mass calculations for BOD loading on a treatment plant Given concentration (C) = 351.0 mg/L; flow rate (Q) = 33.6000 MGD, determine the mass loading (M) in lb/day.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• Everything except M is given, so isolate M 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for M:

   $$M = C\,Q\,(8.34)$$

3. Step 3

   $$List the givens: concentration (C) = 351.0 mg/L, flow rate (Q) = 33.6000 MGD$$

4. Step 4 — Substitute the given values:

   $$M = 351.0\,33.6000\,(8.34)$$

5. Step 5 — Evaluate:

   $$M = 98359\ \text{lb/day}$$

6. Step 6 — Check: returning M = 98,359 lb/day to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 196,717 — kept a factor of two that cancels in the correct rearrangement.
• 49,179 — dropped that same factor in the other direction.
• 108,194 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations converting mg/L concentration and MGD flow to lb/day Given flow rate (Q) = 39.6000 MGD; mass loading (M) = 358.0 lb/day, determine the concentration (C) in mg/L.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{M}{8.34\,Q}$$

3. Step 3

   $$List the givens: flow rate (Q) = 39.6000 MGD, mass loading (M) = 358.0 lb/day$$

4. Step 4 — Substitute the given values:

   $$C = \dfrac{358.0}{8.34\,39.6000}$$

5. Step 5 — Evaluate:

   $$C = 1.0840\ \text{mg/L}$$

6. Step 6 — Check: returning C = 1.0840 mg/L to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2.1680 — kept a factor of two that cancels in the correct rearrangement.
• 0.5420 — dropped that same factor in the other direction.
• 1.1924 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

pollutant mass loading calculation for a discharge permit Given concentration (C) = 287.0 mg/L; mass loading (M) = 10,656 lb/day, determine the flow rate (Q) in MGD.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = \dfrac{M}{8.34\,C}$$

3. Step 3

   $$List the givens: concentration (C) = 287.0 mg/L, mass loading (M) = 10,656 lb/day$$

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{10656}{8.34\,287.0}$$

5. Step 5 — Evaluate:

   $$Q = 4.4519\ \text{MGD}$$

6. Step 6 — Check: returning Q = 4.4519 MGD to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 8.9038 — kept a factor of two that cancels in the correct rearrangement.
• 2.2260 — dropped that same factor in the other direction.
• 4.8971 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations for BOD loading on a treatment plant Given concentration (C) = 267.0 mg/L; flow rate (Q) = 37.1000 MGD, determine the mass loading (M) in lb/day.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• Everything except M is given, so isolate M 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for M:

   $$M = C\,Q\,(8.34)$$

3. Step 3

   $$List the givens: concentration (C) = 267.0 mg/L, flow rate (Q) = 37.1000 MGD$$

4. Step 4 — Substitute the given values:

   $$M = 267.0\,37.1000\,(8.34)$$

5. Step 5 — Evaluate:

   $$M = 82614\ \text{lb/day}$$

6. Step 6 — Check: returning M = 82,614 lb/day to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 165,227 — kept a factor of two that cancels in the correct rearrangement.
• 41,307 — dropped that same factor in the other direction.
• 90,875 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations converting mg/L concentration and MGD flow to lb/day Given flow rate (Q) = 5.6000 MGD; mass loading (M) = 28,825 lb/day, determine the concentration (C) in mg/L.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{M}{8.34\,Q}$$

3. Step 3

   $$List the givens: flow rate (Q) = 5.6000 MGD, mass loading (M) = 28,825 lb/day$$

4. Step 4 — Substitute the given values:

   $$C = \dfrac{28825}{8.34\,5.6000}$$

5. Step 5 — Evaluate:

   $$C = 617.2\ \text{mg/L}$$

6. Step 6 — Check: returning C = 617.2 mg/L to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,234 — kept a factor of two that cancels in the correct rearrangement.
• 308.6 — dropped that same factor in the other direction.
• 678.9 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

pollutant mass loading calculation for a discharge permit Given concentration (C) = 471.0 mg/L; mass loading (M) = 30,286 lb/day, determine the flow rate (Q) in MGD.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = \dfrac{M}{8.34\,C}$$

3. Step 3

   $$List the givens: concentration (C) = 471.0 mg/L, mass loading (M) = 30,286 lb/day$$

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{30286}{8.34\,471.0}$$

5. Step 5 — Evaluate:

   $$Q = 7.7100\ \text{MGD}$$

6. Step 6 — Check: returning Q = 7.7100 MGD to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 15.4200 — kept a factor of two that cancels in the correct rearrangement.
• 3.8550 — dropped that same factor in the other direction.
• 8.4810 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations for BOD loading on a treatment plant Given concentration (C) = 497.0 mg/L; flow rate (Q) = 42.9000 MGD, determine the mass loading (M) in lb/day.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• Everything except M is given, so isolate M 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for M:

   $$M = C\,Q\,(8.34)$$

3. Step 3

   $$List the givens: concentration (C) = 497.0 mg/L, flow rate (Q) = 42.9000 MGD$$

4. Step 4 — Substitute the given values:

   $$M = 497.0\,42.9000\,(8.34)$$

5. Step 5 — Evaluate:

   $$M = 177820\ \text{lb/day}$$

6. Step 6 — Check: returning M = 177,820 lb/day to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 355,639 — kept a factor of two that cancels in the correct rearrangement.
• 88,910 — dropped that same factor in the other direction.
• 195,602 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations converting mg/L concentration and MGD flow to lb/day Given flow rate (Q) = 49.7000 MGD; mass loading (M) = 26,161 lb/day, determine the concentration (C) in mg/L.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{M}{8.34\,Q}$$

3. Step 3

   $$List the givens: flow rate (Q) = 49.7000 MGD, mass loading (M) = 26,161 lb/day$$

4. Step 4 — Substitute the given values:

   $$C = \dfrac{26161}{8.34\,49.7000}$$

5. Step 5 — Evaluate:

   $$C = 63.1149\ \text{mg/L}$$

6. Step 6 — Check: returning C = 63.1149 mg/L to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 126.2 — kept a factor of two that cancels in the correct rearrangement.
• 31.5575 — dropped that same factor in the other direction.
• 69.4264 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

pollutant mass loading calculation for a discharge permit Given concentration (C) = 142.0 mg/L; mass loading (M) = 1,574 lb/day, determine the flow rate (Q) in MGD.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = \dfrac{M}{8.34\,C}$$

3. Step 3

   $$List the givens: concentration (C) = 142.0 mg/L, mass loading (M) = 1,574 lb/day$$

4. Step 4 — Substitute the given values:

   $$Q = \dfrac{1574}{8.34\,142.0}$$

5. Step 5 — Evaluate:

   $$Q = 1.3291\ \text{MGD}$$

6. Step 6 — Check: returning Q = 1.3291 MGD to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2.6582 — kept a factor of two that cancels in the correct rearrangement.
• 0.6645 — dropped that same factor in the other direction.
• 1.4620 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations

mass calculations for BOD loading on a treatment plant Given concentration (C) = 395.0 mg/L; flow rate (Q) = 34.6000 MGD, determine the mass loading (M) in lb/day.

Start with the thinking

• The governing relation printed in this handbook section is Mass Calculations.
• Everything except M is given, so isolate M 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.
• Mass calculations convert a concentration and flow rate into a daily mass loading using the 8.34 conversion factor.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = C \times Q \times 8.34$$

2. Step 2 — Rearrange symbolically for M:

   $$M = C\,Q\,(8.34)$$

3. Step 3

   $$List the givens: concentration (C) = 395.0 mg/L, flow rate (Q) = 34.6000 MGD$$

4. Step 4 — Substitute the given values:

   $$M = 395.0\,34.6000\,(8.34)$$

5. Step 5 — Evaluate:

   $$M = 113983\ \text{lb/day}$$

6. Step 6 — Check: returning M = 113,983 lb/day to

   $$M = C \times Q \times 8.34$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 227,966 — kept a factor of two that cancels in the correct rearrangement.
• 56,991 — dropped that same factor in the other direction.
• 125,381 — rounded an intermediate value before the final step.

Reference: FE Handbook — Mass Calculations