vadose zone penetration time for a spill migrating to groundwater Given depth to water table (d) = 26.5000 m; field capacity (FC) = 0.3900; infiltration rate (I) = 0.0250 m/day, determine the time to reach water table (t) in day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except t is given, so isolate t 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for t:

   $$t = \dfrac{d\,FC}{I}$$

3. Step 3 — List the givens: depth to water table (d) = 26.5000 m, field capacity (FC) = 0.3900, infiltration rate (I) = 0.0250 m/day.

4. Step 4 — Substitute the given values:

   $$t = \dfrac{26.5000\,0.3900}{0.0250}$$

5. Step 5 — Evaluate:

   $$t = 413.4\ \text{day}$$

6. Step 6 — Check: returning t = 413.4 day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

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

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration estimate given field capacity and infiltration rate Given field capacity (FC) = 0.1600; infiltration rate (I) = 0.0300 m/day; time to reach water table (t) = 4,455 day, determine the depth to water table (d) in m.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except d is given, so isolate d 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for d:

   $$d = \dfrac{tI}{FC}$$

3. Step 3 — List the givens: field capacity (FC) = 0.1600, infiltration rate (I) = 0.0300 m/day, time to reach water table (t) = 4,455 day.

4. Step 4 — Substitute the given values:

   $$d = \dfrac{44550.0300}{0.1600}$$

5. Step 5 — Evaluate:

   $$d = 835.3\ \text{m}$$

6. Step 6 — Check: returning d = 835.3 m to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 1,671 — kept a factor of two that cancels in the correct rearrangement.
• 417.7 — dropped that same factor in the other direction.
• 918.8 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration analysis above the water table Given depth to water table (d) = 18.5000 m; field capacity (FC) = 0.1800; time to reach water table (t) = 4,275 day, determine the infiltration rate (I) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except I is given, so isolate I 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for I:

   $$I = \dfrac{d\,FC}{t}$$

3. Step 3 — List the givens: depth to water table (d) = 18.5000 m, field capacity (FC) = 0.1800, time to reach water table (t) = 4,275 day.

4. Step 4 — Substitute the given values:

   $$I = \dfrac{18.5000\,0.1800}{4275}$$

5. Step 5 — Evaluate:

   $$I = 0.0008\ \text{m/day}$$

6. Step 6 — Check: returning I = 0.0008 m/day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 0.0016 — kept a factor of two that cancels in the correct rearrangement.
• 0.0004 — dropped that same factor in the other direction.
• 0.0009 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration time for a spill migrating to groundwater Given depth to water table (d) = 24.5000 m; field capacity (FC) = 0.1500; infiltration rate (I) = 0.0030 m/day, determine the time to reach water table (t) in day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except t is given, so isolate t 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for t:

   $$t = \dfrac{d\,FC}{I}$$

3. Step 3 — List the givens: depth to water table (d) = 24.5000 m, field capacity (FC) = 0.1500, infiltration rate (I) = 0.0030 m/day.

4. Step 4 — Substitute the given values:

   $$t = \dfrac{24.5000\,0.1500}{0.0030}$$

5. Step 5 — Evaluate:

   $$t = 1225\ \text{day}$$

6. Step 6 — Check: returning t = 1,225 day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 2,450 — kept a factor of two that cancels in the correct rearrangement.
• 612.5 — dropped that same factor in the other direction.
• 1,348 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration estimate given field capacity and infiltration rate Given field capacity (FC) = 0.3600; infiltration rate (I) = 0.0540 m/day; time to reach water table (t) = 225.0 day, determine the depth to water table (d) in m.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except d is given, so isolate d 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for d:

   $$d = \dfrac{tI}{FC}$$

3. Step 3 — List the givens: field capacity (FC) = 0.3600, infiltration rate (I) = 0.0540 m/day, time to reach water table (t) = 225.0 day.

4. Step 4 — Substitute the given values:

   $$d = \dfrac{225.00.0540}{0.3600}$$

5. Step 5 — Evaluate:

   $$d = 33.7500\ \text{m}$$

6. Step 6 — Check: returning d = 33.7500 m to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 67.5000 — kept a factor of two that cancels in the correct rearrangement.
• 16.8750 — dropped that same factor in the other direction.
• 37.1250 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration analysis above the water table Given depth to water table (d) = 9.5000 m; field capacity (FC) = 0.4000; time to reach water table (t) = 1,971 day, determine the infiltration rate (I) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except I is given, so isolate I 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for I:

   $$I = \dfrac{d\,FC}{t}$$

3. Step 3 — List the givens: depth to water table (d) = 9.5000 m, field capacity (FC) = 0.4000, time to reach water table (t) = 1,971 day.

4. Step 4 — Substitute the given values:

   $$I = \dfrac{9.5000\,0.4000}{1971}$$

5. Step 5 — Evaluate:

   $$I = 0.0019\ \text{m/day}$$

6. Step 6 — Check: returning I = 0.0019 m/day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 0.0039 — kept a factor of two that cancels in the correct rearrangement.
• 0.0010 — dropped that same factor in the other direction.
• 0.0021 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration time for a spill migrating to groundwater Given depth to water table (d) = 24.5000 m; field capacity (FC) = 0.1700; infiltration rate (I) = 0.0050 m/day, determine the time to reach water table (t) in day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except t is given, so isolate t 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for t:

   $$t = \dfrac{d\,FC}{I}$$

3. Step 3 — List the givens: depth to water table (d) = 24.5000 m, field capacity (FC) = 0.1700, infiltration rate (I) = 0.0050 m/day.

4. Step 4 — Substitute the given values:

   $$t = \dfrac{24.5000\,0.1700}{0.0050}$$

5. Step 5 — Evaluate:

   $$t = 833.0\ \text{day}$$

6. Step 6 — Check: returning t = 833.0 day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 1,666 — kept a factor of two that cancels in the correct rearrangement.
• 416.5 — dropped that same factor in the other direction.
• 916.3 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration estimate given field capacity and infiltration rate Given field capacity (FC) = 0.2200; infiltration rate (I) = 0.0700 m/day; time to reach water table (t) = 4,253 day, determine the depth to water table (d) in m.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except d is given, so isolate d 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for d:

   $$d = \dfrac{tI}{FC}$$

3. Step 3 — List the givens: field capacity (FC) = 0.2200, infiltration rate (I) = 0.0700 m/day, time to reach water table (t) = 4,253 day.

4. Step 4 — Substitute the given values:

   $$d = \dfrac{42530.0700}{0.2200}$$

5. Step 5 — Evaluate:

   $$d = 1353\ \text{m}$$

6. Step 6 — Check: returning d = 1,353 m to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 2,706 — kept a factor of two that cancels in the correct rearrangement.
• 676.6 — dropped that same factor in the other direction.
• 1,489 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration analysis above the water table Given depth to water table (d) = 13.5000 m; field capacity (FC) = 0.2000; time to reach water table (t) = 63.0000 day, determine the infiltration rate (I) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except I is given, so isolate I 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for I:

   $$I = \dfrac{d\,FC}{t}$$

3. Step 3 — List the givens: depth to water table (d) = 13.5000 m, field capacity (FC) = 0.2000, time to reach water table (t) = 63.0000 day.

4. Step 4 — Substitute the given values:

   $$I = \dfrac{13.5000\,0.2000}{63.0000}$$

5. Step 5 — Evaluate:

   $$I = 0.0429\ \text{m/day}$$

6. Step 6 — Check: returning I = 0.0429 m/day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 0.0857 — kept a factor of two that cancels in the correct rearrangement.
• 0.0214 — dropped that same factor in the other direction.
• 0.0471 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration

vadose zone penetration time for a spill migrating to groundwater Given depth to water table (d) = 4.0000 m; field capacity (FC) = 0.3700; infiltration rate (I) = 0.0840 m/day, determine the time to reach water table (t) in day.

Start with the thinking

• The governing relation printed in this handbook section is Vadose Zone Penetration.
• Everything except t is given, so isolate t 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.
• Vadose zone penetration estimates travel time for an infiltrating contaminant to move through the unsaturated zone to the water table.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$t = \dfrac{d \times FC}{I}$$

2. Step 2 — Rearrange symbolically for t:

   $$t = \dfrac{d\,FC}{I}$$

3. Step 3 — List the givens: depth to water table (d) = 4.0000 m, field capacity (FC) = 0.3700, infiltration rate (I) = 0.0840 m/day.

4. Step 4 — Substitute the given values:

   $$t = \dfrac{4.0000\,0.3700}{0.0840}$$

5. Step 5 — Evaluate:

   $$t = 17.6190\ \text{day}$$

6. Step 6 — Check: returning t = 17.6190 day to

   $$t = \dfrac{d \times FC}{I}$$

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

Why the other options are there

• 35.2381 — kept a factor of two that cancels in the correct rearrangement.
• 8.8095 — dropped that same factor in the other direction.
• 19.3810 — rounded an intermediate value before the final step.

Reference: FE Handbook — Vadose Zone Penetration