direct_step {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^{-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]

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.

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")