A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 16.5000 MGD; concentration 1 (C1) = 5.0000 mg/L; flow 2 (Q2) = 7.0000 MGD; concentration 2 (C2) = 43.5000 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) = 5.0000 mg/L, flow 2 (Q2) = 7.0000 MGD, concentration 2 (C2) = 43.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 16.4681\ \text{mg/L}$$

6. Step 6 — Check: returning C = 16.4681 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

• 32.9362 — kept a factor of two that cancels in the correct rearrangement.
• 8.2340 — dropped that same factor in the other direction.
• 18.1149 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 16.0000 MGD; flow 2 (Q2) = 13.0000 MGD; concentration 2 (C2) = 49.5000 mg/L; blended concentration (C) = 22.5000 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) = 16.0000 MGD, flow 2 (Q2) = 13.0000 MGD, concentration 2 (C2) = 49.5000 mg/L, blended concentration (C) = 22.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 0.5625\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 0.5625 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

• 1.1250 — kept a factor of two that cancels in the correct rearrangement.
• 0.2813 — dropped that same factor in the other direction.
• 0.6188 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 15.5000 MGD; concentration 1 (C1) = 46.5000 mg/L; flow 2 (Q2) = 2.0000 MGD; concentration 2 (C2) = 34.0000 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) = 15.5000 MGD, concentration 1 (C1) = 46.5000 mg/L, flow 2 (Q2) = 2.0000 MGD, concentration 2 (C2) = 34.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 45.0714\ \text{mg/L}$$

6. Step 6 — Check: returning C = 45.0714 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

• 90.1429 — kept a factor of two that cancels in the correct rearrangement.
• 22.5357 — dropped that same factor in the other direction.
• 49.5786 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.0000 MGD; flow 2 (Q2) = 3.5000 MGD; concentration 2 (C2) = 18.0000 mg/L; blended concentration (C) = 29.7800 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) = 3.5000 MGD, concentration 2 (C2) = 18.0000 mg/L, blended concentration (C) = 29.7800 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 32.7250\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 32.7250 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

• 65.4500 — kept a factor of two that cancels in the correct rearrangement.
• 16.3625 — dropped that same factor in the other direction.
• 35.9975 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.5000 MGD; concentration 1 (C1) = 29.0000 mg/L; flow 2 (Q2) = 3.0000 MGD; concentration 2 (C2) = 42.0000 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) = 29.0000 mg/L, flow 2 (Q2) = 3.0000 MGD, concentration 2 (C2) = 42.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 31.3636\ \text{mg/L}$$

6. Step 6 — Check: returning C = 31.3636 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

• 62.7273 — kept a factor of two that cancels in the correct rearrangement.
• 15.6818 — dropped that same factor in the other direction.
• 34.5000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 19.5000 MGD; flow 2 (Q2) = 3.5000 MGD; concentration 2 (C2) = 19.5000 mg/L; blended concentration (C) = 32.4400 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) = 19.5000 MGD, flow 2 (Q2) = 3.5000 MGD, concentration 2 (C2) = 19.5000 mg/L, blended concentration (C) = 32.4400 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 34.7626\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 34.7626 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

• 69.5251 — kept a factor of two that cancels in the correct rearrangement.
• 17.3813 — dropped that same factor in the other direction.
• 38.2388 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 19.0000 MGD; concentration 1 (C1) = 18.5000 mg/L; flow 2 (Q2) = 18.5000 MGD; concentration 2 (C2) = 2.0000 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) = 19.0000 MGD, concentration 1 (C1) = 18.5000 mg/L, flow 2 (Q2) = 18.5000 MGD, concentration 2 (C2) = 2.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 10.3600\ \text{mg/L}$$

6. Step 6 — Check: returning C = 10.3600 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

• 20.7200 — kept a factor of two that cancels in the correct rearrangement.
• 5.1800 — dropped that same factor in the other direction.
• 11.3960 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.0000 MGD; flow 2 (Q2) = 8.0000 MGD; concentration 2 (C2) = 7.0000 mg/L; blended concentration (C) = 38.8700 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) = 8.0000 MGD, concentration 2 (C2) = 7.0000 mg/L, blended concentration (C) = 38.8700 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 67.1989\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 67.1989 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

• 134.4 — kept a factor of two that cancels in the correct rearrangement.
• 33.5994 — dropped that same factor in the other direction.
• 73.9188 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.0000 MGD; concentration 1 (C1) = 41.0000 mg/L; flow 2 (Q2) = 4.0000 MGD; concentration 2 (C2) = 23.0000 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) = 18.0000 MGD, concentration 1 (C1) = 41.0000 mg/L, flow 2 (Q2) = 4.0000 MGD, concentration 2 (C2) = 23.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 37.7273\ \text{mg/L}$$

6. Step 6 — Check: returning C = 37.7273 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

• 75.4545 — kept a factor of two that cancels in the correct rearrangement.
• 18.8636 — dropped that same factor in the other direction.
• 41.5000 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.0000 MGD; flow 2 (Q2) = 4.0000 MGD; concentration 2 (C2) = 40.5000 mg/L; blended concentration (C) = 40.6500 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) = 4.0000 MGD, concentration 2 (C2) = 40.5000 mg/L, blended concentration (C) = 40.6500 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 40.7167\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 40.7167 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

• 81.4333 — kept a factor of two that cancels in the correct rearrangement.
• 20.3583 — dropped that same factor in the other direction.
• 44.7883 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Percent of Outdoor Air