A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 11.5000 MGD; concentration 1 (C1) = 2.0000 mg/L; flow 2 (Q2) = 13.0000 MGD; concentration 2 (C2) = 47.5000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 11.5000 MGD, concentration 1 (C1) = 2.0000 mg/L, flow 2 (Q2) = 13.0000 MGD, concentration 2 (C2) = 47.5000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 26.1429\ \text{mg/L}$$

6. Step 6 — Check: returning C = 26.1429 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.

Why the other options are there

• 52.2857 — kept a factor of two that cancels in the correct rearrangement.
• 13.0714 — dropped that same factor in the other direction.
• 28.7571 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 17.5000 MGD; flow 2 (Q2) = 1.5000 MGD; concentration 2 (C2) = 9.5000 mg/L; blended concentration (C) = 36.8100 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 17.5000 MGD, flow 2 (Q2) = 1.5000 MGD, concentration 2 (C2) = 9.5000 mg/L, blended concentration (C) = 36.8100 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C_{1} = 39.1509\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 39.1509 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.

Why the other options are there

• 78.3017 — kept a factor of two that cancels in the correct rearrangement.
• 19.5754 — dropped that same factor in the other direction.
• 43.0659 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 4.5000 MGD; concentration 1 (C1) = 11.5000 mg/L; flow 2 (Q2) = 3.0000 MGD; concentration 2 (C2) = 13.0000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 4.5000 MGD, concentration 1 (C1) = 11.5000 mg/L, flow 2 (Q2) = 3.0000 MGD, concentration 2 (C2) = 13.0000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 12.1000\ \text{mg/L}$$

6. Step 6 — Check: returning C = 12.1000 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.

Why the other options are there

• 24.2000 — kept a factor of two that cancels in the correct rearrangement.
• 6.0500 — dropped that same factor in the other direction.
• 13.3100 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 10.5000 MGD; flow 2 (Q2) = 11.0000 MGD; concentration 2 (C2) = 31.5000 mg/L; blended concentration (C) = 49.0000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 10.5000 MGD, flow 2 (Q2) = 11.0000 MGD, concentration 2 (C2) = 31.5000 mg/L, blended concentration (C) = 49.0000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C_{1} = 67.3333\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 67.3333 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.

Why the other options are there

• 134.7 — kept a factor of two that cancels in the correct rearrangement.
• 33.6667 — dropped that same factor in the other direction.
• 74.0667 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.5000 MGD; concentration 1 (C1) = 17.0000 mg/L; flow 2 (Q2) = 17.0000 MGD; concentration 2 (C2) = 28.0000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 9.5000 MGD, concentration 1 (C1) = 17.0000 mg/L, flow 2 (Q2) = 17.0000 MGD, concentration 2 (C2) = 28.0000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 24.0566\ \text{mg/L}$$

6. Step 6 — Check: returning C = 24.0566 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.

Why the other options are there

• 48.1132 — kept a factor of two that cancels in the correct rearrangement.
• 12.0283 — dropped that same factor in the other direction.
• 26.4623 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.0000 MGD; flow 2 (Q2) = 10.5000 MGD; concentration 2 (C2) = 34.0000 mg/L; blended concentration (C) = 13.4200 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 9.0000 MGD, flow 2 (Q2) = 10.5000 MGD, concentration 2 (C2) = 34.0000 mg/L, blended concentration (C) = 13.4200 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C_{1} = -10.5900\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -10.5900 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.

Why the other options are there

• -21.1800 — kept a factor of two that cancels in the correct rearrangement.
• -5.2950 — dropped that same factor in the other direction.
• -11.6490 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 5.0000 MGD; concentration 1 (C1) = 44.0000 mg/L; flow 2 (Q2) = 6.5000 MGD; concentration 2 (C2) = 5.5000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 5.0000 MGD, concentration 1 (C1) = 44.0000 mg/L, flow 2 (Q2) = 6.5000 MGD, concentration 2 (C2) = 5.5000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 22.2391\ \text{mg/L}$$

6. Step 6 — Check: returning C = 22.2391 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.

Why the other options are there

• 44.4783 — kept a factor of two that cancels in the correct rearrangement.
• 11.1196 — dropped that same factor in the other direction.
• 24.4630 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.5000 MGD; flow 2 (Q2) = 9.5000 MGD; concentration 2 (C2) = 23.5000 mg/L; blended concentration (C) = 9.9100 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 13.5000 MGD, flow 2 (Q2) = 9.5000 MGD, concentration 2 (C2) = 23.5000 mg/L, blended concentration (C) = 9.9100 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C_{1} = 0.3467\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 0.3467 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.

Why the other options are there

• 0.6933 — kept a factor of two that cancels in the correct rearrangement.
• 0.1733 — dropped that same factor in the other direction.
• 0.3813 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.0000 MGD; concentration 1 (C1) = 31.5000 mg/L; flow 2 (Q2) = 12.0000 MGD; concentration 2 (C2) = 6.5000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 9.0000 MGD, concentration 1 (C1) = 31.5000 mg/L, flow 2 (Q2) = 12.0000 MGD, concentration 2 (C2) = 6.5000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 17.2143\ \text{mg/L}$$

6. Step 6 — Check: returning C = 17.2143 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.

Why the other options are there

• 34.4286 — kept a factor of two that cancels in the correct rearrangement.
• 8.6071 — dropped that same factor in the other direction.
• 18.9357 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.0000 MGD; flow 2 (Q2) = 8.0000 MGD; concentration 2 (C2) = 29.5000 mg/L; blended concentration (C) = 30.4000 mg/L, determine the 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

1. Step 1 — State the governing relation:

   $$C = (Q_1 C_1 + Q_2 C_2) / (Q_1 + Q_2)$$

2. Step 2 — Rearrange the relation so that C1 stands alone on the left-hand side.

3. Step 3 — List the givens: flow 1 (Q1) = 13.0000 MGD, flow 2 (Q2) = 8.0000 MGD, concentration 2 (C2) = 29.5000 mg/L, blended concentration (C) = 30.4000 mg/L.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C_{1} = 30.9538\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 30.9538 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.

Why the other options are there

• 61.9077 — kept a factor of two that cancels in the correct rearrangement.
• 15.4769 — dropped that same factor in the other direction.
• 34.0492 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Methanol Requirement for Biologically Treated Wastewater