A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 9.5000 MGD; concentration 1 (C1) = 32.0000 mg/L; flow 2 (Q2) = 11.5000 MGD; concentration 2 (C2) = 28.0000 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) = 9.5000 MGD, concentration 1 (C1) = 32.0000 mg/L, flow 2 (Q2) = 11.5000 MGD, concentration 2 (C2) = 28.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 29.8095\ \text{mg/L}$$

6. Step 6 — Check: returning C = 29.8095 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

• 59.6190 — kept a factor of two that cancels in the correct rearrangement.
• 14.9048 — dropped that same factor in the other direction.
• 32.7905 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Gas Flux

landfill gas and leachate generation estimate for a closed cell Given methane generation potential (L_0) = 150.0 m^3/Mg; waste acceptance rate (R) = 90,200 Mg/yr; methane generation rate constant (k) = 0.0390 1/yr; time since landfill closure (c) = 4.5000 yr; time since waste placement (t) = 34.0000 yr, determine the landfill gas generation rate (Q_gas) in m^3/yr.

Start with the thinking

• The governing relation printed in this handbook section is Landfill (gas/leachate).
• Everything except Q_gas is given, so isolate Q_gas 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.
• Landfill gas and leachate generation models estimate methane production and leachate flow from decomposing municipal solid waste.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

2. Step 2 — Rearrange symbolically for Q_gas:

   $$Q_{gas} = L_0\dfrac{R}{k}\left(e^{-kc}-e^{-kt}\right)$$

3. Step 3 — List the givens: methane generation potential (L_0) = 150.0 m^3/Mg, waste acceptance rate (R) = 90,200 Mg/yr, methane generation rate constant (k) = 0.0390 1/yr, time since landfill closure (c) = 4.5000 yr, time since waste placement (t) = 34.0000 yr.

4. Step 4 — Substitute the given values:

   $$Q_{gas} = L_0\dfrac{90200}{0.0390}\lef34.0000(e^{-k4.5000}-e^{-k34.0000}\righ34.0000)$$

5. Step 5 — Evaluate:

   Q_{gas} = 198960422\ \text{m^3/yr}

6. Step 6 — Check: returning Q_gas = 198,960,422 m^3/yr to

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 397,920,844 — kept a factor of two that cancels in the correct rearrangement.
• 99,480,211 — dropped that same factor in the other direction.
• 218,856,464 — rounded an intermediate value before the final step.

Reference: FE Handbook — Landfill Gas Generation

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.0000 MGD; flow 2 (Q2) = 18.5000 MGD; concentration 2 (C2) = 15.0000 mg/L; blended concentration (C) = 31.2800 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) = 18.5000 MGD, concentration 2 (C2) = 15.0000 mg/L, blended concentration (C) = 31.2800 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 48.0122\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 48.0122 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

• 96.0244 — kept a factor of two that cancels in the correct rearrangement.
• 24.0061 — dropped that same factor in the other direction.
• 52.8134 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Gas Flux

landfill gas collection system sizing based on generation rate Given methane generation potential (L_0) = 98.0000 m^3/Mg; methane generation rate constant (k) = 0.0980 1/yr; time since landfill closure (c) = 0.1000 yr; time since waste placement (t) = 22.5000 yr; landfill gas generation rate (Q_gas) = 46,461,834 m^3/yr, determine the waste acceptance rate (R) in Mg/yr.

Start with the thinking

• The governing relation printed in this handbook section is Landfill (gas/leachate).
• Everything except R is given, so isolate R 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.
• Landfill gas and leachate generation models estimate methane production and leachate flow from decomposing municipal solid waste.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

2. Step 2 — Rearrange symbolically for R:

   $$R = \dfrac{Q_{gas} k}{L_0\left(e^{-kc}-e^{-kt}\right)}$$

3. Step 3 — List the givens: methane generation potential (L_0) = 98.0000 m^3/Mg, methane generation rate constant (k) = 0.0980 1/yr, time since landfill closure (c) = 0.1000 yr, time since waste placement (t) = 22.5000 yr, landfill gas generation rate (Q_gas) = 46,461,834 m^3/yr.

4. Step 4 — Substitute the given values:

   $$R = \dfrac{46461834 0.0980}{L_0\lef22.5000(e^{-k0.1000}-e^{-k22.5000}\righ22.5000)}$$

5. Step 5 — Evaluate:

   $$R = 52798\ \text{Mg/yr}$$

6. Step 6 — Check: returning R = 52,798 Mg/yr to

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 105,595 — kept a factor of two that cancels in the correct rearrangement.
• 26,399 — dropped that same factor in the other direction.
• 58,077 — rounded an intermediate value before the final step.

Reference: FE Handbook — Landfill Gas Generation

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 18.0000 MGD; concentration 1 (C1) = 23.5000 mg/L; flow 2 (Q2) = 5.5000 MGD; concentration 2 (C2) = 41.0000 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) = 23.5000 mg/L, flow 2 (Q2) = 5.5000 MGD, concentration 2 (C2) = 41.0000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 27.5957\ \text{mg/L}$$

6. Step 6 — Check: returning C = 27.5957 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

• 55.1915 — kept a factor of two that cancels in the correct rearrangement.
• 13.7979 — dropped that same factor in the other direction.
• 30.3553 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Gas Flux

landfill gas generation model for a municipal solid waste landfill Given waste acceptance rate (R) = 14,500 Mg/yr; methane generation rate constant (k) = 0.0850 1/yr; time since landfill closure (c) = 0.6000 yr; time since waste placement (t) = 24.0000 yr; landfill gas generation rate (Q_gas) = 5,799,587 m^3/yr, determine the methane generation potential (L_0) in m^3/Mg.

Start with the thinking

• The governing relation printed in this handbook section is Landfill (gas/leachate).
• Everything except L_0 is given, so isolate L_0 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.
• Landfill gas and leachate generation models estimate methane production and leachate flow from decomposing municipal solid waste.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

2. Step 2 — Rearrange symbolically for L_0:

   $$L_{0} = \dfrac{Q_{gas} k}{R\left(e^{-kc}-e^{-kt}\right)}$$

3. Step 3 — List the givens: waste acceptance rate (R) = 14,500 Mg/yr, methane generation rate constant (k) = 0.0850 1/yr, time since landfill closure (c) = 0.6000 yr, time since waste placement (t) = 24.0000 yr, landfill gas generation rate (Q_gas) = 5,799,587 m^3/yr.

4. Step 4 — Substitute the given values:

   $$L_{0} = \dfrac{5799587 0.0850}{14500\lef24.0000(e^{-k0.6000}-e^{-k24.0000}\righ24.0000)}$$

5. Step 5 — Evaluate:

   L_{0} = 41.4478\ \text{m^3/Mg}

6. Step 6 — Check: returning L_0 = 41.4478 m^3/Mg to

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 82.8957 — kept a factor of two that cancels in the correct rearrangement.
• 20.7239 — dropped that same factor in the other direction.
• 45.5926 — rounded an intermediate value before the final step.

Reference: FE Handbook — Landfill Gas Generation

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 6.0000 MGD; flow 2 (Q2) = 8.5000 MGD; concentration 2 (C2) = 23.0000 mg/L; blended concentration (C) = 44.5400 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) = 6.0000 MGD, flow 2 (Q2) = 8.5000 MGD, concentration 2 (C2) = 23.0000 mg/L, blended concentration (C) = 44.5400 mg/L.

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

5. Step 5 — Evaluate:

   $$C_{1} = 75.0550\ \text{mg/L}$$

6. Step 6 — Check: returning C1 = 75.0550 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

• 150.1 — kept a factor of two that cancels in the correct rearrangement.
• 37.5275 — dropped that same factor in the other direction.
• 82.5605 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Gas Flux

landfill gas and leachate generation estimate for a closed cell Given methane generation potential (L_0) = 99.0000 m^3/Mg; waste acceptance rate (R) = 2,000 Mg/yr; methane generation rate constant (k) = 0.1180 1/yr; time since landfill closure (c) = 3.9000 yr; time since waste placement (t) = 34.5000 yr, determine the landfill gas generation rate (Q_gas) in m^3/yr.

Start with the thinking

• The governing relation printed in this handbook section is Landfill (gas/leachate).
• Everything except Q_gas is given, so isolate Q_gas 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.
• Landfill gas and leachate generation models estimate methane production and leachate flow from decomposing municipal solid waste.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

2. Step 2 — Rearrange symbolically for Q_gas:

   $$Q_{gas} = L_0\dfrac{R}{k}\left(e^{-kc}-e^{-kt}\right)$$

3. Step 3 — List the givens: methane generation potential (L_0) = 99.0000 m^3/Mg, waste acceptance rate (R) = 2,000 Mg/yr, methane generation rate constant (k) = 0.1180 1/yr, time since landfill closure (c) = 3.9000 yr, time since waste placement (t) = 34.5000 yr.

4. Step 4 — Substitute the given values:

   $$Q_{gas} = L_0\dfrac{2000}{0.1180}\lef34.5000(e^{-k3.9000}-e^{-k34.5000}\righ34.5000)$$

5. Step 5 — Evaluate:

   Q_{gas} = 1030434\ \text{m^3/yr}

6. Step 6 — Check: returning Q_gas = 1,030,434 m^3/yr to

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,060,868 — kept a factor of two that cancels in the correct rearrangement.
• 515,217 — dropped that same factor in the other direction.
• 1,133,477 — rounded an intermediate value before the final step.

Reference: FE Handbook — Landfill Gas Generation

A environmental engineering problem uses Steady-state mass balance. Given flow 1 (Q1) = 14.5000 MGD; concentration 1 (C1) = 48.5000 mg/L; flow 2 (Q2) = 19.0000 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) = 14.5000 MGD, concentration 1 (C1) = 48.5000 mg/L, flow 2 (Q2) = 19.0000 MGD, concentration 2 (C2) = 47.5000 mg/L.

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

5. Step 5 — Evaluate:

   $$C = 47.9328\ \text{mg/L}$$

6. Step 6 — Check: returning C = 47.9328 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

• 95.8657 — kept a factor of two that cancels in the correct rearrangement.
• 23.9664 — dropped that same factor in the other direction.
• 52.7261 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Gas Flux

landfill gas collection system sizing based on generation rate Given methane generation potential (L_0) = 134.0 m^3/Mg; methane generation rate constant (k) = 0.0300 1/yr; time since landfill closure (c) = 2.6000 yr; time since waste placement (t) = 20.0000 yr; landfill gas generation rate (Q_gas) = 26,716,531 m^3/yr, determine the waste acceptance rate (R) in Mg/yr.

Start with the thinking

• The governing relation printed in this handbook section is Landfill (gas/leachate).
• Everything except R is given, so isolate R 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.
• Landfill gas and leachate generation models estimate methane production and leachate flow from decomposing municipal solid waste.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

2. Step 2 — Rearrange symbolically for R:

   $$R = \dfrac{Q_{gas} k}{L_0\left(e^{-kc}-e^{-kt}\right)}$$

3. Step 3 — List the givens: methane generation potential (L_0) = 134.0 m^3/Mg, methane generation rate constant (k) = 0.0300 1/yr, time since landfill closure (c) = 2.6000 yr, time since waste placement (t) = 20.0000 yr, landfill gas generation rate (Q_gas) = 26,716,531 m^3/yr.

4. Step 4 — Substitute the given values:

   $$R = \dfrac{26716531 0.0300}{L_0\lef20.0000(e^{-k2.6000}-e^{-k20.0000}\righ20.0000)}$$

5. Step 5 — Evaluate:

   $$R = 15901\ \text{Mg/yr}$$

6. Step 6 — Check: returning R = 15,901 Mg/yr to

   $$Q_{gas} = L_0 \dfrac{R}{k}\left(e^{-kc} - e^{-kt}\right)$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 31,803 — kept a factor of two that cancels in the correct rearrangement.
• 7,951 — dropped that same factor in the other direction.
• 17,491 — rounded an intermediate value before the final step.

Reference: FE Handbook — Landfill Gas Generation