Soil Landfill Cover Water Balance

Example 1

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance

A community of 155,292 people generates 1.7 kg/person/day of MSW and diverts 30% through recycling. Compacted in place at 626 kg/m³ with 20% additional daily cover volume, find the airspace needed for 26 years.

Given

$Population = 155,292$
$Generation = 1.7 kg/cap/d$
$Diversion = 0.30$
$Compacted density = 626 kg/m^{3}$
$Cover = 20%, design life 26 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$155292(1.7)(1 - 0.30) = 184,797 kg/day$
Formula
$V = mass/density$
Substituting
$V = 184,797/626 = 295.2 m^{3}/day$
Annual with cover
$295.2 \times 365 \times 1.20 = 129,299 m^{3}/yr$
Design life
$129,299 \times 26 = 3,361,779 m^{3}$

Answer:

≈ 129,299 m³/yr, or 3,361,779 m³ over 26 years

Why the other options are there

4,002,118 m³ (diversion and cover ignored)
1,753,728,085 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 2

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (2)

A community of 241,169 people generates 2.2 kg/person/day of MSW and diverts 20% through recycling. Compacted in place at 844 kg/m³ with 20% additional daily cover volume, find the airspace needed for 17 years.

Given

$Population = 241,169$
$Generation = 2.2 kg/cap/d$
$Diversion = 0.20$
$Compacted density = 844 kg/m^{3}$
$Cover = 20%, design life 17 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$241169(2.2)(1 - 0.20) = 424,457 kg/day$
Formula
$V = mass/density$
Substituting
$V = 424,457/844 = 502.9 m^{3}/day$
Annual with cover
$502.9 \times 365 \times 1.20 = 220,275 m^{3}/yr$
Design life
$220,275 \times 17 = 3,744,680 m^{3}$

Answer:

≈ 220,275 m³/yr, or 3,744,680 m³ over 17 years

Why the other options are there

3,900,709 m³ (diversion and cover ignored)
2,633,758,415 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 3

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (3)

A community of 189,352 people generates 3.2 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 844 kg/m³ with 10% additional daily cover volume, find the airspace needed for 19 years.

Given

$Population = 189,352$
$Generation = 3.2 kg/cap/d$
$Diversion = 0.25$
$Compacted density = 844 kg/m^{3}$
$Cover = 10%, design life 19 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$189352(3.2)(1 - 0.25) = 454,445 kg/day$
Formula
$V = mass/density$
Substituting
$V = 454,445/844 = 538.4 m^{3}/day$
Annual with cover
$538.4 \times 365 \times 1.10 = 216,184 m^{3}/yr$
Design life
$216,184 \times 19 = 4,107,503 m^{3}$

Answer:

≈ 216,184 m³/yr, or 4,107,503 m³ over 19 years

Why the other options are there

4,978,791 m³ (diversion and cover ignored)
3,151,574,688 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 4

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (4)

A community of 108,785 people generates 2.4 kg/person/day of MSW and diverts 30% through recycling. Compacted in place at 770 kg/m³ with 10% additional daily cover volume, find the airspace needed for 29 years.

Given

$Population = 108,785$
$Generation = 2.4 kg/cap/d$
$Diversion = 0.30$
$Compacted density = 770 kg/m^{3}$
$Cover = 10%, design life 29 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$108785(2.4)(1 - 0.30) = 182,759 kg/day$
Formula
$V = mass/density$
Substituting
$V = 182,759/770 = 237.3 m^{3}/day$
Annual with cover
$237.3 \times 365 \times 1.10 = 95,296 m^{3}/yr$
Design life
$95,296 \times 29 = 2,763,574 m^{3}$

Answer:

≈ 95,296 m³/yr, or 2,763,574 m³ over 29 years

Why the other options are there

3,589,057 m³ (diversion and cover ignored)
1,934,501,898 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 5

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (5)

A community of 193,767 people generates 2.1 kg/person/day of MSW and diverts 35% through recycling. Compacted in place at 664 kg/m³ with 20% additional daily cover volume, find the airspace needed for 13 years.

Given

$Population = 193,767$
$Generation = 2.1 kg/cap/d$
$Diversion = 0.35$
$Compacted density = 664 kg/m^{3}$
$Cover = 20%, design life 13 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$193767(2.1)(1 - 0.35) = 264,492 kg/day$
Formula
$V = mass/density$
Substituting
$V = 264,492/664 = 398.3 m^{3}/day$
Annual with cover
$398.3 \times 365 \times 1.20 = 174,469 m^{3}/yr$
Design life
$174,469 \times 13 = 2,268,098 m^{3}$

Answer:

≈ 174,469 m³/yr, or 2,268,098 m³ over 13 years

Why the other options are there

2,907,818 m³ (diversion and cover ignored)
1,255,014,326 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 6

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (6)

A community of 24,300 people generates 3.0 kg/person/day of MSW and diverts 15% through recycling. Compacted in place at 698 kg/m³ with 15% additional daily cover volume, find the airspace needed for 20 years.

Given

$Population = 24,300$
$Generation = 3.0 kg/cap/d$
$Diversion = 0.15$
$Compacted density = 698 kg/m^{3}$
$Cover = 15%, design life 20 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$24300(3.0)(1 - 0.15) = 61,965 kg/day$
Formula
$V = mass/density$
Substituting
$V = 61,965/698 = 88.8 m^{3}/day$
Annual with cover
$88.8 \times 365 \times 1.15 = 37,263 m^{3}/yr$
Design life
$37,263 \times 20 = 745,267 m^{3}$

Answer:

≈ 37,263 m³/yr, or 745,267 m³ over 20 years

Why the other options are there

762,421 m³ (diversion and cover ignored)
452,344,500 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 7

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (7)

A community of 208,268 people generates 3.0 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 790 kg/m³ with 10% additional daily cover volume, find the airspace needed for 11 years.

Given

$Population = 208,268$
$Generation = 3.0 kg/cap/d$
$Diversion = 0.25$
$Compacted density = 790 kg/m^{3}$
$Cover = 10%, design life 11 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$208268(3.0)(1 - 0.25) = 468,603 kg/day$
Formula
$V = mass/density$
Substituting
$V = 468,603/790 = 593.2 m^{3}/day$
Annual with cover
$593.2 \times 365 \times 1.10 = 238,157 m^{3}/yr$
Design life
$238,157 \times 11 = 2,619,728 m^{3}$

Answer:

≈ 238,157 m³/yr, or 2,619,728 m³ over 11 years

Why the other options are there

3,175,428 m³ (diversion and cover ignored)
1,881,441,045 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 8

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (8)

A community of 62,645 people generates 3.1 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 664 kg/m³ with 15% additional daily cover volume, find the airspace needed for 17 years.

Given

$Population = 62,645$
$Generation = 3.1 kg/cap/d$
$Diversion = 0.25$
$Compacted density = 664 kg/m^{3}$
$Cover = 15%, design life 17 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$62645(3.1)(1 - 0.25) = 145,650 kg/day$
Formula
$V = mass/density$
Substituting
$V = 145,650/664 = 219.4 m^{3}/day$
Annual with cover
$219.4 \times 365 \times 1.15 = 92,073 m^{3}/yr$
Design life
$92,073 \times 17 = 1,565,240 m^{3}$

Answer:

≈ 92,073 m³/yr, or 1,565,240 m³ over 17 years

Why the other options are there

1,814,771 m³ (diversion and cover ignored)
903,755,923 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 9

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (9)

A community of 199,924 people generates 2.8 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 635 kg/m³ with 15% additional daily cover volume, find the airspace needed for 19 years.

Given

$Population = 199,924$
$Generation = 2.8 kg/cap/d$
$Diversion = 0.25$
$Compacted density = 635 kg/m^{3}$
$Cover = 15%, design life 19 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$199924(2.8)(1 - 0.25) = 419,840 kg/day$
Formula
$V = mass/density$
Substituting
$V = 419,840/635 = 661.2 m^{3}/day$
Annual with cover
$661.2 \times 365 \times 1.15 = 277,524 m^{3}/yr$
Design life
$277,524 \times 19 = 5,272,964 m^{3}$

Answer:

≈ 277,524 m³/yr, or 5,272,964 m³ over 19 years

Why the other options are there

6,113,581 m³ (diversion and cover ignored)
2,911,593,174 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Example 10

Landfill volume required for a community's solid waste — Soil Landfill Cover Water Balance (10)

A community of 25,933 people generates 1.9 kg/person/day of MSW and diverts 20% through recycling. Compacted in place at 822 kg/m³ with 15% additional daily cover volume, find the airspace needed for 15 years.

Given

$Population = 25,933$
$Generation = 1.9 kg/cap/d$
$Diversion = 0.20$
$Compacted density = 822 kg/m^{3}$
$Cover = 15%, design life 15 yr$

Find

Annual and total landfill airspace

Start with the thinking

Only the landfilled fraction consumes airspace — diverted material is subtracted first.
Daily cover soil is real volume and must be added to the waste volume.

Step-by-step solution

Formula
$landfilled mass = population \times rate \times (1 - diversion)$
Substituting
$25933(1.9)(1 - 0.20) = 39,418 kg/day$
Formula
$V = mass/density$
Substituting
$V = 39,418/822 = 48.0 m^{3}/day$
Annual with cover
$48.0 \times 365 \times 1.15 = 20,129 m^{3}/yr$
Design life
$20,129 \times 15 = 301,930 m^{3}$

Answer:

≈ 20,129 m³/yr, or 301,930 m³ over 15 years

Why the other options are there

328,185 m³ (diversion and cover ignored)
215,814,426 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Soil Landfill Cover Water Balance

Soil Landfill Cover Water Balance

Core formulas for this FE topic

Worked exam-style examples

Soil Landfill Cover Water Balance

Core formulas for this FE topic

∆SLC=P−R−ET−PERsw∆SLC = P - R - ET - PERsw∆SLC=P−R−ET−PERsw

∆SLC=changeintheamountofwaterheldinstorageinaunitvolumeoflandfillcover(in.)∆SLC = change in the amount of water held in storage in a unit volume of landfill cover (in.)∆SLC=changeintheamountofwaterheldinstorageinaunitvolumeoflandfillcover(in.)

P=amountofprecipitationperunitarea(in.)P = amount of precipitation per unit area (in.)P=amountofprecipitationperunitarea(in.)

R=amountofrunoffperunitarea(in.)R = amount of runoff per unit area (in.)R=amountofrunoffperunitarea(in.)

ET=amountofwaterlostthroughevapotranspirationperunitarea(in.)ET = amount of water lost through evapotranspiration per unit area (in.)ET=amountofwaterlostthroughevapotranspirationperunitarea(in.)

Worked exam-style examples