sequent_depth: Solves the Momentum Equation for sequent (or conjugate) depth in a trapezoidal channel
Description
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.
Usage
sequent_depth(
Q = NULL,
b = NULL,
y = NULL,
m = NULL,
units = c("SI", "Eng"),
ret_units = FALSE
)
Value
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
Arguments
Q
numeric vector that contains the flow rate [\(m^3 s^{-1}\) or \(ft^3 s^{-1}\)]
b
numeric vector that contains the channel bottom width [\(m\) or \(ft\)]
y
numeric vector that contains the water depth [\(m\) or \(ft\)]
m
numeric vector that contains the side slope of the channel (m:1 H:V) [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 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.
#Solving for sequent depth: SI Units#Flow of 0.2 m^3/s, bottom width = 0.5 m, Depth = 0.1 m, side slope = 1:1sequent_depth(Q=0.2,b=0.5,y=0.1,m=1,units = "SI", ret_units = TRUE)