If 15,000 gallons of sludge containing 4% solids is processed to produce a 25% cake, how many dry metric tons of sludge are disposed of?

To determine how many dry metric tons of sludge are disposed of, we first need to calculate the amount of solids present in the initial volume of sludge. Given that there are 15,000 gallons of sludge with a concentration of 4% solids, we can calculate the total amount of solids as follows:

1. Calculate the mass of the solids in the sludge:

[

\text{Total solids} = \text{Total volume} \times \text{Concentration of solids}

]

[

\text{Total solids} = 15,000 , \text{gallons} \times 0.04 = 600 , \text{gallons of solids}

]

2. Convert the volume of solids to weight:

The weight of sludge and solids can vary, but a common conversion is that 1 gallon of water weighs approximately 8.34 pounds. Assuming the density of the solids is similar to water for this conversion:

[

\text{Weight of solids} = 600 , \text{gallons} \times 8.34 , \text{lbs/gallon} \approx 5004