A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.5000 MGD; concentration 1 (C1) = 5.0000 mg/L; flow 2 (Q2) = 6.5000 MGD; concentration 2 (C2) = 25.0000 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) = 13.5000 MGD, concentration 1 (C1) = 5.0000 mg/L, flow 2 (Q2) = 6.5000 MGD, concentration 2 (C2) = 25.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 11.5000\ \text{mg/L}$$

6. Step 6 — Check: returning C = 11.5000 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

• 23.0000 — kept a factor of two that cancels in the correct rearrangement.
• 5.7500 — dropped that same factor in the other direction.
• 12.6500 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.0000 MGD; flow 2 (Q2) = 4.5000 MGD; concentration 2 (C2) = 39.0000 mg/L; blended concentration (C) = 38.7900 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) = 18.0000 MGD, flow 2 (Q2) = 4.5000 MGD, concentration 2 (C2) = 39.0000 mg/L, blended concentration (C) = 38.7900 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 38.7375\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 38.7375 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

• 77.4750 — kept a factor of two that cancels in the correct rearrangement.
• 19.3688 — dropped that same factor in the other direction.
• 42.6113 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 15.5000 MGD; concentration 1 (C1) = 5.0000 mg/L; flow 2 (Q2) = 4.0000 MGD; concentration 2 (C2) = 30.5000 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) = 15.5000 MGD, concentration 1 (C1) = 5.0000 mg/L, flow 2 (Q2) = 4.0000 MGD, concentration 2 (C2) = 30.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 10.2308\ \text{mg/L}$$

6. Step 6 — Check: returning C = 10.2308 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

• 20.4615 — kept a factor of two that cancels in the correct rearrangement.
• 5.1154 — dropped that same factor in the other direction.
• 11.2538 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 11.0000 MGD; flow 2 (Q2) = 16.0000 MGD; concentration 2 (C2) = 14.0000 mg/L; blended concentration (C) = 6.8000 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) = 11.0000 MGD, flow 2 (Q2) = 16.0000 MGD, concentration 2 (C2) = 14.0000 mg/L, blended concentration (C) = 6.8000 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = -3.6727\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -3.6727 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

• -7.3455 — kept a factor of two that cancels in the correct rearrangement.
• -1.8364 — dropped that same factor in the other direction.
• -4.0400 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 17.5000 MGD; concentration 1 (C1) = 30.0000 mg/L; flow 2 (Q2) = 18.5000 MGD; concentration 2 (C2) = 42.5000 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) = 17.5000 MGD, concentration 1 (C1) = 30.0000 mg/L, flow 2 (Q2) = 18.5000 MGD, concentration 2 (C2) = 42.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 36.4236\ \text{mg/L}$$

6. Step 6 — Check: returning C = 36.4236 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

• 72.8472 — kept a factor of two that cancels in the correct rearrangement.
• 18.2118 — dropped that same factor in the other direction.
• 40.0660 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 5.5000 MGD; flow 2 (Q2) = 5.5000 MGD; concentration 2 (C2) = 33.5000 mg/L; blended concentration (C) = 13.4900 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) = 5.5000 MGD, flow 2 (Q2) = 5.5000 MGD, concentration 2 (C2) = 33.5000 mg/L, blended concentration (C) = 13.4900 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = -6.5200\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -6.5200 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

• -13.0400 — kept a factor of two that cancels in the correct rearrangement.
• -3.2600 — dropped that same factor in the other direction.
• -7.1720 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 10.5000 MGD; concentration 1 (C1) = 4.0000 mg/L; flow 2 (Q2) = 2.0000 MGD; concentration 2 (C2) = 7.5000 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) = 10.5000 MGD, concentration 1 (C1) = 4.0000 mg/L, flow 2 (Q2) = 2.0000 MGD, concentration 2 (C2) = 7.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 4.5600\ \text{mg/L}$$

6. Step 6 — Check: returning C = 4.5600 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

• 9.1200 — kept a factor of two that cancels in the correct rearrangement.
• 2.2800 — dropped that same factor in the other direction.
• 5.0160 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.0000 MGD; flow 2 (Q2) = 2.0000 MGD; concentration 2 (C2) = 31.5000 mg/L; blended concentration (C) = 32.8800 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) = 18.0000 MGD, flow 2 (Q2) = 2.0000 MGD, concentration 2 (C2) = 31.5000 mg/L, blended concentration (C) = 32.8800 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 33.0333\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 33.0333 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

• 66.0667 — kept a factor of two that cancels in the correct rearrangement.
• 16.5167 — dropped that same factor in the other direction.
• 36.3367 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 17.5000 MGD; concentration 1 (C1) = 41.5000 mg/L; flow 2 (Q2) = 1.5000 MGD; concentration 2 (C2) = 35.0000 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) = 17.5000 MGD, concentration 1 (C1) = 41.5000 mg/L, flow 2 (Q2) = 1.5000 MGD, concentration 2 (C2) = 35.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 40.9868\ \text{mg/L}$$

6. Step 6 — Check: returning C = 40.9868 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

• 81.9737 — kept a factor of two that cancels in the correct rearrangement.
• 20.4934 — dropped that same factor in the other direction.
• 45.0855 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 8.0000 MGD; flow 2 (Q2) = 20.0000 MGD; concentration 2 (C2) = 17.5000 mg/L; blended concentration (C) = 10.5000 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) = 8.0000 MGD, flow 2 (Q2) = 20.0000 MGD, concentration 2 (C2) = 17.5000 mg/L, blended concentration (C) = 10.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = -7.0000\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -7.0000 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

• -14.0000 — kept a factor of two that cancels in the correct rearrangement.
• -3.5000 — dropped that same factor in the other direction.
• -7.7000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Octanol-Water Partition Coefficient