A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 956,000 gal; flow rate (Q) = 4,907,000 gal/day, determine the detention time (theta) in day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except theta is given, so isolate theta 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 956,000 gal, flow rate (Q) = 4,907,000 gal/day$$

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

5. Step 5 — Evaluate:

   $$\theta = 0.1948\ \text{day}$$

6. Step 6 — Check: returning theta = 0.1948 day to

   $$\theta = V / Q$$

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

Why the other options are there

• 0.3896 — kept a factor of two that cancels in the correct rearrangement.
• 0.0974 — dropped that same factor in the other direction.
• 0.2143 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given flow rate (Q) = 3,129,000 gal/day; detention time (theta) = 2.7900 day, determine the tank volume (V) in gal.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except V is given, so isolate V 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow rate (Q) = 3,129,000 gal/day, detention time (theta) = 2.7900 day$$

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

5. Step 5 — Evaluate:

   $$V = 8729910\ \text{gal}$$

6. Step 6 — Check: returning V = 8,729,910 gal to

   $$\theta = V / Q$$

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

Why the other options are there

• 17,459,820 — kept a factor of two that cancels in the correct rearrangement.
• 4,364,955 — dropped that same factor in the other direction.
• 9,602,901 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 823,000 gal; detention time (theta) = 0.3300 day, determine the flow rate (Q) in gal/day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except Q is given, so isolate Q 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 823,000 gal, detention time (theta) = 0.3300 day$$

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

5. Step 5 — Evaluate:

   $$Q = 2493939\ \text{gal/day}$$

6. Step 6 — Check: returning Q = 2,493,939 gal/day to

   $$\theta = V / Q$$

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

Why the other options are there

• 4,987,879 — kept a factor of two that cancels in the correct rearrangement.
• 1,246,970 — dropped that same factor in the other direction.
• 2,743,333 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 495,000 gal; flow rate (Q) = 4,481,000 gal/day, determine the detention time (theta) in day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except theta is given, so isolate theta 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 495,000 gal, flow rate (Q) = 4,481,000 gal/day$$

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

5. Step 5 — Evaluate:

   $$\theta = 0.1105\ \text{day}$$

6. Step 6 — Check: returning theta = 0.1105 day to

   $$\theta = V / Q$$

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

Why the other options are there

• 0.2209 — kept a factor of two that cancels in the correct rearrangement.
• 0.0552 — dropped that same factor in the other direction.
• 0.1215 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given flow rate (Q) = 1,928,000 gal/day; detention time (theta) = 6.6900 day, determine the tank volume (V) in gal.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except V is given, so isolate V 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow rate (Q) = 1,928,000 gal/day, detention time (theta) = 6.6900 day$$

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

5. Step 5 — Evaluate:

   $$V = 12898320\ \text{gal}$$

6. Step 6 — Check: returning V = 12,898,320 gal to

   $$\theta = V / Q$$

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

Why the other options are there

• 25,796,640 — kept a factor of two that cancels in the correct rearrangement.
• 6,449,160 — dropped that same factor in the other direction.
• 14,188,152 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 1,091,000 gal; detention time (theta) = 1.5100 day, determine the flow rate (Q) in gal/day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except Q is given, so isolate Q 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 1,091,000 gal, detention time (theta) = 1.5100 day$$

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

5. Step 5 — Evaluate:

   $$Q = 722517\ \text{gal/day}$$

6. Step 6 — Check: returning Q = 722,517 gal/day to

   $$\theta = V / Q$$

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

Why the other options are there

• 1,445,033 — kept a factor of two that cancels in the correct rearrangement.
• 361,258 — dropped that same factor in the other direction.
• 794,768 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 1,025,000 gal; flow rate (Q) = 2,557,000 gal/day, determine the detention time (theta) in day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except theta is given, so isolate theta 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 1,025,000 gal, flow rate (Q) = 2,557,000 gal/day$$

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

5. Step 5 — Evaluate:

   $$\theta = 0.4009\ \text{day}$$

6. Step 6 — Check: returning theta = 0.4009 day to

   $$\theta = V / Q$$

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

Why the other options are there

• 0.8017 — kept a factor of two that cancels in the correct rearrangement.
• 0.2004 — dropped that same factor in the other direction.
• 0.4409 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given flow rate (Q) = 2,283,000 gal/day; detention time (theta) = 7.3300 day, determine the tank volume (V) in gal.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except V is given, so isolate V 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

3. Step 3

   $$List the givens: flow rate (Q) = 2,283,000 gal/day, detention time (theta) = 7.3300 day$$

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

5. Step 5 — Evaluate:

   $$V = 16734390\ \text{gal}$$

6. Step 6 — Check: returning V = 16,734,390 gal to

   $$\theta = V / Q$$

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

Why the other options are there

• 33,468,780 — kept a factor of two that cancels in the correct rearrangement.
• 8,367,195 — dropped that same factor in the other direction.
• 18,407,829 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 373,000 gal; detention time (theta) = 6.1200 day, determine the flow rate (Q) in gal/day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except Q is given, so isolate Q 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 373,000 gal, detention time (theta) = 6.1200 day$$

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

5. Step 5 — Evaluate:

   $$Q = 60948\ \text{gal/day}$$

6. Step 6 — Check: returning Q = 60,948 gal/day to

   $$\theta = V / Q$$

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

Why the other options are there

• 121,895 — kept a factor of two that cancels in the correct rearrangement.
• 30,474 — dropped that same factor in the other direction.
• 67,042 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate

A environmental engineering problem uses Hydraulic detention time. Given tank volume (V) = 1,484,000 gal; flow rate (Q) = 4,365,000 gal/day, determine the detention time (theta) in day.

Start with the thinking

• The governing relation printed in this handbook section is Hydraulic detention time.
• Everything except theta is given, so isolate theta 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:

   $$\theta = V / Q$$

2. Step 2 — Rearrange the relation so that theta stands alone on the left-hand side.

3. Step 3

   $$List the givens: tank volume (V) = 1,484,000 gal, flow rate (Q) = 4,365,000 gal/day$$

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

5. Step 5 — Evaluate:

   $$\theta = 0.3400\ \text{day}$$

6. Step 6 — Check: returning theta = 0.3400 day to

   $$\theta = V / Q$$

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

Why the other options are there

• 0.6800 — kept a factor of two that cancels in the correct rearrangement.
• 0.1700 — dropped that same factor in the other direction.
• 0.3740 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Environmental Engineering → Standard Rate