hydraulics (version 0.7.0)

direct_step: 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
)

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

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]

Author

Ed Maurer

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.

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")