In reference to the test tube metaphor, species which exhibit this type of growth will reproduce geometrically until they have reached the limit of the resources present
E-folding Residence Time
The time interval in which an exponentially-growing quantity increases by a factor of e
Instantaneous Rate of Change
P=P0ekt where P0 is initial concentration and P is concentration at time t
The period of time it takes for a substance undergoing decay to decrease by half (opposite of doubling time).T1/2=ln(2)/λ=half-life
Doubling Time/ Rule of 70
Doubling time equals 70/growth rate
Sewage Treatment Goals
Removal of suspended sediments, biological oxygen demand, pathogens, and nutrients (nitrogen and phosphorus)
Biochemical Oxygen Demand
A measure of the degree of organic pollution in the water– milligrams of O2 consumed by one liter of sample during 5 days of incubation at 20o Celsius
Primary Sewage Treatment
1. Inflow to course screening and grit removal2. Primary clarifier3. (Primary sludge to anaerobic digester) At least 30% of BOD and SS must be removed at this stage
Secondary Sewage Treatment
1. Sludge from primary clarifier to activated sludge or trickling filter2. Sludge to secondary clarifier3.
Sludge back to activated sludge/trickling filter, to chlorination, or to anaerobic digester4. Chlorinated sludge to effluent 85% of BOD and SS must be removed at this stage
Remove heavy organic solids. Method: grit (sand, gravel, clay, metal filings) is heavier than the organic solids that should be kept in suspension for subsequent treatment. Centrifugal motion is used to separate the solids from the waste water.
Tank with residence time of a few hours, collects primary sludge for anaerobic digester.
Fixed-film or attached growth systems– 70% of organic waste from effluent of primary clarifier is oxidized here.
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