If a plant produces 100,000 gallons of 2% sludge and then thickens it to 30%, what is the volume of the 30% sludge?

To determine the final volume of the thickened sludge, it's important to understand the relationship between the concentration of the sludge and its volume. When the sludge is thickened from 2% to 30%, the solid content increases while the liquid content decreases.

Initially, the plant produces 100,000 gallons of sludge at a concentration of 2%. This means that the total amount of solids in the sludge can be calculated as follows:

• Solids in 2% sludge = 100,000 gallons x 2% = 100,000 gallons x 0.02 = 2,000 gallons of solids.

When the sludge is thickened to a concentration of 30%, the volume of the thickened sludge needs to be determined while maintaining the same amount of solids. At 30%, the total volume of the thickened sludge can be calculated using the formula for concentration:

• Concentration (as a decimal) = solids / total volume.

Rearranging this formula gives us:

• Total volume = solids / concentration.

Substituting the values:

• Total volume = 2,000 gallons / 0.30 = 6,666.67 gallons.

Since volumes should be rounded to a practical number used in water treatment