Landfill

Environmental Engineering · FE Reference Handbook section

Environmental Engineering

7 formulas

10 exam-style examples

~59 min

All Environmental Engineering lectures

Learning objectives

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

This chapter section covers Landfill 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 landfill describes physically and when it applies.
State every one of the 7 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. Landfill 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.

Aeration basin at a wastewater treatment plant with churning aerated water and walkways. — Photo 1. Where this shows up in practice: landfill.
Capstone Studio instructional photograph

Environmental Engineering — Landfill: 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 7 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

t	Quantity produced by "t = breakthrough time (yr)" — read its definition and unit from the handbook line directly above the equation.
d	Quantity produced by "d = thickness of clay liner (ft)" — read its definition and unit from the handbook line directly above the equation.
η	Quantity produced by "η = porosity" — read its definition and unit from the handbook line directly above the equation.
K	Quantity produced by "K = hydraulic conductivity (ft/yr)" — read its definition and unit from the handbook line directly above the equation.
h	Quantity produced by "h = hydraulic head (ft)" — 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.

Typical Densities of As-Received Source-Separated Materials
Typical density, Baled density,*
Material lb/yd3
lb/yd3
Paper
Newspaper 475 950
Corrugated cardboard 350 800
High grades 300−400
Glass−whole bottles
Clear 500
Green or amber 550
Glass−crushed
Semicrushed 1,000
1 1/2-in. mechanically crushed 1,800
1/4-in. furnace ready 2,700
Aluminum Cans
Whole 50 950
Flattened 175
Tin plated steel cans ("tin cans")
Whole 150 1,400
Flattened 850
Plastics
PET, whole 34 750
PET, flattened 75

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 — Landfill

A community of 127,814 people generates 2.1 kg/person/day of MSW and diverts 45% through recycling. Compacted in place at 635 kg/m³ with 10% additional daily cover volume, find the airspace needed for 22 years.

Given

Population = 127,814
Generation = 2.1 kg/cap/d
Diversion = 0.45
Compacted density = 635 kg/m³
Cover = 10%, design life 22 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
$127814 (2.1) (1 - 0.45) = 147, 625 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 147, 625/635 = 232.5 m^{3} / d a y$
Annual with cover
$232.5 \times 365 \times 1.10 = 93, 341 m^{3} / y r$
Design life
$93, 341 \times 22 = 2, 053, 501 m^{3}$

Answer: ≈ 93,341 m³/yr, or 2,053,501 m³ over 22 years

Why the other options are there

3,394,217 m³ (diversion and cover ignored)
1,185,430,115 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 2

Landfill volume required for a community's solid waste — Landfill (2)

A community of 144,134 people generates 2.8 kg/person/day of MSW and diverts 35% through recycling. Compacted in place at 727 kg/m³ with 10% additional daily cover volume, find the airspace needed for 28 years.

Given

Population = 144,134
Generation = 2.8 kg/cap/d
Diversion = 0.35
Compacted density = 727 kg/m³
Cover = 10%, design life 28 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
$144134 (2.8) (1 - 0.35) = 262, 324 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 262, 324/727 = 360.8 m^{3} / d a y$
Annual with cover
$360.8 \times 365 \times 1.10 = 144, 874 m^{3} / y r$
Design life
$144, 874 \times 28 = 4, 056, 458 m^{3}$

Answer: ≈ 144,874 m³/yr, or 4,056,458 m³ over 28 years

Why the other options are there

5,673,368 m³ (diversion and cover ignored)
2,680,950,054 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 3

Landfill volume required for a community's solid waste — Landfill (3)

A community of 167,528 people generates 3.1 kg/person/day of MSW and diverts 45% through recycling. Compacted in place at 514 kg/m³ with 25% additional daily cover volume, find the airspace needed for 10 years.

Given

Population = 167,528
Generation = 3.1 kg/cap/d
Diversion = 0.45
Compacted density = 514 kg/m³
Cover = 25%, design life 10 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
$167528 (3.1) (1 - 0.45) = 285, 635 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 285, 635/514 = 555.7 m^{3} / d a y$
Annual with cover
$555.7 \times 365 \times 1.25 = 253, 543 m^{3} / y r$
Design life
$253, 543 \times 10 = 2, 535, 430 m^{3}$

Answer: ≈ 253,543 m³/yr, or 2,535,430 m³ over 10 years

Why the other options are there

3,687,898 m³ (diversion and cover ignored)
1,042,568,626 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 4

Landfill volume required for a community's solid waste — Landfill (4)

A community of 232,481 people generates 3.0 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 733 kg/m³ with 20% additional daily cover volume, find the airspace needed for 12 years.

Given

Population = 232,481
Generation = 3.0 kg/cap/d
Diversion = 0.25
Compacted density = 733 kg/m³
Cover = 20%, design life 12 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
$232481 (3.0) (1 - 0.25) = 523, 082 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 523, 082/733 = 713.6 m^{3} / d a y$
Annual with cover
$713.6 \times 365 \times 1.20 = 312, 565 m^{3} / y r$
Design life
$312, 565 \times 12 = 3, 750, 778 m^{3}$

Answer: ≈ 312,565 m³/yr, or 3,750,778 m³ over 12 years

Why the other options are there

4,167,531 m³ (diversion and cover ignored)
2,291,100,255 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 5

Landfill volume required for a community's solid waste — Landfill (5)

A community of 123,919 people generates 3.0 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 627 kg/m³ with 20% additional daily cover volume, find the airspace needed for 10 years.

Given

Population = 123,919
Generation = 3.0 kg/cap/d
Diversion = 0.25
Compacted density = 627 kg/m³
Cover = 20%, design life 10 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
$123919 (3.0) (1 - 0.25) = 278, 818 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 278, 818/627 = 444.7 m^{3} / d a y$
Annual with cover
$444.7 \times 365 \times 1.20 = 194, 772 m^{3} / y r$
Design life
$194, 772 \times 10 = 1, 947, 722 m^{3}$

Answer: ≈ 194,772 m³/yr, or 1,947,722 m³ over 10 years

Why the other options are there

2,164,136 m³ (diversion and cover ignored)
1,017,684,788 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 6

Landfill volume required for a community's solid waste — Landfill (6)

A community of 160,286 people generates 1.9 kg/person/day of MSW and diverts 35% through recycling. Compacted in place at 808 kg/m³ with 15% additional daily cover volume, find the airspace needed for 13 years.

Given

Population = 160,286
Generation = 1.9 kg/cap/d
Diversion = 0.35
Compacted density = 808 kg/m³
Cover = 15%, 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
$160286 (1.9) (1 - 0.35) = 197, 953 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 197, 953/808 = 245.0 m^{3} / d a y$
Annual with cover
$245.0 \times 365 \times 1.15 = 102, 835 m^{3} / y r$
Design life
$102, 835 \times 13 = 1, 336, 858 m^{3}$

Answer: ≈ 102,835 m³/yr, or 1,336,858 m³ over 13 years

Why the other options are there

1,788,439 m³ (diversion and cover ignored)
939,287,981 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 7

Landfill volume required for a community's solid waste — Landfill (7)

A community of 141,697 people generates 1.9 kg/person/day of MSW and diverts 25% through recycling. Compacted in place at 605 kg/m³ with 15% additional daily cover volume, find the airspace needed for 23 years.

Given

Population = 141,697
Generation = 1.9 kg/cap/d
Diversion = 0.25
Compacted density = 605 kg/m³
Cover = 15%, design life 23 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
$141697 (1.9) (1 - 0.25) = 201, 918 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 201, 918/605 = 333.7 m^{3} / d a y$
Annual with cover
$333.7 \times 365 \times 1.15 = 140, 091 m^{3} / y r$
Design life
$140, 091 \times 23 = 3, 222, 098 m^{3}$

Answer: ≈ 140,091 m³/yr, or 3,222,098 m³ over 23 years

Why the other options are there

3,735,765 m³ (diversion and cover ignored)
1,695,103,499 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 8

Landfill volume required for a community's solid waste — Landfill (8)

A community of 79,158 people generates 2.0 kg/person/day of MSW and diverts 40% through recycling. Compacted in place at 882 kg/m³ with 10% additional daily cover volume, find the airspace needed for 26 years.

Given

Population = 79,158
Generation = 2.0 kg/cap/d
Diversion = 0.40
Compacted density = 882 kg/m³
Cover = 10%, 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
$79158 (2.0) (1 - 0.40) = 94, 990 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 94, 990/882 = 107.7 m^{3} / d a y$
Annual with cover
$107.7 \times 365 \times 1.10 = 43, 241 m^{3} / y r$
Design life
$43, 241 \times 26 = 1, 124, 259 m^{3}$

Answer: ≈ 43,241 m³/yr, or 1,124,259 m³ over 26 years

Why the other options are there

1,703,423 m³ (diversion and cover ignored)
901,451,304 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 9

Landfill volume required for a community's solid waste — Landfill (9)

A community of 203,092 people generates 2.2 kg/person/day of MSW and diverts 45% through recycling. Compacted in place at 506 kg/m³ with 20% additional daily cover volume, find the airspace needed for 19 years.

Given

Population = 203,092
Generation = 2.2 kg/cap/d
Diversion = 0.45
Compacted density = 506 kg/m³
Cover = 20%, 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
$203092 (2.2) (1 - 0.45) = 245, 741 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 245, 741/506 = 485.7 m^{3} / d a y$
Annual with cover
$485.7 \times 365 \times 1.20 = 212, 717 m^{3} / y r$
Design life
$212, 717 \times 19 = 4, 041, 619 m^{3}$

Answer: ≈ 212,717 m³/yr, or 4,041,619 m³ over 19 years

Why the other options are there

6,123,665 m³ (diversion and cover ignored)
1,704,216,054 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

Example 10

Landfill volume required for a community's solid waste — Landfill (10)

A community of 89,270 people generates 1.5 kg/person/day of MSW and diverts 35% through recycling. Compacted in place at 539 kg/m³ with 25% additional daily cover volume, find the airspace needed for 14 years.

Given

Population = 89,270
Generation = 1.5 kg/cap/d
Diversion = 0.35
Compacted density = 539 kg/m³
Cover = 25%, design life 14 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
$89270 (1.5) (1 - 0.35) = 87, 038 k g / d a y$
Formula
$V = ma ss / d e n s i t y$
Substituting
$V = 87, 038/539 = 161.5 m^{3} / d a y$
Annual with cover
$161.5 \times 365 \times 1.25 = 73, 676 m^{3} / y r$
Design life
$73, 676 \times 14 = 1, 031, 460 m^{3}$

Answer: ≈ 73,676 m³/yr, or 1,031,460 m³ over 14 years

Why the other options are there

1,269,489 m³ (diversion and cover ignored)
444,765,458 m³ (mass reported as volume)

Reference: FE Reference Handbook — Environmental Engineering → Landfill

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

Landfill contains 7 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.

Landfill

Learning objectives

Lecture

Theory, developed

Notation used in this section

Handbook notes for this section

Core formulas for this FE topic

∗Basedonbalesizeof45×30×62in.

t=Needs technical review

t=breakthroughtime(yr)

d=thicknessofclayliner(ft)

η=porosity

K=hydraulicconductivity(ft/yr)

h=hydraulichead(ft)

Worked exam-style examples

Self-check

Chapter summary

Common traps in this section