A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 1.0000 MGD; concentration 1 (C1) = 32.0000 mg/L; flow 2 (Q2) = 9.0000 MGD; concentration 2 (C2) = 44.5000 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) = 1.0000 MGD, concentration 1 (C1) = 32.0000 mg/L, flow 2 (Q2) = 9.0000 MGD, concentration 2 (C2) = 44.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 43.2500\ \text{mg/L}$$

6. Step 6 — Check: returning C = 43.2500 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

• 86.5000 — kept a factor of two that cancels in the correct rearrangement.
• 21.6250 — dropped that same factor in the other direction.
• 47.5750 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 12.5000 MGD; flow 2 (Q2) = 11.0000 MGD; concentration 2 (C2) = 27.0000 mg/L; blended concentration (C) = 19.9600 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) = 11.0000 MGD, concentration 2 (C2) = 27.0000 mg/L, blended concentration (C) = 19.9600 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 13.7648\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 13.7648 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

• 27.5296 — kept a factor of two that cancels in the correct rearrangement.
• 6.8824 — dropped that same factor in the other direction.
• 15.1413 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 16.5000 MGD; concentration 1 (C1) = 46.0000 mg/L; flow 2 (Q2) = 14.0000 MGD; concentration 2 (C2) = 9.0000 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) = 46.0000 mg/L, flow 2 (Q2) = 14.0000 MGD, concentration 2 (C2) = 9.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 29.0164\ \text{mg/L}$$

6. Step 6 — Check: returning C = 29.0164 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

• 58.0328 — kept a factor of two that cancels in the correct rearrangement.
• 14.5082 — dropped that same factor in the other direction.
• 31.9180 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 20.0000 MGD; flow 2 (Q2) = 1.0000 MGD; concentration 2 (C2) = 6.0000 mg/L; blended concentration (C) = 25.2900 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) = 20.0000 MGD, flow 2 (Q2) = 1.0000 MGD, concentration 2 (C2) = 6.0000 mg/L, blended concentration (C) = 25.2900 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 26.2545\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 26.2545 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

• 52.5090 — kept a factor of two that cancels in the correct rearrangement.
• 13.1273 — dropped that same factor in the other direction.
• 28.8800 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.5000 MGD; concentration 1 (C1) = 43.5000 mg/L; flow 2 (Q2) = 15.5000 MGD; concentration 2 (C2) = 35.5000 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) = 9.5000 MGD, concentration 1 (C1) = 43.5000 mg/L, flow 2 (Q2) = 15.5000 MGD, concentration 2 (C2) = 35.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 38.5400\ \text{mg/L}$$

6. Step 6 — Check: returning C = 38.5400 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

• 77.0800 — kept a factor of two that cancels in the correct rearrangement.
• 19.2700 — dropped that same factor in the other direction.
• 42.3940 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 3.0000 MGD; flow 2 (Q2) = 7.0000 MGD; concentration 2 (C2) = 41.5000 mg/L; blended concentration (C) = 34.8900 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) = 3.0000 MGD, flow 2 (Q2) = 7.0000 MGD, concentration 2 (C2) = 41.5000 mg/L, blended concentration (C) = 34.8900 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 19.4667\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 19.4667 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

• 38.9333 — kept a factor of two that cancels in the correct rearrangement.
• 9.7333 — dropped that same factor in the other direction.
• 21.4133 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.5000 MGD; concentration 1 (C1) = 12.5000 mg/L; flow 2 (Q2) = 10.0000 MGD; concentration 2 (C2) = 44.0000 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) = 12.5000 mg/L, flow 2 (Q2) = 10.0000 MGD, concentration 2 (C2) = 44.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 25.9043\ \text{mg/L}$$

6. Step 6 — Check: returning C = 25.9043 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

• 51.8085 — kept a factor of two that cancels in the correct rearrangement.
• 12.9521 — dropped that same factor in the other direction.
• 28.4947 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 7.0000 MGD; flow 2 (Q2) = 3.0000 MGD; concentration 2 (C2) = 44.5000 mg/L; blended concentration (C) = 26.3300 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) = 7.0000 MGD, flow 2 (Q2) = 3.0000 MGD, concentration 2 (C2) = 44.5000 mg/L, blended concentration (C) = 26.3300 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 18.5429\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 18.5429 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

• 37.0857 — kept a factor of two that cancels in the correct rearrangement.
• 9.2714 — dropped that same factor in the other direction.
• 20.3971 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 13.5000 MGD; concentration 1 (C1) = 38.0000 mg/L; flow 2 (Q2) = 9.0000 MGD; concentration 2 (C2) = 20.0000 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) = 38.0000 mg/L, flow 2 (Q2) = 9.0000 MGD, concentration 2 (C2) = 20.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 30.8000\ \text{mg/L}$$

6. Step 6 — Check: returning C = 30.8000 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

• 61.6000 — kept a factor of two that cancels in the correct rearrangement.
• 15.4000 — dropped that same factor in the other direction.
• 33.8800 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 4.5000 MGD; flow 2 (Q2) = 12.0000 MGD; concentration 2 (C2) = 39.5000 mg/L; blended concentration (C) = 49.8700 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) = 4.5000 MGD, flow 2 (Q2) = 12.0000 MGD, concentration 2 (C2) = 39.5000 mg/L, blended concentration (C) = 49.8700 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 77.5233\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 77.5233 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

• 155.0 — kept a factor of two that cancels in the correct rearrangement.
• 38.7617 — dropped that same factor in the other direction.
• 85.2757 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Bioconcentration Factor BCF