water flux across a reverse osmosis membrane in desalination Given membrane permeability coefficient (K_w) = 0.0081 m/day/kPa; applied pressure differential (deltaP) = 2,060 kPa; osmotic pressure differential (deltapi) = 1,110 kPa, determine the water flux (F_w) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except F_w is given, so isolate F_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for F_w:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0081 m/day/kPa, applied pressure differential (deltaP) = 2,060 kPa, osmotic pressure differential (deltapi) = 1,110 kPa.

4. Step 4 — Substitute the given values:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

5. Step 5 — Evaluate:

   $$F_{w} = 7.6950\ \text{m/day}$$

6. Step 6 — Check: returning F_w = 7.6950 m/day to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 15.3900 — kept a factor of two that cancels in the correct rearrangement.
• 3.8475 — dropped that same factor in the other direction.
• 8.4645 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux through the membrane driven by net applied pressure Given applied pressure differential (deltaP) = 1,020 kPa; osmotic pressure differential (deltapi) = 800.0 kPa; water flux (F_w) = 70.0500 m/day, determine the membrane permeability coefficient (K_w) in m/day/kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except K_w is given, so isolate K_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for K_w:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

3. Step 3 — List the givens: applied pressure differential (deltaP) = 1,020 kPa, osmotic pressure differential (deltapi) = 800.0 kPa, water flux (F_w) = 70.0500 m/day.

4. Step 4 — Substitute the given values:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

5. Step 5 — Evaluate:

   $$K_{w} = 0.3184\ \text{m/day/kPa}$$

6. Step 6 — Check: returning K_w = 0.3184 m/day/kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 0.6368 — kept a factor of two that cancels in the correct rearrangement.
• 0.1592 — dropped that same factor in the other direction.
• 0.3503 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux calculation for a membrane treatment system Given membrane permeability coefficient (K_w) = 0.0334 m/day/kPa; osmotic pressure differential (deltapi) = 350.0 kPa; water flux (F_w) = 76.2200 m/day, determine the applied pressure differential (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except deltaP is given, so isolate deltaP 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0334 m/day/kPa, osmotic pressure differential (deltapi) = 350.0 kPa, water flux (F_w) = 76.2200 m/day.

4. Step 4 — Substitute the given values:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

5. Step 5 — Evaluate:

   $$deltaP = 2632\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 2,632 kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 5,264 — kept a factor of two that cancels in the correct rearrangement.
• 1,316 — dropped that same factor in the other direction.
• 2,895 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux across a reverse osmosis membrane in desalination Given membrane permeability coefficient (K_w) = 0.0130 m/day/kPa; applied pressure differential (deltaP) = 1,050 kPa; osmotic pressure differential (deltapi) = 1,140 kPa, determine the water flux (F_w) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except F_w is given, so isolate F_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for F_w:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0130 m/day/kPa, applied pressure differential (deltaP) = 1,050 kPa, osmotic pressure differential (deltapi) = 1,140 kPa.

4. Step 4 — Substitute the given values:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

5. Step 5 — Evaluate:

   $$F_{w} = -1.1700\ \text{m/day}$$

6. Step 6 — Check: returning F_w = -1.1700 m/day to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• -2.3400 — kept a factor of two that cancels in the correct rearrangement.
• -0.5850 — dropped that same factor in the other direction.
• -1.2870 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux through the membrane driven by net applied pressure Given applied pressure differential (deltaP) = 3,890 kPa; osmotic pressure differential (deltapi) = 400.0 kPa; water flux (F_w) = 95.1500 m/day, determine the membrane permeability coefficient (K_w) in m/day/kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except K_w is given, so isolate K_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for K_w:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

3. Step 3 — List the givens: applied pressure differential (deltaP) = 3,890 kPa, osmotic pressure differential (deltapi) = 400.0 kPa, water flux (F_w) = 95.1500 m/day.

4. Step 4 — Substitute the given values:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

5. Step 5 — Evaluate:

   $$K_{w} = 0.0273\ \text{m/day/kPa}$$

6. Step 6 — Check: returning K_w = 0.0273 m/day/kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 0.0545 — kept a factor of two that cancels in the correct rearrangement.
• 0.0136 — dropped that same factor in the other direction.
• 0.0300 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux calculation for a membrane treatment system Given membrane permeability coefficient (K_w) = 0.0456 m/day/kPa; osmotic pressure differential (deltapi) = 370.0 kPa; water flux (F_w) = 56.8500 m/day, determine the applied pressure differential (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except deltaP is given, so isolate deltaP 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0456 m/day/kPa, osmotic pressure differential (deltapi) = 370.0 kPa, water flux (F_w) = 56.8500 m/day.

4. Step 4 — Substitute the given values:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

5. Step 5 — Evaluate:

   $$deltaP = 1617\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 1,617 kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 3,233 — kept a factor of two that cancels in the correct rearrangement.
• 808.4 — dropped that same factor in the other direction.
• 1,778 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux across a reverse osmosis membrane in desalination Given membrane permeability coefficient (K_w) = 0.0075 m/day/kPa; applied pressure differential (deltaP) = 2,800 kPa; osmotic pressure differential (deltapi) = 510.0 kPa, determine the water flux (F_w) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except F_w is given, so isolate F_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for F_w:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0075 m/day/kPa, applied pressure differential (deltaP) = 2,800 kPa, osmotic pressure differential (deltapi) = 510.0 kPa.

4. Step 4 — Substitute the given values:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

5. Step 5 — Evaluate:

   $$F_{w} = 17.1750\ \text{m/day}$$

6. Step 6 — Check: returning F_w = 17.1750 m/day to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 34.3500 — kept a factor of two that cancels in the correct rearrangement.
• 8.5875 — dropped that same factor in the other direction.
• 18.8925 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux through the membrane driven by net applied pressure Given applied pressure differential (deltaP) = 2,300 kPa; osmotic pressure differential (deltapi) = 1,260 kPa; water flux (F_w) = 31.3000 m/day, determine the membrane permeability coefficient (K_w) in m/day/kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except K_w is given, so isolate K_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for K_w:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

3. Step 3 — List the givens: applied pressure differential (deltaP) = 2,300 kPa, osmotic pressure differential (deltapi) = 1,260 kPa, water flux (F_w) = 31.3000 m/day.

4. Step 4 — Substitute the given values:

   $$K_{w} = \dfrac{F_w}{\Delta P-\Delta \pi}$$

5. Step 5 — Evaluate:

   $$K_{w} = 0.0301\ \text{m/day/kPa}$$

6. Step 6 — Check: returning K_w = 0.0301 m/day/kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 0.0602 — kept a factor of two that cancels in the correct rearrangement.
• 0.0150 — dropped that same factor in the other direction.
• 0.0331 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux calculation for a membrane treatment system Given membrane permeability coefficient (K_w) = 0.0492 m/day/kPa; osmotic pressure differential (deltapi) = 1,410 kPa; water flux (F_w) = 97.5400 m/day, determine the applied pressure differential (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except deltaP is given, so isolate deltaP 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0492 m/day/kPa, osmotic pressure differential (deltapi) = 1,410 kPa, water flux (F_w) = 97.5400 m/day.

4. Step 4 — Substitute the given values:

   $$deltaP = \dfrac{F_w}{K_w}+\Delta\pi$$

5. Step 5 — Evaluate:

   $$deltaP = 3393\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 3,393 kPa to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 6,785 — kept a factor of two that cancels in the correct rearrangement.
• 1,696 — dropped that same factor in the other direction.
• 3,732 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux

water flux across a reverse osmosis membrane in desalination Given membrane permeability coefficient (K_w) = 0.0374 m/day/kPa; applied pressure differential (deltaP) = 1,710 kPa; osmotic pressure differential (deltapi) = 1,120 kPa, determine the water flux (F_w) in m/day.

Start with the thinking

• The governing relation printed in this handbook section is Water Flux.
• Everything except F_w is given, so isolate F_w 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.
• Water flux across a reverse osmosis membrane is driven by the net pressure differential minus the osmotic pressure differential.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_w = K_w (\Delta P - \Delta \pi)$$

2. Step 2 — Rearrange symbolically for F_w:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

3. Step 3 — List the givens: membrane permeability coefficient (K_w) = 0.0374 m/day/kPa, applied pressure differential (deltaP) = 1,710 kPa, osmotic pressure differential (deltapi) = 1,120 kPa.

4. Step 4 — Substitute the given values:

   $$F_{w} = K_w(\Delta P-\Delta \pi)$$

5. Step 5 — Evaluate:

   $$F_{w} = 22.0660\ \text{m/day}$$

6. Step 6 — Check: returning F_w = 22.0660 m/day to

   $$F_w = K_w (\Delta P - \Delta \pi)$$

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

Why the other options are there

• 44.1320 — kept a factor of two that cancels in the correct rearrangement.
• 11.0330 — dropped that same factor in the other direction.
• 24.2726 — rounded an intermediate value before the final step.

Reference: FE Handbook — Water Flux