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In water and wastewater treatment processes a filtration device may be used to remove water from the sludge formed by a precipitation reaction. The initial concentration of sludge from a softening reaction (Chapter 4) is 3 2 percent (20,000 mg/L) and the volume of sludge is 100 m . After filtra- tion the sludge solids concentration is 35 percent. Assume that the sludge does not change density during filtration, and that liquid removed from the sludge contains no sludge. Using the mass balance method, determine the volume of sludge after filtration.

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Answer:

The volume of sludge after filtration is 0.914 m

Explanation:

Solution

Given that:

We have to find the Volume of sludge after filtration

Now,

The  Sludge concentration is = 32%,

The sludge volume = 100 m,

The sludge concentration after filtration = 35%

Then,

The mass balance equation is stated below

Cin∀in = Cout∀out

Now,

We Solve for ∀out

∀out =Cin∀in/Cout

By substituting the values

∀out = (0.32)(100 m)/(0.35) = 0.914 m

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