Soil Landfill Cover Water Balance

Environmental Engineering · FE Reference Handbook section

Environmental Engineering

6 formulas

10 exam-style examples

~57 min

All Environmental Engineering lectures

Learning objectives

What you must be able to do before leaving this section.

This chapter section covers Soil Landfill Cover Water Balance within Environmental Engineering. Read it the way you would read a textbook chapter: the theory first so the relations mean something, then every equation with its use and its trap, then 10 fully worked examples with the arithmetic shown line by line, and finally a self-check you should be able to answer without notes.

Explain, in your own words, what soil landfill cover water balance describes physically and when it applies.
State every one of the 6 relations the handbook lists here and name each symbol with its unit.
Select the correct relation from the wording of an exam stem within 20 seconds.
Carry a complete solution from givens to a "most nearly" answer with the correct unit.
Recognise the distractors generated by the unit trap: mg/L × MGD × 8.34 = lb/day is the single most used conversion.

Lecture

Why this section exists. Soil Landfill Cover Water Balance is the part of Environmental Engineering that lets you connect a treatment unit or receiving water body to a number you can defend. Before any equation is useful you must be able to picture the physical situation it describes; the schematic below is that picture.

How the theory is built. The handbook prints results, not derivations. Each relation in this section comes from one governing principle applied to the idealised system: state the principle, impose the stated assumptions, and the printed equation follows. Knowing which assumption each relation rests on is what lets you reject a wrong answer choice in seconds.

How it is examined. Items from this page are written as a mass balance across one reactor or one unit process. Roughly two thirds are direct substitution, one third require one intermediate quantity from a neighbouring relation, and a small number are conceptual — testing whether you know the assumption, not the arithmetic.

The habit that earns the points. Unit discipline. mg/L × MGD × 8.34 = lb/day is the single most used conversion. Every relation below is dimensionally consistent only when that rule is honoured, and the distractor set is deliberately built from candidates who ignored it. Write the unit next to every number you substitute, every time.

How to study this page. Read the theory, then cover the formula cards and try to reproduce each relation from its description. Then work the examples with the solution hidden, revealing one line at a time. Finish with the self-check questions; if you cannot answer one, return to the matching formula card.

Truck-mounted drill rig taking a soil boring beside a bridge, with sample jars in the foreground. — Photo 1. Where this shows up in practice: soil landfill cover water balance.
Capstone Studio instructional photograph

Environmental Engineering — Soil Landfill Cover Water Balance: reference schematic for orienting the symbols used in this section.

Theory, developed

Read this before the equations — it is what makes them memorable.

The physical situation

Every item from this section describes a treatment unit or receiving water body. Sketch it before you compute — a labelled sketch with the givens on it converts a wordy stem into a solvable problem and exposes the quantity the examiner left out on purpose.

The governing principle

The 6 relations on this page are consequences of one principle applied to that idealised system. Identify which quantity is conserved, balanced, or defined, and the correct equation follows without memorisation.

Assumptions and limits of validity

Each printed relation carries silent assumptions — linearity, steady state, uniformity, small deformation, or standard conditions, depending on the subject. Conceptual exam items are written by violating exactly one of these, so read the sentence above the equation as carefully as the equation itself.

Solution procedure you should automate

1) Read the last sentence of the stem to identify the requested quantity. 2) Locate the relation on this page whose left-hand side is that quantity. 3) Tabulate the givens with units and mark the missing symbol. 4) If a symbol is missing, find the one relation that produces it. 5) Rearrange symbolically, substitute once, evaluate, and round only at the end.

Notation used in this section

∆SLC	Quantity produced by "∆SLC = P – R – ET – PERsw" — read its definition and unit from the handbook line directly above the equation.
P	Quantity produced by "P = amount of precipitation per unit area (in.)" — read its definition and unit from the handbook line directly above the equation.
R	Quantity produced by "R = amount of runoff per unit area (in.)" — read its definition and unit from the handbook line directly above the equation.
ET	Quantity produced by "ET = amount of water lost through evapotranspiration per unit area (in.)" — read its definition and unit from the handbook line directly above the equation.
PERsw	Quantity produced by "PERsw = amount of water percolating through the unit area of landfill cover into compacted solid waste (in.)" — read its definition and unit from the handbook line directly above the equation.

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

where
Tchobanoglous and Kreith, Handbook of Solid Waste Management, 2nd ed., McGraw-Hill, 2002.

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$155292 (1.7) (1 - 0.30) = 184, 797 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 184, 797/626 = 295.2 m^{3} / d a y$
Annual with cover
$295.2 \times 365 \times 1.20 = 129, 299 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$241169 (2.2) (1 - 0.20) = 424, 457 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 424, 457/844 = 502.9 m^{3} / d a y$
Annual with cover
$502.9 \times 365 \times 1.20 = 220, 275 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$189352 (3.2) (1 - 0.25) = 454, 445 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 454, 445/844 = 538.4 m^{3} / d a y$
Annual with cover
$538.4 \times 365 \times 1.10 = 216, 184 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$108785 (2.4) (1 - 0.30) = 182, 759 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 182, 759/770 = 237.3 m^{3} / d a y$
Annual with cover
$237.3 \times 365 \times 1.10 = 95, 296 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$193767 (2.1) (1 - 0.35) = 264, 492 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 264, 492/664 = 398.3 m^{3} / d a y$
Annual with cover
$398.3 \times 365 \times 1.20 = 174, 469 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$24300 (3.0) (1 - 0.15) = 61, 965 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 61, 965/698 = 88.8 m^{3} / d a y$
Annual with cover
$88.8 \times 365 \times 1.15 = 37, 263 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$208268 (3.0) (1 - 0.25) = 468, 603 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 468, 603/790 = 593.2 m^{3} / d a y$
Annual with cover
$593.2 \times 365 \times 1.10 = 238, 157 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$62645 (3.1) (1 - 0.25) = 145, 650 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 145, 650/664 = 219.4 m^{3} / d a y$
Annual with cover
$219.4 \times 365 \times 1.15 = 92, 073 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$199924 (2.8) (1 - 0.25) = 419, 840 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 419, 840/635 = 661.2 m^{3} / d a y$
Annual with cover
$661.2 \times 365 \times 1.15 = 277, 524 m^{3} / y r$
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/m³
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
$l an df i l l e d ma ss = p o p u l a t i o n \times r a t e \times (1 - d i v er s i o n)$
Substituting
$25933 (1.9) (1 - 0.20) = 39, 418 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 39, 418/822 = 48.0 m^{3} / d a y$
Annual with cover
$48.0 \times 365 \times 1.15 = 20, 129 m^{3} / y r$
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

Self-check

Answer these without notes before moving on.

Without looking, state the relation on this page whose left-hand side is the quantity most often requested, and name every symbol in it.
Which assumption, if violated, makes the main relation of this section invalid?
Given a treatment unit or receiving water body, what is the first quantity you would compute, and why that one first?
Which unit conversion in this subject most often produces a wrong answer choice, and what is its numerical factor?
Rework Example 1 above from the givens alone, without reading the solution lines.

Chapter summary

Soil Landfill Cover Water Balance contains 6 relations; you must be able to find this page in under 15 seconds.
Exam style: a mass balance across one reactor or one unit process.
Unit rule: mg/L × MGD × 8.34 = lb/day is the single most used conversion.
Work the 10 examples until the solution path, not the answer, is automatic.

Common traps in this section

mg/L × MGD × 8.34 = lb/day is the single most used conversion
Answering the intermediate quantity instead of the quantity requested.
Rounding intermediate values before the final step.
Using a relation from an adjacent handbook section that shares a symbol.
Skipping the sketch — most lost points on this page start with a misread geometry.