A lime softening sludge flow of 30,000 gpd is gravity thickened from 2.0% to 5.0% in a mechanical gravity thickener. The gravity thickener is to be designed using a solids loading rate of 10 lb/(ft2⋅d) and a solids capture of 85%. Assume that the thickener has a side water depth (SWD) of 10 ft, an overflow rate of 500 gpd/ft2 will be used in design, and that the specific gravity of all sludge streams is approximately 1. Determine the following:
a. The thickened sludge flow rate (gpd) if 800 mg/L of SS are contained in the supernatant.
b. The diameter (ft) of the gravity thickener considering both the solids loading rate and overflow rate.
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