Problem 1 - A ferric iron sludge contains 15% solids.  If the density of iron is 2,500 kg/m³, estimate the density of wet sludge at 11^oC.

1. Calculate the specfic gravity of the sludge.

2. Calculate the density of the sludge.

Problem 2 - Determine the total kg of sludge on a dry-solids basis which will be produced for each kilogram of alum (Al₂(SO₄)₃) added. Assume the TSS is equal to 12 mg/L and a 50 mg/L dose of alum. The value of the bound water is 18.

1. Calculate the molecular weight of the alum added and the precipitated aluminum hydroxide.

2. Calculate the total sludge per liter of influent water.

3. Calculate the total sludge per kg of alum.

Problem 3 - Determine the mass and volume of sludge produced and the volume of sludge as a percentage of the total flow from the use of PACl for the removal of turbidity.  Assume the following conditions apply:

a) the flow rate is 0.1 m³/s

b) average raw-water turbidity is 20 NTU

c) average alume or PACl dose is 45 mg/L

d) sludge solids concentration is 5% with a corresponding specific gravity of 1.05

e) temperature is 15°C

Assume the ratio between total suspended solids and turbidity expressed as NTU is 1.5, the PACl contains 13% AL by weight and that 1.25 mg/L of a coagulant will also be used.

1. Determine the amount of dry sludge produced from the removal of turbidity, the addition of PACl, and the use of the coagulant aid.

2. Determine the volume of the sludge.

Problem 4 - Using a loading rate of 50 kg/m², estimate the effective area of lagoons required to handle alum sludge from a water treatment plant with a flow rate of 0.35 m³/s.

Assume the following:

1) Average raw-water turbidity is 45 NTU

2) Average alum dose is 40 mg/L

3) Sludge solids concentration is 5% with a corresponding specific gravity of 1.05 and a temperature of 10^oC.

4) The ratio between total suspended solids and turbidity expressed as NTU is 1.33 and 0.3 kg of alum sludge is produced per kilogram of alum added

5) 1 mg/L of a coagulant aid will also be used.

6) Use 18 as the value of bound water

7) At least two lagoons will be used and that two cycles (filling and drying) will be used per year.  Allow an additional area of 40% times the lagoon area for berms and access roads.

1. Determine the mass of dry solids for this problem.

2. Calculate the effective lagoon area for each lagoon.

3. Calculate the total land area needed.