sequent_depth: Solves the Momentum Equation for sequent (or conjugate) depth...

sequent_depthR Documentation

Solves the Momentum Equation for sequent (or conjugate) depth in a trapezoidal channel


This function solves the Momentum equation for water flow in an open channel with a trapezoidal shape and determines the sequent (conjugate) depth. This is the flow depth either upstream or downstream of a hydraulic jump, whichever is not provided as input.


  Q = NULL,
  b = NULL,
  y = NULL,
  m = NULL,
  units = c("SI", "Eng"),
  ret_units = FALSE



numeric vector that contains the flow rate [m^3 s^{-1} or ft^3 s^{-1}]


numeric vector that contains the channel bottom width [m or ft]


numeric vector that contains the water depth [m or ft]


numeric vector that contains the side slope of the channel (m:1 H:V) [unitless]


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.


If set to TRUE the value(s) returned are of class units with units attached to the value. [Default is FALSE]


The Momentum equation for open channel flow conditions in a trapezoidal channel:

M = \frac{by^2}{2}+\frac{my^3}{3}+\frac{Q^2}{gy\left(b+my\right)}

where C is 1.0 for SI units and 1.49 for Eng (U.S. Customary) units. The momentum function is assumed to be the same on both sides of a hydraulic jump, allowing the determination of the sequent depth.


Returns a list including:

  • y - input depth

  • y_seq - sequent depth

  • yc - critical depth

  • Fr - Froude number for input depth

  • Fr_seq - Froude number for sequent depth

  • E - specific energy for input depth

  • E_seq - specific energy for sequent depth


Ed Maurer


#Solving for sequent depth: SI Units
#Flow of 0.2 m^3/s, bottom width = 0.5 m, Depth = 0.1 m, side slope = 1:1
sequent_depth(Q=0.2,b=0.5,y=0.1,m=1,units = "SI", ret_units = TRUE)

hydraulics documentation built on June 22, 2024, 7:38 p.m.