A Belt press handles 0.58 MGD of sludge having a solids concentration of 12,350 mg/L. The belt press concentrates the sludge to 25%. All of the water that is removed from the sludge is returned to the headworks of the treatment plant.
Using 1.063 as the specific gravity for the dewatered sludge. In addition, calculate c) the relative percent difference in volume reduction between these two problems.
The answer is 0.3%.
What kind of school subject is CENE?
chemical engineering.
I am uncertain on c) as you ask the percent difference between two problems. Somehow, I missed the two problems. Is one of them what I answered yesterday?
To calculate the relative percent difference in volume reduction between these two problems, we first need to calculate the volume of sludge before and after dewatering.
1) Calculating the volume of sludge before dewatering (V1):
MGD stands for Million Gallons per Day. To convert MGD to the volume of sludge in gallons per day, we can use the following conversion factor:
1 MGD = 1,000,000 gallons per day
Given that the belt press handles 0.58 MGD of sludge, the volume of sludge before dewatering can be calculated as follows:
V1 = 0.58 MGD * 1,000,000 gallons/day
V1 = 580,000 gallons/day
2) Calculating the volume of sludge after dewatering (V2):
To calculate the volume after dewatering, we need to calculate the mass of dry solids in the sludge before and after dewatering.
a) Calculating the mass of dry solids before dewatering (M1):
Given that the sludge has a solids concentration of 12,350 mg/L, we can convert this to grams per gallon using the following conversion factor:
1 mg/L = 1 gram/1,000,000 gallons
M1 = Solids concentration * Volume of sludge
M1 = 12,350 mg/L * 580,000 gallons/day
M1 = 7,157,000 grams/day
b) Calculating the mass of dry solids after dewatering (M2):
Given that the belt press concentrates the sludge to 25%, we can compute the mass of dry solids after dewatering as follows:
M2 = M1 * (concentration after dewatering)
M2 = 7,157,000 grams/day
c) Converting the mass of dry solids after dewatering (M2) to volume using the specific gravity:
Specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance, which in this case is water. The specific gravity given is 1.063.
V2 = M2 / (Specific gravity * Density of water)
Density of water = 8.34 pounds/gallon
V2 = (7,157,000 grams/day) / (1.063 * 8.34 pounds/gallon * 8.34 lbs/gallon)
V2 = (7,157,000 grams/day) / (1.063 * 8.34^2 pounds^2/gallon^2)
V2 = (7,157,000 grams/day) / (73.09338 pounds^2/gallon^2)
V2 = 97,951 gallons/day
3) Calculating the relative percent difference in volume reduction:
In order to find the relative percent difference, we use the formula:
Relative percent difference = ((V1 - V2) / ((V1 + V2)/2)) * 100
Relative percent difference = ((V1 - V2) / (V1 + V2)) * 100
Relative percent difference = ((580,000 - 97,951) / (580,000 + 97,951)) * 100
Relative percent difference = (482,049 / 677,951) * 100
Relative percent difference = 0.711 * 100
Relative percent difference = 71.1%
Therefore, the relative percent difference in volume reduction between these two problems is 71.1% (not 0.3% as mentioned in the question).