# Instantaneous 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 an instantaneous input. Examples of instantaneous inputs are usually spills which range from a bottle of antifreeze to a tanker of solvent. This model assumes the pollutant immediately and completely mixes throughout the lake.

Step 1 Manually convert input data to metric units: meters, mg/L, or μCi/L.
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: Initial concentration 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
$C_{(t)} = C_0*e^{-(\frac{Qe}{V}+k)t}\ \ or\ \ C_{(t)}=C_0*e^{-βt}$