmetric "cross-sectional side slope of m1:V (horizontal:vertical)", if known.
m2	numeric vector that contains the non-symmetric "cross-sectional side slope of m2:V (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.
b	numeric vector that contains the bottom width, 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)
type	character vector that contains the type of trapezoid (symmetrical or non-symmetrical). The symmetrical trapezoid uses m while the non- symmetrical trapezoid uses m1 and m2.
critical	character vector that contains the type of critical parameters calculations (approximate or accurate). The accurate calculation provides parameters where the Froude number is 1. The approximate calculation calculates the values without having the Froude number return 1.
output	character vector that contains the output type, either it will be a list or data.table. The list is the easiest to obtain a singular value.

Details

Critical State Discussion from Chow pages 13, 63 "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."

Value

the missing parameters (Q, n, b, m, m1, m2, Sf, or y) & V (velocity), Flow depth (y), Bottom width (b), symmetric side slope (m), Slope (Sf), A (area), P (wetted perimeters), R (hydraulic radius), B (top width), D (hydraulic depth), w (Wetted Length), w1 (Wetted Length for a non-symmetric trapezoid), w2 (Wetted Length for a non-symmetric trapezoid), Z (Section Factor), E (Specific Energy), K (conveyance), Vel_Head (Velocity Head), Re (Reynolds number), Fr (Froude number), taud (maximum shear stress), tau0 (average shear stress), yc (critical depth), Ac (critical area), Pc (critical wetted perimeters), Bc (critical top width), Rc (critical hydraulic radius), Dc (critical hydraulic depth), Vc (critical velocity), Qc (critical discharge), Sfc (critical slope), Frc (critical Froude number), Zc (critical Section Factor), Ec (critical Specific Energy) as a list. Alternatively, the Flow depth (y), Flow area (A), Wetted Perimeters (P), Top Width (B), Bottom width (b), Hydraulic Radius (R), Hydraulic Depth (D), Flow Mean Velocity (V), Flow Discharge (Q), Manning's roughness coefficient (n), Slope (Sf), Temperature, Absolute Temperature, Saturated Liquid Density, Absolute or Dynamic Viscosity, Kinematic Viscosity, Froude number (Fr), Reynolds number (Re), symmetric side slope (m), non-symmetric side slope (m1), non-symmetric side slope (m2), Wetted Length (w), Wetted Length for a non-symmetric trapezoid (w1), Wetted Length for a non-symmetric trapezoid (w2), Section Factor (Z), conveyance (K), Specific Energy (E), Velocity Head (Vel_Head), Maximum Shear Stress (taud), Average Shear Stress (tau0) along with the associated units can be returned in a data.table. Both the normal and the critical values (where present) are returned in the table.

Author(s)

Irucka Embry

References

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.

Examples

# Example 1

library(iemisc)
# Exercise 4.1 from Sturm (page 153)

uuc <- Manningtrap_critical(Q = 3000, b = 40, m = 3, Sf = 0.002, n = 0.025,
units = "Eng", type = "symmetrical", critical = "accurate", output = "list")
# Q = 3000 cfs, b = 40 ft, 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

uuc$y # only returns y

uuc # returns all results



# Example 2

# 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

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