The calculation in SITRA is based on a linear function of the density ρ to the concentration c. The general equation for a concentration-dependent density ρ(c) is:

With:

ρ(c) = concentration dependent density of the solution [kg/m³]

c = concentration [kg mass / m³ solution]

c₀ = reference concentration [kg mass / m³ solution]

ρ₀ = density of the reference concentration c₀ in [kg/m³]: ρ₀ = ρ(c = c₀)

α = constant density gradient

These parameters are defined within the dialog of the Input parameters of the density-dependent mass transport calculation. The following has to be considered:

The calculation module uses internally the concentrations (c_kg) in the unit [kg mass/kg solution]. In practice, however, often a unit in [g/l] = [kg/m³] is usual.

The following relationship applies to the two sizes:

ρ(c) = 1000 kg/m³ for water.

All inputs of the model data files (*.net, *.3d, additional files and transient input files) (KONZ, AKON and 1KON) are interpreted in a density-dependent calculation as inputs in the unit [kg/kg]. However, the results (= calculated concentrations) are converted during a density-dependent calculation in the unit [kg/m³] = [g/l], so the resulting concentrations and the input values are not directly comparable. This also applies to the plot generation!

Since the calculation module internally uses the pressure equation, some attributes have to be converted in other sizes:

Water course levels (VORF), initial potential heads (EICH) and fixed potential heads (POTE) of the model files and the transient input file are converted in pressure sizes. If the corresponding node has a concentration c ≠ 0 (AKON), the starting values (EICH, VORF, POTE in the model file) can initially be corrected with the entered parameters via the menu item Attributes - Computation - Density-corrected initial potentials. For transient calculations is it possible, to correct the water levels with the density parameters during the time steps. For this purpose the button "Pressure" has to be activated in the input dialog of the density-dependent mass transport ("Boundary condition"). If the potential heights should not be corrected with the density during the transient calculation, they can be kept constant by activating the button "potential".

All quantities of the model files and transient input file (affects KNOT, FLAE, RAND/Q/X, EFLA) are always converted from m³ to kg (solution) using the density ρ(c = 0). This should be considered especially when a quantity should be entered with an inflow concentration c_in > 0. In this case, the used density is wrong (for the conversion actually the density ρ(c_in) should be used ). This uncertainty may be circumvented by converting the actual quantity (Q_Start) in the input value (Q_korr).

The K-values defined in the model files are converted into permeabilities. In this conversion is always the density ρ(c = 0) used.

Input parameters