# ex_tube: Water Tube System, Mechanics problem, DAE of Index 2 In deTestSet: Test Set for Differential Equations

## Description

The tube problem describes the water flow through a tube system, taking into account turbulence and the roughness of the tube walls.

It is an index 2 system of 49 non-linear Differential-Algebraic Equations.

## Usage

 ```1 2 3``` ```tube (times = seq(0, 17.0*3600, by = 100), yini = NULL, dyini = NULL, parms = list(), printmescd = TRUE, method = radau, atol = 1e-6, rtol = 1e-6, maxsteps = 1e+05, ...) ```

## Arguments

 `yini ` the initial (state) values for the DE system. If `y` has a name attribute, the names will be used to label the output matrix. `dyini ` the initial derivatives of the state variables of the DE system. `times ` time sequence for which output is wanted; the first value of `times` must be the initial time. `parms ` list of parameters that overrule the default parameter values `method ` the solver to use; only `mebdfi` available for now `maxsteps ` maximal number of steps per output interval taken by the solver `atol ` absolute error tolerance, either a scalar or a vector, one value for each y. `rtol ` relative error tolerance, either a scalar or a vector, one value for each y, `printmescd ` if TRUE the mixed error significant digits computed using the reference solution at time 1e13 are printed `... ` additional arguments passed to the solver .

## Details

parameter <- c(nu = 1.31e-6, g = 9.8, rho = 1.0e3, rcrit = 2.3e3, length= 1.0e3, k = 2.0e-4, d= 1.0e0, b = 2.0e2)

## Value

A matrix of class `deSolve` with up to as many rows as elements in `times` and as many columns as elements in `yini`, plus an additional column (the first) for the time value.

There will be one row for each element in `times` unless the solver returns with an unrecoverable error. If `yini` has a names attribute, it will be used to label the columns of the output value.

## Author(s)

Karline Soetaert <[email protected]>

Francesca Mazzia

## Examples

 ```1 2 3 4 5 6 7``` ```out <- tube() plot(out, lwd = 2, which = 1:9) plot(out, which = "phi3.4", lwd = 2, xlim = c(10000, 60000), ylim = c(0.000145, 0.000185)) # compare with reference solution max(abs(out[nrow(out),-1]- reference("tube"))) ```

deTestSet documentation built on May 29, 2017, 2:56 p.m.