critical_depth: Critical depth

Description Usage Arguments Details Value Examples

Description

Calculate the critical depth.

Usage

1
critical_depth(Q, yopt, g, B, SS)

Arguments

Q

Flow rate [L^3 T^{-1}].

yopt

Initial guess for normal depth [L].

g

Gravitational acceleration [L T^{-2}].

B

Channel bottom width [L].

SS

Channel sideslope [L L^{-1}].

Details

The critical depth is the water depth at which a channel flow regime will transition from supercritical to subcritical (or vice versa). Calculation of the critical depth is based on a specific energy formulation, i.e.

E = y + z + \frac{Q^2}{2gB^2y^2}

where y is the flow depth, z is the elevation relative to some datum (assumed to be 0), and the last term represents kinetic energy. More specifically, the function operates by finding the point where the derivative of specific energy w.r.t. y is zero, i.e. y = y_c when

\frac{dE}{dy} = 1 - \frac{Q^2}{gA^3}\frac{dA}{dy} = 0

.

Value

The critical depth y_c [L].

Examples

1
2
critical_depth(250, 2, 32.2, 100, 0) # rectangular channel
critical_depth(126, 1, 9.81, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V


Search within the rivr package
Search all R packages, documentation and source code

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.