direct_step: Uses the direct step method to find the distance between two...

In hydraulics: Basic Pipe and Open Channel Hydraulics

Uses the direct step method to find the distance between two known depths in a trapezoidal channel

Description

This function applies the direct step method for a gradually-varying water surface profile for flow in an open channel with a trapezoidal shape.

Usage

direct_step(
  So = NULL,
  n = NULL,
  Q = NULL,
  y1 = NULL,
  y2 = NULL,
  b = NULL,
  m = NULL,
  nsteps = 1,
  units = c("SI", "Eng"),
  ret_units = FALSE
)

Arguments

So	numeric channel bed slope [unitless]
n	numeric vector that contains the Manning roughness coefficient
Q	numeric vector that contains the flow rate [m^3/s or ft^3/s]
y1	numeric vector that contains the initial water depth [m or ft]
y2	numeric vector that contains the final water depth [m or ft]
b	numeric vector that contains the channel bottom width [m or ft]
m	numeric vector that contains the side slope of the channel (m:1 H:V) [unitless]
nsteps	integer of the number of calculation steps between y1 and y2 [unitless]
units	character vector that contains the system of units [options are SI for International System of Units and Eng for English (US customary) units. This is used for compatibility with iemisc package.
ret_units	If set to TRUE the value(s) returned are of class units with units attached to the value. [Default is FALSE]

Details

The direct step method applies the energy equation to gradually-varied open channel flow conditions, assuming each increment is approximately uniform. This function works with a trapezoidal channel shape. The water depths at two locations are input with channel geometry and flow rate, and the distance between the two locations, {Δ}X, is calculated:

{Δ}X = \frac{E_1 - E_2}{S_f-S_o}

where E1 and E2 are the specific energy values at the locations of y1 and y2, Sf is the slope of the energy grade line, and So is the slope of the channel bed.

Value

Returns a data frame (tibble) with the columns:

• x - cumulative distance from position of y1

• z - elevation of the channel bed at location x

• y - depth of the water at location x

• A - cross-sectional area at location x

• Sf - slope of the energy grade line at location x

• E - specific energy at location x

• Fr - Froude number at location x

Author(s)

Ed Maurer

Examples

#Solving for profile between depths 3.1 ft and 3.4 ft in a rectangular channel
#Flow of 140 ft^3/s, bottom width = 6 ft:
direct_step(So=0.0015, n=0.013, Q=140, y1=3.1, y2=3.4, b=6, m=0, nsteps=2, units="Eng")

hydraulics documentation built on Dec. 7, 2022, 1:11 a.m.