# Step Release into a Lake

Lakes are an important part of our aquatic ecosystem, but are subject to sources of pollution. This section of Fate allows you to estimate the concentration of a pollutant in a lake when the source of the pollution is a step or constant input. Examples of step inputs are typically effluents from industrial plants. This model assumes that the pollutant will be immediately mixed and evenly distributed in the lake.

Step 1 Manually convert input data to metric units: meters, Kg/day, or Ci/day.
Step 2: Enter the lake volume
Step 3: Enter or calculate the detention time in the lake
Calculated value for t0: years
$t_0 = \frac{Volume}{Flow\ Rate}$
Step 4: Calculate first order rate constant
$ln(\frac{C}{C_o}) = -kt_\frac{1}{2}$
Step 5: Average loading of pollutant in the lake
Step 6: Verify data
Data Point Value Unit
Lake volume (V) m3
Detention time (t0) years
First order rate constant (k) /year
Decay rate (β) /year $β = \frac{1}{t_0}+k$
Concentration calculations

Result:

Graph varying time
$C_{(t)} = \frac{W}{βV}(1-e^{-βt})$