filtration equations used to size a rapid sand filter Given filtered flow rate (Q) = 99,010 m^3/day; filter area (A_f) = 372.0 m^2, determine the filtration rate (v_f) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except v_f is given, so isolate v_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for v_f:

   $$v_{f} = \dfrac{Q}{A_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 99,010 m^3/day, filter area (A_f) = 372.0 m^2.

4. Step 4 — Substitute the given values:

   $$v_{f} = \dfrac{99010}{A_f}$$

5. Step 5 — Evaluate:

   $$v_{f} = 266.2\ \text{m/day}$$

6. Step 6 — Check: returning v_f = 266.2 m/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

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

Reference: FE Handbook — Filtration Equations

filtration rate calculation for a granular media filter Given filter area (A_f) = 477.0 m^2; filtration rate (v_f) = 148.0 m/day, determine the filtered flow rate (Q) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = v_f A_f$$

3. Step 3

   $$List the givens: filter area (A_f) = 477.0 m^2, filtration rate (v_f) = 148.0 m/day$$

4. Step 4 — Substitute the given values:

   $$Q = v_f A_f$$

5. Step 5 — Evaluate:

   Q = 70596\ \text{m^3/day}

6. Step 6 — Check: returning Q = 70,596 m^3/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 141,192 — kept a factor of two that cancels in the correct rearrangement.
• 35,298 — dropped that same factor in the other direction.
• 77,656 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations

filtration equations applied to a water treatment plant filter bank Given filtered flow rate (Q) = 60,120 m^3/day; filtration rate (v_f) = 286.0 m/day, determine the filter area (A_f) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except A_f is given, so isolate A_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for A_f:

   $$A_{f} = \dfrac{Q}{v_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 60,120 m^3/day, filtration rate (v_f) = 286.0 m/day.

4. Step 4 — Substitute the given values:

   $$A_{f} = \dfrac{60120}{v_f}$$

5. Step 5 — Evaluate:

   A_{f} = 210.2\ \text{m^2}

6. Step 6 — Check: returning A_f = 210.2 m^2 to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

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

Reference: FE Handbook — Filtration Equations

filtration equations used to size a rapid sand filter Given filtered flow rate (Q) = 90,250 m^3/day; filter area (A_f) = 251.0 m^2, determine the filtration rate (v_f) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except v_f is given, so isolate v_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for v_f:

   $$v_{f} = \dfrac{Q}{A_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 90,250 m^3/day, filter area (A_f) = 251.0 m^2.

4. Step 4 — Substitute the given values:

   $$v_{f} = \dfrac{90250}{A_f}$$

5. Step 5 — Evaluate:

   $$v_{f} = 359.6\ \text{m/day}$$

6. Step 6 — Check: returning v_f = 359.6 m/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

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

Reference: FE Handbook — Filtration Equations

filtration rate calculation for a granular media filter Given filter area (A_f) = 330.0 m^2; filtration rate (v_f) = 73.0000 m/day, determine the filtered flow rate (Q) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = v_f A_f$$

3. Step 3

   $$List the givens: filter area (A_f) = 330.0 m^2, filtration rate (v_f) = 73.0000 m/day$$

4. Step 4 — Substitute the given values:

   $$Q = v_f A_f$$

5. Step 5 — Evaluate:

   Q = 24090\ \text{m^3/day}

6. Step 6 — Check: returning Q = 24,090 m^3/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 48,180 — kept a factor of two that cancels in the correct rearrangement.
• 12,045 — dropped that same factor in the other direction.
• 26,499 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations

filtration equations applied to a water treatment plant filter bank Given filtered flow rate (Q) = 29,260 m^3/day; filtration rate (v_f) = 245.0 m/day, determine the filter area (A_f) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except A_f is given, so isolate A_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for A_f:

   $$A_{f} = \dfrac{Q}{v_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 29,260 m^3/day, filtration rate (v_f) = 245.0 m/day.

4. Step 4 — Substitute the given values:

   $$A_{f} = \dfrac{29260}{v_f}$$

5. Step 5 — Evaluate:

   A_{f} = 119.4\ \text{m^2}

6. Step 6 — Check: returning A_f = 119.4 m^2 to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 238.9 — kept a factor of two that cancels in the correct rearrangement.
• 59.7143 — dropped that same factor in the other direction.
• 131.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations

filtration equations used to size a rapid sand filter Given filtered flow rate (Q) = 97,470 m^3/day; filter area (A_f) = 346.0 m^2, determine the filtration rate (v_f) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except v_f is given, so isolate v_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for v_f:

   $$v_{f} = \dfrac{Q}{A_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 97,470 m^3/day, filter area (A_f) = 346.0 m^2.

4. Step 4 — Substitute the given values:

   $$v_{f} = \dfrac{97470}{A_f}$$

5. Step 5 — Evaluate:

   $$v_{f} = 281.7\ \text{m/day}$$

6. Step 6 — Check: returning v_f = 281.7 m/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

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

Reference: FE Handbook — Filtration Equations

filtration rate calculation for a granular media filter Given filter area (A_f) = 489.0 m^2; filtration rate (v_f) = 127.0 m/day, determine the filtered flow rate (Q) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = v_f A_f$$

3. Step 3

   $$List the givens: filter area (A_f) = 489.0 m^2, filtration rate (v_f) = 127.0 m/day$$

4. Step 4 — Substitute the given values:

   $$Q = v_f A_f$$

5. Step 5 — Evaluate:

   Q = 62103\ \text{m^3/day}

6. Step 6 — Check: returning Q = 62,103 m^3/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 124,206 — kept a factor of two that cancels in the correct rearrangement.
• 31,052 — dropped that same factor in the other direction.
• 68,313 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations

filtration equations applied to a water treatment plant filter bank Given filtered flow rate (Q) = 70,690 m^3/day; filtration rate (v_f) = 105.0 m/day, determine the filter area (A_f) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except A_f is given, so isolate A_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for A_f:

   $$A_{f} = \dfrac{Q}{v_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 70,690 m^3/day, filtration rate (v_f) = 105.0 m/day.

4. Step 4 — Substitute the given values:

   $$A_{f} = \dfrac{70690}{v_f}$$

5. Step 5 — Evaluate:

   A_{f} = 673.2\ \text{m^2}

6. Step 6 — Check: returning A_f = 673.2 m^2 to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 1,346 — kept a factor of two that cancels in the correct rearrangement.
• 336.6 — dropped that same factor in the other direction.
• 740.6 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations

filtration equations used to size a rapid sand filter Given filtered flow rate (Q) = 15,590 m^3/day; filter area (A_f) = 132.0 m^2, determine the filtration rate (v_f) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Filtration Equations.
• Everything except v_f is given, so isolate v_f 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.
• Filtration equations relate filtration rate to plant flow rate and total filter surface area in a granular media filter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$v_f = \dfrac{Q}{A_f}$$

2. Step 2 — Rearrange symbolically for v_f:

   $$v_{f} = \dfrac{Q}{A_f}$$

3. Step 3 — List the givens: filtered flow rate (Q) = 15,590 m^3/day, filter area (A_f) = 132.0 m^2.

4. Step 4 — Substitute the given values:

   $$v_{f} = \dfrac{15590}{A_f}$$

5. Step 5 — Evaluate:

   $$v_{f} = 118.1\ \text{m/day}$$

6. Step 6 — Check: returning v_f = 118.1 m/day to

   $$v_f = \dfrac{Q}{A_f}$$

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

Why the other options are there

• 236.2 — kept a factor of two that cancels in the correct rearrangement.
• 59.0530 — dropped that same factor in the other direction.
• 129.9 — rounded an intermediate value before the final step.

Reference: FE Handbook — Filtration Equations