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50px|none|Symbol System Element Point Source Transport reaches map the translation and retention behavior of natural water courses or pipelines. There are different approaches for the calculation of pipes or natural channels.

The following options are implemented: frame|none|Calculation options of transport routes

Translation

The inflow wave is moved to the outlet with a time offset that corresponds to the flow time in the transport reach. If the flow time is smaller than the calculation time step, the translation behavior is not visible in the simulation results.

Open Channel Pipeline

A wave runoff calculation is performed for pipes according to Kalinin-Miljukov. The parameters of the Kalinin-Miljukov method are estimated internally by the program according to /Euler, 1983/ for circular pipes, or are determined for non-circular profiles by specifying the hydraulic diameter and the cross-sectional area at full filling.

charakteristische Länge:	[math]\displaystyle{ L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} }[/math]
Retentionskonstante:	[math]\displaystyle{ 0.64 \cdot L \cdot \frac{D^2}{Q_v} ~\mbox{[s]} }[/math]

with:

[math]\displaystyle{ D~\mbox{[m]} }[/math]:	Circular pipe diameter or hydraulic diameter
[math]\displaystyle{ I_S~\mbox{[-]} }[/math]:	Bottom gradient of the pipe
[math]\displaystyle{ Q_v ~\mbox{[m³/s]} }[/math]:	peak discharge capacity of the pipe

The peak discharge capacity of the pipe is calculated according to the flow law of Prandtl-Colebrook:

[math]\displaystyle{ Q_v=A_v \left [ -2 \cdot \lg \left [\frac{251 \cdot \nu}{D \sqrt{2 g D I_S}} + \frac{k_b}{3.71 \cdot D} \right ] \cdot \sqrt{2gDI_s} \right ] }[/math]

with:

[math]\displaystyle{ A_v~\mbox{[m²]} }[/math]:	Sectional area of the profile
[math]\displaystyle{ \nu~\mbox{[m²/s]} }[/math]:	kinematic viscosity
[math]\displaystyle{ k_b ~\mbox{[m³/s]} }[/math]:	Operating roughness
[math]\displaystyle{ g ~\mbox{[m/s²]} }[/math]:	Gravitational Acceleration

According to the characteristic length [math]\displaystyle{ L }[/math] the transport distance of the collector [math]\displaystyle{ L_g }[/math] is divided into [math]\displaystyle{ n }[/math] calculation sections of equal length with

[math]\displaystyle{ n=L_g/L }[/math] (where [math]\displaystyle{ n }[/math] is an integer number)

The adjusted parameters apply to the individual calculation sections

[math]\displaystyle{ L^*=L_g/n }[/math]

[math]\displaystyle{ K^*=K \cdot L^*/L }[/math]

Based on these parameters, after [math]\displaystyle{ n }[/math]-times the recursion formula

[math]\displaystyle{ Q_{a,i}=Q_{a,i-1}+C_1 \cdot \left(Q_{z,i-1} - Q_{a,i-1} \right ) + C_2 \cdot \left(Q_{z,i}-Q_{z,i-1} \right) }[/math]

with:

[math]\displaystyle{ Q_z }[/math]:	Inflow to calculation section
[math]\displaystyle{ Q_a }[/math]:	Discharge from calculation section
[math]\displaystyle{ i }[/math]:	Current calculation time step
[math]\displaystyle{ i-1 }[/math]:	Previous calculation time step
[math]\displaystyle{ dt }[/math]:	Calculation time interval
[math]\displaystyle{ C_1=1- e^{-dt/K^*} }[/math]
[math]\displaystyle{ C_2=1- \frac{K^*}{dt}/C_1 }[/math]

Open channel with specification of a cross profile

Also here, the translation and retention behavior is mapped with help of the Kalinin-Miljukov waveform calculation. The characteristic length is derived from the normal runoff relationship according to Manning-Strickler as a parameter of the Kalinin-Miljukov method /Rosemann, 1970/.

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With the characteristic length, the channel is divided into individual segments. For each segment the calculation of the transfer behavior is done with the help of the normal flow relation via a nonlinear memory calculation.

Kennlinie (Wasserspiegel – Querschnittsfläche – Abfluss)

Ist das Übertragungsverhalten der Transportstrecke durch vorangegangene Wasserspiegellagenberechnung bekannt, kann das Ergebnis in Form einer Wasserspiegel-Querschnitt-Abfluss Kennlinie benutzt werden.