Develop a model to estimate concentration of pollutant against time As a first a

Question

Develop a model to estimate concentration of pollutant against time As a first approximation it can be assumed that the rates of uptake and discharge are directly proportional to pollutant concentration in water and in the fish body respectively. ( , first order) Develop a model to estimate concentration of pollutant against time in a fish in a lake where the pollutant concentration is equal to Cp mg/L. The concentration of pollutant in fish body is CF. State your assumptions. Verify the model. If concentration of the pollutant in water Cp = 0.1 mg/L and kf = 0.01 d-1, k1 = 0.006 d-1 k2 = 0.0001 d-1 , ke= 0.00004 d-1 , km= 0.00002 d-1 Calculate the time required to reach to CF = Cp and CF = 1.478 mg

Explanation / Answer

me uptake of pollutants as positive and release of pollutants negative.

If Cp=concentration of water pollutants.

==>rate of uptake of water pollutants...

(i)from gills=dCg/dt=k1Cp

(ii)from food=dCf/dt=kfCp

loss of pollutants (i)from gills=-dCg1/dt=-k2Cp

(ii)from metabolism=dCm/dt=-kmCp

(iii)from egestion=dCe/dt=-keCp................

Therefore concentration of pollutant against time in a fish in a lake where the pollutant concentration is equal to Cp

mg/L.=dCf/dt= (k1+kf-k2-km-ke)Cp.......................ANS

b)If concentration of the pollutant in water Cp = 0.1 mg/L

and kf = 0.01 d-1, k1 = 0.006 d-1 k2 = 0.0001 d-1 ,

ke= 0.00004 d-1 , km= 0.00002 d-1 .................................................................................................

dCf/dt=1.584*10^-3 d-1 *mg/L

==>dt=dCf/1.584*10^-3=

1.478/1.584*10^-3=933.08s..

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