Calculating Concentration of Bacteria
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Please see the attached Word file and help answer the questions regarding concentration of bacteria in a water reservoir.
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Solution Summary
Using calculas, expression for concentration of bacteria in a water reservoir is estimated. Water with bacteria is continuously added in the reservoir and also being used by human society.
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Mass of bacteria added/time, k = 0.02*60000 = 1200 gm/day
Water in reservoir W = 400,000
At t =0, mass of bacteria in reservoir,
yo = 0.005*W = 0.005*400000 = 5*400 = 2000 gm
In dt time water added dW, such that,
r = dW/dt = 60,000 m^3/day
At t, mass of bacteria = y(t)
At t+dt, mass of bacteria,due to adding water:
y(t+dt) = y(t) + kdt
Total volume of water becomes = W + dW
Concentration of bacteria = (y(t) + kdt)/(W+dW)
same amount of water (dW) taken out of the reservoir in dt time, ...
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