Dynamical Concentration Equation for Water Tank System with Flow and Cleansing

In summary, you are looking for a differential equation to describe the concentration in the system, which can be described by the mass balance equation: dCs/dt = -Vo'/Vs + Ci/Vs.
  • #1
putbear
1
0
hope someone can help me to find a mathematical decription for the following problem:
- there is a system (water tank) with a volume Vs in which a substance is dissolved with the concentraiton Cs
- volume is drained out of the tank with a flow Vo' ("o" for out)
- the volume is cleansed (decrease in concentraion) so has afterwards a concentration Ci ("i" for in)and pumped back into the system

so I'm searching for a (differential?) equation to describe the concentration in the system Cs depending on Vo' and Ci

EDIT: seen to late, that the title should be "dynamical" - sorry dumb typo :-(
 
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  • #2
The differential equation you are looking for describes the change in concentration of the dissolved substance in the system over time. This is sometimes called a mass balance equation, and it can be written as: dCs/dt = -Vo'/Vs + Ci/VsWhere dCs/dt is the rate of change of concentration of the dissolved substance in the system, Vo' is the outflow rate, Vs is the total volume of the system, and Ci is the inflow concentration. This equation describes how the concentration of the dissolved substance changes over time, based on the outflow rate and the inflow concentration.
 

What is "Dynamical Concentration"?

"Dynamical Concentration" is a term used in physics and chemistry to describe the process by which particles or molecules move towards regions of higher concentration. This can occur through diffusion, osmosis, or other mechanisms.

How does "Dynamical Concentration" differ from other types of concentration?

The term "Dynamical Concentration" specifically refers to the movement of particles or molecules towards regions of higher concentration. This is different from other types of concentration, such as thermodynamic concentration, which takes into account energy considerations.

What factors affect "Dynamical Concentration"?

The rate of "Dynamical Concentration" is affected by several factors, including temperature, pressure, and the presence of other substances that may interact with the particles or molecules being studied. Additionally, the size and shape of the particles can also affect the rate of concentration.

Why is understanding "Dynamical Concentration" important?

Understanding "Dynamical Concentration" is crucial in fields such as chemistry and biology, where the movement of particles and molecules plays a significant role in the behavior and function of systems. It also has practical applications in industries such as pharmaceuticals, where the rate of concentration can impact the effectiveness of drugs.

How is "Dynamical Concentration" studied?

Scientists use various techniques and methods to study "Dynamical Concentration", including mathematical models, computer simulations, and experimental techniques such as spectroscopy and microscopy. These methods allow researchers to observe and measure the movement of particles and molecules towards regions of higher concentration.

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