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# Comp1FlowPlus

Models single compartment with inflowing and outflowing concentration of a single substance.

Model number: 0282

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## Description

A Flow carries an inflow concentration, Cin, into a one compartment model with a given Volume. Cin is constantly and instantaneously well mixed becoming C, the concentration in the compartment. C empties out of the compartment and is designated Cout. No reactions occur in this system. For a constant concentration of inflowing material the analytic solution is given. Various methods for checking the calculations in a model are illustrated: (1) comparison with an analytic solution, (2) two methods of calculating the amount of material in a compartment with flow, (3) comparison of the running integrals of inflow and outflow concentrations, and (4) calculation of the system transit time of a compartment model with flow by two different methods.

## Equations

#### Ordinary Differential Equation

$\large {\frac {d}{dt}}C \left( t \right) ={\frac {{\it Flow} \cdot \, \left( {\it Cin} \left( t \right) -{\it Cout} \left( t \right) \right) }{{\it Volume}}}$

#### Initial Condition

$\large {\it C} \left( 0 \right) ={\it C0}$

#### Analytic Solution when Cin(t) is constant

$\large {\it analyticC}={\it Cin}- \left( {\it Cin}-{\it C0} \right) \cdot {e^{-{ \frac {t \cdot {\it Flow}}{{\it Volume}}}}}$

The equations for this model may also be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

## References

 None.



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## Key Terms

Course, compartment, compartmental, tutorial, flow