Disinfection

Environmental Engineering · FE Reference Handbook section

Environmental Engineering

8 formulas

10 exam-style examples

~60 min

All Environmental Engineering lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

Adapted from Guidance Manual LT1ESWTR Disinfection Profiling and Benchmarking, U.S. Environmental Protection Agency, 2003.
Unbaffled 0.1 None, agitated basin, very low
(mixed flow) length to width ratio, high inlet
Poor 0.3 Single or multiple unbaffled
Average 0.5 Baffled inlet or outlet with some
Perfect 1.0 Very high length to width ratio
Guidance Manual LT1ESWTR Disinfection Profiling and Benchmarking, U.S. Environmental Protection Agency, 2003.

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

Steady-state mass balance — solve for blended concentration — Disinfection

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 10.5000 MGD; concentration 1 (C1) = 23.0000 mg/L; flow 2 (Q2) = 10.0000 MGD; concentration 2 (C2) = 22.0000 mg/L, determine the blended concentration (C) in mg/L.

Given

$flow 1 (Q_{1}) = 10.5000 MGD$
$concentration 1 (C_{1}) = 23.0000 mg/L$
$flow 2 (Q_{2}) = 10.0000 MGD$
$concentration 2 (C_{2}) = 22.0000 mg/L$

Find

blended concentration (C), in mg/L

Start with the thinking

The governing relation printed in this handbook section is Steady-state mass balance.
Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
Step 2 — Rearrange the relation so that C stands alone on the left-hand side.
Step 3 — List the givens: flow 1 (Q1) = 10.5000 MGD, concentration 1 (C1) = 23.0000 mg/L, flow 2 (Q2) = 10.0000 MGD, concentration 2 (C2) = 22.0000 mg/L.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$C = 22.5122\ \text{mg/L}$
Step 6 — Check: returning C = 22.5122 mg/L to
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
reproduces the given quantities, and both sides carry the same units.

Answer:

C = 22.5122\ \text{mg/L}

Why the other options are there

45.0244 — kept a factor of two that cancels in the correct rearrangement.
11.2561 — dropped that same factor in the other direction.
24.7634 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 2

Hydraulic detention time — solve for detention time — Disinfection (2)

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 1,540,000 gal; flow rate (Q) = 281,000 gal/day, determine the detention time (theta) in day.

Given

$tank volume (V) = 1,540,000 gal$
$flow rate (Q) = 281,000 gal/day$

Find

detention time (theta), in day

Start with the thinking

The governing relation printed in this handbook section is Hydraulic detention time.
Everything except theta is given, so isolate theta symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$\theta = V / Q$
Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.
Step 3
$List the givens: tank volume (V) = 1,540,000 gal, flow rate (Q) = 281,000 gal/day$
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$\theta = 5.4804\ \text{day}$
Step 6 — Check: returning theta = 5.4804 day to
$\theta = V / Q$
reproduces the given quantities, and both sides carry the same units.

Answer:

\theta = 5.4804\ \text{day}

Why the other options are there

10.9609 — kept a factor of two that cancels in the correct rearrangement.
2.7402 — dropped that same factor in the other direction.
6.0285 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 3

Steady-state mass balance — solve for concentration 1 — Disinfection (3)

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.5000 MGD; flow 2 (Q2) = 13.0000 MGD; concentration 2 (C2) = 16.5000 mg/L; blended concentration (C) = 18.2600 mg/L, determine the concentration 1 (C1) in mg/L.

Given

$flow 1 (Q_{1}) = 14.5000 MGD$
$flow 2 (Q_{2}) = 13.0000 MGD$
$concentration 2 (C_{2}) = 16.5000 mg/L$
$blended concentration (C) = 18.2600 mg/L$

Find

concentration 1 (C1), in mg/L

Start with the thinking

The governing relation printed in this handbook section is Steady-state mass balance.
Everything except C1 is given, so isolate C1 symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.
Step 3 — List the givens: flow 1 (Q1) = 14.5000 MGD, flow 2 (Q2) = 13.0000 MGD, concentration 2 (C2) = 16.5000 mg/L, blended concentration (C) = 18.2600 mg/L.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$C_{1} = 19.8379\ \text{mg/L}$
Step 6 — Check: returning C1 = 19.8379 mg/L to
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
reproduces the given quantities, and both sides carry the same units.

Answer:

C_{1} = 19.8379\ \text{mg/L}

Why the other options are there

39.6759 — kept a factor of two that cancels in the correct rearrangement.
9.9190 — dropped that same factor in the other direction.
21.8217 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 4

Hydraulic detention time — solve for tank volume — Disinfection (4)

A environmental engineering problem uses Hydraulic detention time. Given flow rate (Q) = 3,137,000 gal/day; detention time (theta) = 2.8100 day, determine the tank volume (V) in gal.

Given

$flow rate (Q) = 3,137,000 gal/day$
$detention time (theta) = 2.8100 day$

Find

tank volume (V), in gal

Start with the thinking

The governing relation printed in this handbook section is Hydraulic detention time.
Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$\theta = V / Q$
Step 2 — Rearrange the relation so that V stands alone on the left-hand side.
Step 3
$List the givens: flow rate (Q) = 3,137,000 gal/day, detention time (theta) = 2.8100 day$
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$V = 8814970\ \text{gal}$
Step 6 — Check: returning V = 8,814,970 gal to
$\theta = V / Q$
reproduces the given quantities, and both sides carry the same units.

Answer:

V = 8814970\ \text{gal}

Why the other options are there

17,629,940 — kept a factor of two that cancels in the correct rearrangement.
4,407,485 — dropped that same factor in the other direction.
9,696,467 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 5

Steady-state mass balance — solve for blended concentration (case 2) — Disinfection (5)

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 12.5000 MGD; concentration 1 (C1) = 14.0000 mg/L; flow 2 (Q2) = 8.0000 MGD; concentration 2 (C2) = 27.5000 mg/L, determine the blended concentration (C) in mg/L.

Given

$flow 1 (Q_{1}) = 12.5000 MGD$
$concentration 1 (C_{1}) = 14.0000 mg/L$
$flow 2 (Q_{2}) = 8.0000 MGD$
$concentration 2 (C_{2}) = 27.5000 mg/L$

Find

blended concentration (C), in mg/L

Start with the thinking

The governing relation printed in this handbook section is Steady-state mass balance.
Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
Step 2 — Rearrange the relation so that C stands alone on the left-hand side.
Step 3 — List the givens: flow 1 (Q1) = 12.5000 MGD, concentration 1 (C1) = 14.0000 mg/L, flow 2 (Q2) = 8.0000 MGD, concentration 2 (C2) = 27.5000 mg/L.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$C = 19.2683\ \text{mg/L}$
Step 6 — Check: returning C = 19.2683 mg/L to
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
reproduces the given quantities, and both sides carry the same units.

Answer:

C = 19.2683\ \text{mg/L}

Why the other options are there

38.5366 — kept a factor of two that cancels in the correct rearrangement.
9.6341 — dropped that same factor in the other direction.
21.1951 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 6

Hydraulic detention time — solve for flow rate — Disinfection (6)

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 299,000 gal; detention time (theta) = 2.9500 day, determine the flow rate (Q) in gal/day.

Given

$tank volume (V) = 299,000 gal$
$detention time (theta) = 2.9500 day$

Find

flow rate (Q), in gal/day

Start with the thinking

The governing relation printed in this handbook section is Hydraulic detention time.
Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$\theta = V / Q$
Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.
Step 3
$List the givens: tank volume (V) = 299,000 gal, detention time (theta) = 2.9500 day$
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$Q = 101356\ \text{gal/day}$
Step 6 — Check: returning Q = 101,356 gal/day to
$\theta = V / Q$
reproduces the given quantities, and both sides carry the same units.

Answer:

Q = 101356\ \text{gal/day}

Why the other options are there

202,712 — kept a factor of two that cancels in the correct rearrangement.
50,678 — dropped that same factor in the other direction.
111,492 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 7

Steady-state mass balance — solve for concentration 1 (case 2) — Disinfection (7)

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 11.5000 MGD; flow 2 (Q2) = 8.0000 MGD; concentration 2 (C2) = 19.0000 mg/L; blended concentration (C) = 4.5200 mg/L, determine the concentration 1 (C1) in mg/L.

Given

$flow 1 (Q_{1}) = 11.5000 MGD$
$flow 2 (Q_{2}) = 8.0000 MGD$
$concentration 2 (C_{2}) = 19.0000 mg/L$
$blended concentration (C) = 4.5200 mg/L$

Find

concentration 1 (C1), in mg/L

Start with the thinking

The governing relation printed in this handbook section is Steady-state mass balance.
Everything except C1 is given, so isolate C1 symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.
Step 3 — List the givens: flow 1 (Q1) = 11.5000 MGD, flow 2 (Q2) = 8.0000 MGD, concentration 2 (C2) = 19.0000 mg/L, blended concentration (C) = 4.5200 mg/L.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$C_{1} = -5.5530\ \text{mg/L}$
Step 6 — Check: returning C1 = -5.5530 mg/L to
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
reproduces the given quantities, and both sides carry the same units.

Answer:

C_{1} = -5.5530\ \text{mg/L}

Why the other options are there

-11.1061 — kept a factor of two that cancels in the correct rearrangement.
-2.7765 — dropped that same factor in the other direction.
-6.1083 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 8

Hydraulic detention time — solve for detention time (case 2) — Disinfection (8)

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 903,000 gal; flow rate (Q) = 2,096,000 gal/day, determine the detention time (theta) in day.

Given

$tank volume (V) = 903,000 gal$
$flow rate (Q) = 2,096,000 gal/day$

Find

detention time (theta), in day

Start with the thinking

The governing relation printed in this handbook section is Hydraulic detention time.
Everything except theta is given, so isolate theta symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$\theta = V / Q$
Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.
Step 3
$List the givens: tank volume (V) = 903,000 gal, flow rate (Q) = 2,096,000 gal/day$
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$\theta = 0.4308\ \text{day}$
Step 6 — Check: returning theta = 0.4308 day to
$\theta = V / Q$
reproduces the given quantities, and both sides carry the same units.

Answer:

\theta = 0.4308\ \text{day}

Why the other options are there

0.8616 — kept a factor of two that cancels in the correct rearrangement.
0.2154 — dropped that same factor in the other direction.
0.4739 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 9

Steady-state mass balance — solve for blended concentration (case 3) — Disinfection (9)

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 4.5000 MGD; concentration 1 (C1) = 26.0000 mg/L; flow 2 (Q2) = 16.5000 MGD; concentration 2 (C2) = 6.5000 mg/L, determine the blended concentration (C) in mg/L.

Given

$flow 1 (Q_{1}) = 4.5000 MGD$
$concentration 1 (C_{1}) = 26.0000 mg/L$
$flow 2 (Q_{2}) = 16.5000 MGD$
$concentration 2 (C_{2}) = 6.5000 mg/L$

Find

blended concentration (C), in mg/L

Start with the thinking

The governing relation printed in this handbook section is Steady-state mass balance.
Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
Step 2 — Rearrange the relation so that C stands alone on the left-hand side.
Step 3 — List the givens: flow 1 (Q1) = 4.5000 MGD, concentration 1 (C1) = 26.0000 mg/L, flow 2 (Q2) = 16.5000 MGD, concentration 2 (C2) = 6.5000 mg/L.
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$C = 10.6786\ \text{mg/L}$
Step 6 — Check: returning C = 10.6786 mg/L to
$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$
reproduces the given quantities, and both sides carry the same units.

Answer:

C = 10.6786\ \text{mg/L}

Why the other options are there

21.3571 — kept a factor of two that cancels in the correct rearrangement.
5.3393 — dropped that same factor in the other direction.
11.7464 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Example 10

Hydraulic detention time — solve for tank volume (case 2) — Disinfection (10)

A environmental engineering problem uses Hydraulic detention time. Given flow rate (Q) = 1,628,000 gal/day; detention time (theta) = 9.0100 day, determine the tank volume (V) in gal.

Given

$flow rate (Q) = 1,628,000 gal/day$
$detention time (theta) = 9.0100 day$

Find

tank volume (V), in gal

Start with the thinking

The governing relation printed in this handbook section is Hydraulic detention time.
Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
Environmental Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

Step 1 — State the governing relation:
$\theta = V / Q$
Step 2 — Rearrange the relation so that V stands alone on the left-hand side.
Step 3
$List the givens: flow rate (Q) = 1,628,000 gal/day, detention time (theta) = 9.0100 day$
Step 4 — Substitute the given values into the rearranged relation.
Step 5 — Evaluate:
$V = 14668280\ \text{gal}$
Step 6 — Check: returning V = 14,668,280 gal to
$\theta = V / Q$
reproduces the given quantities, and both sides carry the same units.

Answer:

V = 14668280\ \text{gal}

Why the other options are there

29,336,560 — kept a factor of two that cancels in the correct rearrangement.
7,334,140 — dropped that same factor in the other direction.
16,135,108 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Disinfection

Disinfection

Handbook notes for this section

Core formulas for this FE topic

Chlorinecontactchamberlength−to−widthratio=20:1to50:1Chlorine contact chamber length-to-width ratio = 20:1 to 50:1Chlorinecontactchamberlength−to−widthratio=20:1to50:1

CTcalc=C×t10CTcalc = C \times t10CTcalc=C×t10

CTcalc=calculatedCTvalue(mg•mm/L)CTcalc = calculated CT value (mg • mm/L)CTcalc=calculatedCTvalue(mg•mm/L)

C=residualdisinfectantconcentrationmeasuredduringpeakhourlyflow(mg/L)C = residual disinfectant concentration measured during peak hourly flow (mg/L)C=residualdisinfectantconcentrationmeasuredduringpeakhourlyflow(mg/L)

t10=timeittakes10t10 = time it takes 10% of the water to flow through the reactor measured during peak hourly flow (\min )t10=timeittakes10

=canbedeterminedfromtracesstudydataorthefollowingrelationship,t10(approx)=θ×BF= can be determined from traces study data or the following relationship, t10(approx) = \theta \times BF=canbedeterminedfromtracesstudydataorthefollowingrelationship,t10(approx)=θ×BF

θ=hydraulicresidencetime(min⁡)\theta = hydraulic residence time (\min )θ=hydraulicresidencetime(min)

BF=bafflingfactorBF = baffling factorBF=bafflingfactor

Worked exam-style examples