A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.0000 MGD; concentration 1 (C1) = 49.0000 mg/L; flow 2 (Q2) = 9.5000 MGD; concentration 2 (C2) = 17.0000 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) = 14.0000 MGD, concentration 1 (C1) = 49.0000 mg/L, flow 2 (Q2) = 9.5000 MGD, concentration 2 (C2) = 17.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 36.0638\ \text{mg/L}$$

6. Step 6 — Check: returning C = 36.0638 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

• 72.1277 — kept a factor of two that cancels in the correct rearrangement.
• 18.0319 — dropped that same factor in the other direction.
• 39.6702 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 2.0000 MGD; flow 2 (Q2) = 9.0000 MGD; concentration 2 (C2) = 40.5000 mg/L; blended concentration (C) = 27.6500 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) = 2.0000 MGD, flow 2 (Q2) = 9.0000 MGD, concentration 2 (C2) = 40.5000 mg/L, blended concentration (C) = 27.6500 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = -30.1750\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = -30.1750 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

• -60.3500 — kept a factor of two that cancels in the correct rearrangement.
• -15.0875 — dropped that same factor in the other direction.
• -33.1925 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 11.0000 MGD; concentration 1 (C1) = 22.0000 mg/L; flow 2 (Q2) = 6.0000 MGD; concentration 2 (C2) = 37.0000 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) = 11.0000 MGD, concentration 1 (C1) = 22.0000 mg/L, flow 2 (Q2) = 6.0000 MGD, concentration 2 (C2) = 37.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 27.2941\ \text{mg/L}$$

6. Step 6 — Check: returning C = 27.2941 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

• 54.5882 — kept a factor of two that cancels in the correct rearrangement.
• 13.6471 — dropped that same factor in the other direction.
• 30.0235 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 15.5000 MGD; flow 2 (Q2) = 1.5000 MGD; concentration 2 (C2) = 35.5000 mg/L; blended concentration (C) = 12.9500 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) = 15.5000 MGD, flow 2 (Q2) = 1.5000 MGD, concentration 2 (C2) = 35.5000 mg/L, blended concentration (C) = 12.9500 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 10.7677\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 10.7677 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

• 21.5355 — kept a factor of two that cancels in the correct rearrangement.
• 5.3839 — dropped that same factor in the other direction.
• 11.8445 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 8.0000 MGD; concentration 1 (C1) = 39.5000 mg/L; flow 2 (Q2) = 16.5000 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) = 8.0000 MGD, concentration 1 (C1) = 39.5000 mg/L, flow 2 (Q2) = 16.5000 MGD, concentration 2 (C2) = 47.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 44.8878\ \text{mg/L}$$

6. Step 6 — Check: returning C = 44.8878 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

• 89.7755 — kept a factor of two that cancels in the correct rearrangement.
• 22.4439 — dropped that same factor in the other direction.
• 49.3765 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 20.0000 MGD; flow 2 (Q2) = 17.5000 MGD; concentration 2 (C2) = 22.0000 mg/L; blended concentration (C) = 29.8300 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) = 20.0000 MGD, flow 2 (Q2) = 17.5000 MGD, concentration 2 (C2) = 22.0000 mg/L, blended concentration (C) = 29.8300 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 36.6813\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 36.6813 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

• 73.3625 — kept a factor of two that cancels in the correct rearrangement.
• 18.3406 — dropped that same factor in the other direction.
• 40.3494 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 4.0000 MGD; concentration 1 (C1) = 42.0000 mg/L; flow 2 (Q2) = 4.0000 MGD; concentration 2 (C2) = 49.5000 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) = 4.0000 MGD, concentration 1 (C1) = 42.0000 mg/L, flow 2 (Q2) = 4.0000 MGD, concentration 2 (C2) = 49.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 45.7500\ \text{mg/L}$$

6. Step 6 — Check: returning C = 45.7500 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

• 91.5000 — kept a factor of two that cancels in the correct rearrangement.
• 22.8750 — dropped that same factor in the other direction.
• 50.3250 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 3.5000 MGD; flow 2 (Q2) = 6.5000 MGD; concentration 2 (C2) = 30.0000 mg/L; blended concentration (C) = 37.2900 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) = 3.5000 MGD, flow 2 (Q2) = 6.5000 MGD, concentration 2 (C2) = 30.0000 mg/L, blended concentration (C) = 37.2900 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 50.8286\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 50.8286 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

• 101.7 — kept a factor of two that cancels in the correct rearrangement.
• 25.4143 — dropped that same factor in the other direction.
• 55.9114 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.5000 MGD; concentration 1 (C1) = 12.0000 mg/L; flow 2 (Q2) = 3.0000 MGD; concentration 2 (C2) = 37.5000 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) = 18.5000 MGD, concentration 1 (C1) = 12.0000 mg/L, flow 2 (Q2) = 3.0000 MGD, concentration 2 (C2) = 37.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 15.5581\ \text{mg/L}$$

6. Step 6 — Check: returning C = 15.5581 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

• 31.1163 — kept a factor of two that cancels in the correct rearrangement.
• 7.7791 — dropped that same factor in the other direction.
• 17.1140 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 4.5000 MGD; flow 2 (Q2) = 5.5000 MGD; concentration 2 (C2) = 8.0000 mg/L; blended concentration (C) = 46.0600 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) = 4.5000 MGD, flow 2 (Q2) = 5.5000 MGD, concentration 2 (C2) = 8.0000 mg/L, blended concentration (C) = 46.0600 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 92.5778\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 92.5778 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

• 185.2 — kept a factor of two that cancels in the correct rearrangement.
• 46.2889 — dropped that same factor in the other direction.
• 101.8 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Outdoor Air Changes per Hour