A municipal landfill has available space of 16.2 ha at an average depth of 10
m. Seven hundred sixty-five (765) m3 of solid waste is dumped at the site 5 days a
week. The waste is compacted to twice its delivered density. Draw a mass-balance
diagram and estimate the expected life of the landfill in years.
Divide the available volume by the annual volume of compacted waste.
The annual volume of compacted waste is (1/2)*765*5*52 = 9.95*10^4 m^3
The 16.2 hectares piled 10 m deep is an available volume of 16.2*10^4*10 = 1.62*10^6 m^3
It will be full in 16.3 years
Well, buckle up and get ready for a trashy joke, because we're diving into landfill calculations!
First, let's talk trash! We have a landfill with available space of 16.2 hectares (aka Ha) at an average depth of 10 meters. So, if you're ever in need of a really deep hole, you know where to go!
Now, 765 cubic meters (m3) of solid waste is dumped at the site 5 days a week. But hold your nose, because this waste gets compacted to twice its delivered density. It's like squishing your garbage into a tiny trash cube!
To estimate the expected life of the landfill, we need to do a little mass-balance magic. We multiply the volume of waste dumped each day (765 m3) by the number of dumping days in a year. Assuming 52 weeks in a year, that's 5 days * 52 weeks = 260 dumping days in a year.
Now, we need to take into account the compaction. Since the waste is compacted to twice its delivered density, we can adjust the volume by dividing it by 2. So, 765 m3 / 2 = 382.5 m3 of "compacted" waste per dumping day.
Now, we multiply the adjusted volume of waste per dumping day (382.5 m3) by the landfill's available space (16.2 Ha * 10 m). This gives us the total volume of waste the landfill can handle over its lifespan.
Finally, we divide the total volume of waste the landfill can handle by the adjusted volume of waste per dumping day to get the expected life of the landfill in years.
But wait, before we get the final answer, let me ask you a landfill-related joke:
Why do landfills always win races?
Because they never take shortcuts! They go straight to the dump!
Now that we've had our giggles, let's calculate the expected life of the landfill:
Total volume of waste landfill can handle = (16.2 Ha * 10 m) * 382.5 m3 = ______ (I'll let you do the math!)
Expected life of the landfill = Total volume of waste landfill can handle / (382.5 m3 * 260 dumping days) = ______ (I'll leave the final calculations up to you!)
Remember, this is just an estimate based on the information given. So, take it with a pinch of landfill dust!
To estimate the expected life of the landfill, we can start by calculating the daily volume of waste being dumped, the total volume of waste that can be accommodated in the available space, and then dividing the total volume by the daily volume to determine the expected lifespan.
1. Calculate the daily volume of waste:
Given that 765 m3 of waste is dumped at the site 5 days a week, we can calculate the daily volume as follows:
Daily volume = 765 m3/day * 5 days/week = 3,825 m3/day
2. Calculate the total volume of waste the landfill can accommodate:
Given that the landfill has available space of 16.2 ha (1 ha = 10,000 m2) at an average depth of 10 m, we can calculate the total volume of waste the landfill can hold as follows:
Total volume = 16.2 ha * 10,000 m2/ha * 10 m = 1,620,000 m3
3. Calculate the effective capacity of the landfill:
Since the waste is compacted to twice its delivered density, the effective capacity of the landfill will be half of the total volume, so we calculate:
Effective capacity = 1,620,000 m3 / 2 = 810,000 m3
4. Calculate the expected lifespan of the landfill:
To estimate the lifespan, we divide the effective capacity of the landfill by the daily volume:
Expected lifespan = Effective capacity / Daily volume
Expected lifespan = 810,000 m3 / 3,825 m3/day = 211.8 days
However, since the landfill is operational only 5 days a week, we need to adjust the expected lifespan accordingly:
Expected lifespan in years = (Number of days in a year) * (Expected lifespan in days) / (Number of days the landfill operates in a week)
Expected lifespan in years = (365 days/year) * (211.8 days) / (5 days/week)
Expected lifespan in years ≈ 31.35 years
Therefore, the estimated life of the landfill is approximately 31.35 years.
To estimate the expected life of the landfill, we need to calculate the total volume of solid waste that can be accommodated in the available space.
Step 1: Calculate the volume of waste dumped in a week:
Since 765 m3 of solid waste is dumped at the site every day, the volume of waste dumped in a week can be found by multiplying it by the number of days in a week:
Volume dumped in a week = 765 m3/day * 5 days = 3825 m3/week
Step 2: Calculate the compacted volume of waste dumped in a week:
Given that the waste is compacted to twice its delivered density, we can calculate the compacted volume by multiplying the delivered volume by 2:
Compacted volume dumped in a week = 3825 m3/week * 2 = 7650 m3/week
Step 3: Calculate the volume of waste dumped in a year:
Since there are 52 weeks in a year, we can multiply the volume dumped in a week by 52 to get the annual volume:
Volume dumped in a year = 7650 m3/week * 52 weeks = 397,800 m3/year
Step 4: Calculate the volume of waste that can be accommodated in the available space:
The available space of the landfill is given as 16.2 hectares with an average depth of 10 meters. To calculate the volume in cubic meters, we multiply the area by the depth and convert hectares to square meters:
Available volume of the landfill = 16.2 hectares * 10 m * 10,000 m2/hectare = 1,620,000 m3
Step 5: Calculate the expected life of the landfill:
To estimate the expected life of the landfill in years, we divide the available volume of the landfill by the volume dumped in a year:
Expected life of the landfill = Available volume of the landfill / Volume dumped in a year
Expected life of the landfill = 1,620,000 m3 / 397,800 m3/year
Calculating the above expression:
Expected life of the landfill ≈ 4.07 years
Therefore, the estimated expected life of the landfill is approximately 4.07 years.