Lime-Soda Softening Equations

Environmental Engineering · FE Reference Handbook section

Environmental Engineering

0 formulas

10 exam-style examples

~45 min

All Environmental Engineering lectures

Core formulas for this FE topic

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

This section is conceptual; there are no equations to memorise.

Worked exam-style examples

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

Example 1

Chemical feed rate from dosage — Lime-Soda Softening Equations

A plant treating 1.2 MGD requires a 10.0 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 1.2 MGD$
$Dose = 10.0 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 1.2(10.0)(8.34)$
Evaluate — 100.1 lb/day
At 65% available strength — 154.0 lb/day of product

Answer:

≈ 100.1 lb/day

Why the other options are there

12.0 lb/day (8.34 omitted)
1.44 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 2

Chemical feed rate from dosage — Lime-Soda Softening Equations (2)

A plant treating 4.7 MGD requires a 6.5 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 4.7 MGD$
$Dose = 6.5 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 4.7(6.5)(8.34)$
Evaluate — 254.8 lb/day
At 65% available strength — 392.0 lb/day of product

Answer:

≈ 254.8 lb/day

Why the other options are there

30.6 lb/day (8.34 omitted)
3.66 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 3

Chemical feed rate from dosage — Lime-Soda Softening Equations (3)

A plant treating 0.6 MGD requires a 3.5 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 0.6 MGD$
$Dose = 3.5 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 0.6(3.5)(8.34)$
Evaluate — 17.5 lb/day
At 65% available strength — 26.9 lb/day of product

Answer:

≈ 18 lb/day

Why the other options are there

2.1 lb/day (8.34 omitted)
0.25 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 4

Chemical feed rate from dosage — Lime-Soda Softening Equations (4)

A plant treating 6.1 MGD requires a 2.0 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 6.1 MGD$
$Dose = 2.0 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 6.1(2.0)(8.34)$
Evaluate — 101.7 lb/day
At 65% available strength — 156.5 lb/day of product

Answer:

≈ 101.7 lb/day

Why the other options are there

12.2 lb/day (8.34 omitted)
1.46 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 5

Chemical feed rate from dosage — Lime-Soda Softening Equations (5)

A plant treating 1.7 MGD requires a 6.0 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 1.7 MGD$
$Dose = 6.0 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 1.7(6.0)(8.34)$
Evaluate — 85.1 lb/day
At 65% available strength — 130.9 lb/day of product

Answer:

≈ 85 lb/day

Why the other options are there

10.2 lb/day (8.34 omitted)
1.22 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 6

Chemical feed rate from dosage — Lime-Soda Softening Equations (6)

A plant treating 2.9 MGD requires a 2.5 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 2.9 MGD$
$Dose = 2.5 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 2.9(2.5)(8.34)$
Evaluate — 60.5 lb/day
At 65% available strength — 93.0 lb/day of product

Answer:

≈ 60 lb/day

Why the other options are there

7.3 lb/day (8.34 omitted)
0.87 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 7

Chemical feed rate from dosage — Lime-Soda Softening Equations (7)

A plant treating 2.8 MGD requires a 5.0 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 2.8 MGD$
$Dose = 5.0 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 2.8(5.0)(8.34)$
Evaluate — 116.8 lb/day
At 65% available strength — 179.6 lb/day of product

Answer:

≈ 116.8 lb/day

Why the other options are there

14.0 lb/day (8.34 omitted)
1.68 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 8

Chemical feed rate from dosage — Lime-Soda Softening Equations (8)

A plant treating 3.1 MGD requires a 2.0 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 3.1 MGD$
$Dose = 2.0 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 3.1(2.0)(8.34)$
Evaluate — 51.7 lb/day
At 65% available strength — 79.6 lb/day of product

Answer:

≈ 52 lb/day

Why the other options are there

6.2 lb/day (8.34 omitted)
0.74 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 9

Chemical feed rate from dosage — Lime-Soda Softening Equations (9)

A plant treating 0.5 MGD requires a 6.5 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 0.5 MGD$
$Dose = 6.5 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 0.5(6.5)(8.34)$
Evaluate — 27.1 lb/day
At 65% available strength — 41.7 lb/day of product

Answer:

≈ 27 lb/day

Why the other options are there

3.3 lb/day (8.34 omitted)
0.39 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations

Example 10

Chemical feed rate from dosage — Lime-Soda Softening Equations (10)

A plant treating 7.8 MGD requires a 5.5 mg/L dose. What is the daily chemical demand in pounds?

Given

$Q = 7.8 MGD$
$Dose = 5.5 mg/L$
8.34 lb/gal

Find

lb/day of chemical

Start with the thinking

The 8.34 factor converts mg/L·MGD to lb/day.
Adjust for purity if the product is not 100% active.

Step-by-step solution

Feed
$lb/day = Q(MGD) \times dose(mg/L) \times 8.34$
Substituting
$lb/day = 7.8(5.5)(8.34)$
Evaluate — 357.8 lb/day
At 65% available strength — 550.4 lb/day of product

Answer:

≈ 357.8 lb/day

Why the other options are there

42.9 lb/day (8.34 omitted)
5.14 lb/day (factor divided)

Reference: FE Reference Handbook — Environmental Engineering → Lime-Soda Softening Equations