To estimate the life of a landfill, we need to consider several factors including the population size, available area, waste generation rate, compaction ratio, and landfill design. Let's calculate the estimated life of the landfill based on the given information:
1. Determine the waste generation rate:
Let's assume an average waste generation rate per person of 3 pounds per day. Since the user population is 10,000, the total waste generation rate would be 10,000 * 3 = 30,000 pounds per day.
2. Calculate the compacted waste volume:
To calculate the compacted waste volume, we need to account for the air voids in the waste. Given that the soil occupies 20% of the compacted volume, the waste volume would be 100% - 20% = 80% of the total compacted volume.
3. Calculate the required landfill volume:
The landfill volume can be estimated by multiplying the waste generation rate by the number of days in the lifespan of the landfill. Let's assume a landfill lifespan of 20 years (365 days * 20 years = 7,300 days).
Required landfill volume = Waste generation rate * Lifespan
Required landfill volume = 30,000 pounds per day * 7,300 days
Required landfill volume = 219,000,000 pounds
4. Calculate the landfill dimensions:
Since we have the available area of 10 acres, we can calculate the dimensions of the landfill based on the desired side slope and final surface slope.
Landfill area = Length * Width
10 acres = Length * Width
Given that the side slope is 1:3, the height of the landfill (H) would be 3 times the width (W). Similarly, the final surface slope of 1:4 indicates that the height (H) is 4 times the length (L).
H = 3W
H = 4L
Substituting the values:
10 acres = (4L) * (L/4)
10 acres = L^2
Solving for L:
L = sqrt(10 acres) ≈ 3.16 acres
W = H/3 = 3.16 acres / 3 ≈ 1.05 acres
Converting acres to square feet:
1 acre = 43,560 square feet
L = 3.16 acres * 43,560 square feet/acre ≈ 137,699 square feet
W = 1.05 acres * 43,560 square feet/acre ≈ 45,918 square feet
5. Calculate the landfill volume:
The landfill volume can be calculated by multiplying the landfill area by the average height (H) of the landfill.
Landfill volume = Landfill area * Height
Landfill volume = (137,699 square feet + 45,918 square feet) * (3.16 acres) * (3 ft/acre)
Landfill volume ≈ 1,256,789 cubic feet
6. Adjust for water table:
Since the water table is estimated at 20 feet below the ground surface, we need to adjust the landfill volume to account for this.
Effective landfill volume = Landfill volume * (Depth above water table / Total depth)
Effective landfill volume = 1,256,789 cubic feet * (20 ft / (20 ft + 20 ft))
Effective landfill volume ≈ 628,395 cubic feet
7. Calculate the lifespan of the landfill:
The lifespan of the landfill can be calculated by dividing the effective landfill volume by the required landfill volume.
Lifespan = Effective landfill volume / Required