A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 16.5000 MGD; concentration 1 (C1) = 39.5000 mg/L; flow 2 (Q2) = 13.0000 MGD; concentration 2 (C2) = 24.5000 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) = 16.5000 MGD, concentration 1 (C1) = 39.5000 mg/L, flow 2 (Q2) = 13.0000 MGD, concentration 2 (C2) = 24.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 32.8898\ \text{mg/L}$$

6. Step 6 — Check: returning C = 32.8898 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

• 65.7797 — kept a factor of two that cancels in the correct rearrangement.
• 16.4449 — dropped that same factor in the other direction.
• 36.1788 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.5000 MGD; flow 2 (Q2) = 9.0000 MGD; concentration 2 (C2) = 40.5000 mg/L; blended concentration (C) = 42.8600 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) = 9.5000 MGD, flow 2 (Q2) = 9.0000 MGD, concentration 2 (C2) = 40.5000 mg/L, blended concentration (C) = 42.8600 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 45.0958\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 45.0958 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

• 90.1916 — kept a factor of two that cancels in the correct rearrangement.
• 22.5479 — dropped that same factor in the other direction.
• 49.6054 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 12.0000 MGD; concentration 1 (C1) = 50.0000 mg/L; flow 2 (Q2) = 11.0000 MGD; concentration 2 (C2) = 11.5000 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) = 12.0000 MGD, concentration 1 (C1) = 50.0000 mg/L, flow 2 (Q2) = 11.0000 MGD, concentration 2 (C2) = 11.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 31.5870\ \text{mg/L}$$

6. Step 6 — Check: returning C = 31.5870 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

• 63.1739 — kept a factor of two that cancels in the correct rearrangement.
• 15.7935 — dropped that same factor in the other direction.
• 34.7457 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.0000 MGD; flow 2 (Q2) = 5.5000 MGD; concentration 2 (C2) = 10.0000 mg/L; blended concentration (C) = 25.6400 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) = 14.0000 MGD, flow 2 (Q2) = 5.5000 MGD, concentration 2 (C2) = 10.0000 mg/L, blended concentration (C) = 25.6400 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 31.7843\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 31.7843 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

• 63.5686 — kept a factor of two that cancels in the correct rearrangement.
• 15.8921 — dropped that same factor in the other direction.
• 34.9627 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 12.5000 MGD; concentration 1 (C1) = 38.0000 mg/L; flow 2 (Q2) = 18.0000 MGD; concentration 2 (C2) = 16.0000 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) = 12.5000 MGD, concentration 1 (C1) = 38.0000 mg/L, flow 2 (Q2) = 18.0000 MGD, concentration 2 (C2) = 16.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 25.0164\ \text{mg/L}$$

6. Step 6 — Check: returning C = 25.0164 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

• 50.0328 — kept a factor of two that cancels in the correct rearrangement.
• 12.5082 — dropped that same factor in the other direction.
• 27.5180 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.0000 MGD; flow 2 (Q2) = 8.5000 MGD; concentration 2 (C2) = 37.0000 mg/L; blended concentration (C) = 37.5400 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) = 14.0000 MGD, flow 2 (Q2) = 8.5000 MGD, concentration 2 (C2) = 37.0000 mg/L, blended concentration (C) = 37.5400 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 37.8679\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 37.8679 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

• 75.7357 — kept a factor of two that cancels in the correct rearrangement.
• 18.9339 — dropped that same factor in the other direction.
• 41.6546 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 3.5000 MGD; concentration 1 (C1) = 1.5000 mg/L; flow 2 (Q2) = 3.5000 MGD; concentration 2 (C2) = 31.0000 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) = 3.5000 MGD, concentration 1 (C1) = 1.5000 mg/L, flow 2 (Q2) = 3.5000 MGD, concentration 2 (C2) = 31.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 16.2500\ \text{mg/L}$$

6. Step 6 — Check: returning C = 16.2500 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

• 32.5000 — kept a factor of two that cancels in the correct rearrangement.
• 8.1250 — dropped that same factor in the other direction.
• 17.8750 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 2.0000 MGD; flow 2 (Q2) = 16.5000 MGD; concentration 2 (C2) = 2.0000 mg/L; blended concentration (C) = 36.5100 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) = 2.0000 MGD, flow 2 (Q2) = 16.5000 MGD, concentration 2 (C2) = 2.0000 mg/L, blended concentration (C) = 36.5100 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 321.2\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 321.2 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

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

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 16.5000 MGD; concentration 1 (C1) = 13.0000 mg/L; flow 2 (Q2) = 9.0000 MGD; concentration 2 (C2) = 49.0000 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) = 16.5000 MGD, concentration 1 (C1) = 13.0000 mg/L, flow 2 (Q2) = 9.0000 MGD, concentration 2 (C2) = 49.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 25.7059\ \text{mg/L}$$

6. Step 6 — Check: returning C = 25.7059 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

• 51.4118 — kept a factor of two that cancels in the correct rearrangement.
• 12.8529 — dropped that same factor in the other direction.
• 28.2765 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 12.5000 MGD; flow 2 (Q2) = 3.5000 MGD; concentration 2 (C2) = 42.5000 mg/L; blended concentration (C) = 8.6800 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) = 12.5000 MGD, flow 2 (Q2) = 3.5000 MGD, concentration 2 (C2) = 42.5000 mg/L, blended concentration (C) = 8.6800 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = -0.7896\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -0.7896 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

• -1.5792 — kept a factor of two that cancels in the correct rearrangement.
• -0.3948 — dropped that same factor in the other direction.
• -0.8686 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Organic Carbon Partition Coefficient Koc