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 Lake volume
V = m³ (only used for calculated t₀)

Step 3: Enter or calculate the detention time in the lake Outlet flow rate
Q = m³/year (only used for calculated t₀)

Calculated value for t₀: years

\[t_0 = \frac{Volume}{Flow\ Rate}\]

Entered detention time
t₀ = years

Step 4: Calculate first order rate constant

Half-life

\[ln(\frac{C}{C_o}) = -kt_\frac{1}{2} \]

Step 5: Initial concentration of pollutant in the Lake C₀ =

Step 6: Verify data

Data Point	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 Time

Result:

Graph varying time

\[C_{(t)} = C_0*e^{-(\frac{Qe}{V}+k)t}\ \ or\ \ C_{(t)}=C_0*e^{-βt} \]