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

Source: R/direct_step.R
direct_step.Rd

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 [\(m^3 s^{-1}\) or \(ft^3 s^{-1}\)]

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]

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

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, \({\Delta}X\), is calculated: $${\Delta}X = \frac{E_1 - E_2}{S_f-S_o}$$ where \(E_1\) and \(E_2\) are the specific energy values at the locations of \(y_1\) and \(y_2\), \(S_f\) is the slope of the energy grade line, and \(S_o\) is the slope of the channel bed.

Author

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")
#> y1=3.100, y2=3.400, yn=3.750, yc=2.566646
#> Profile type  = M2
#> # A tibble: 3 × 7
#>        x     z     y     A      Sf     E    Fr
#>    <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl> <dbl>
#> 1    0   0      3.1   18.6 0.00247  3.98 0.753
#> 2  -85.6 0.128  3.25  19.5 0.00218  4.05 0.702
#> 3 -230.  0.346  3.4   20.4 0.00194  4.13 0.656