ultrafiltration membrane permeate flux for drinking water treatment Given transmembrane pressure (deltaP) = 57.0000 kPa; dynamic viscosity (mu) = 0.0011 Pa*s; membrane resistance (R_m) = 910,000,000,000 1/m, determine the ultrafiltration permeate flux (J_w) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except J_w is given, so isolate J_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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for J_w:

   $$J_{w} = \dfrac{\Delta P}{\mu R_m}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 57.0000 kPa, dynamic viscosity (mu) = 0.0011 Pa*s, membrane resistance (R_m) = 910,000,000,000 1/m.

4. Step 4 — Substitute the given values:

   $$J_{w} = \dfrac{\Delta P}{0.0011 R_m}$$

5. Step 5 — Evaluate:

   $$J_{w} = 0.0001\ \text{m/s}$$

6. Step 6 — Check: returning J_w = 0.0001 m/s to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 0.0001 — kept a factor of two that cancels in the correct rearrangement.
• 0.0000 — dropped that same factor in the other direction.
• 0.0001 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration flux calculation from transmembrane pressure Given dynamic viscosity (mu) = 0.0018 Pa*s; membrane resistance (R_m) = 567,000,000,000 1/m; ultrafiltration permeate flux (J_w) = 0.0007 m/s, determine the transmembrane pressure (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = J_w \mu R_m$$

3. Step 3 — List the givens: dynamic viscosity (mu) = 0.0018 Pa*s, membrane resistance (R_m) = 567,000,000,000 1/m, ultrafiltration permeate flux (J_w) = 0.0007 m/s.

4. Step 4 — Substitute the given values:

   $$deltaP = J_w 0.0018 R_m$$

5. Step 5 — Evaluate:

   $$deltaP = 689.6\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 689.6 kPa to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 1,379 — kept a factor of two that cancels in the correct rearrangement.
• 344.8 — dropped that same factor in the other direction.
• 758.5 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane resistance and flux relationship Given transmembrane pressure (deltaP) = 200.0 kPa; dynamic viscosity (mu) = 0.0017 Pa*s; ultrafiltration permeate flux (J_w) = 0.0008 m/s, determine the membrane resistance (R_m) in 1/m.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except R_m is given, so isolate R_m 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for R_m:

   $$R_{m} = \dfrac{\Delta P}{\mu J_w}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 200.0 kPa, dynamic viscosity (mu) = 0.0017 Pa*s, ultrafiltration permeate flux (J_w) = 0.0008 m/s.

4. Step 4 — Substitute the given values:

   $$R_{m} = \dfrac{\Delta P}{0.0017 J_w}$$

5. Step 5 — Evaluate:

   $$R_{m} = 143255187628\ \text{1/m}$$

6. Step 6 — Check: returning R_m = 143,255,187,628 1/m to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 286,510,375,257 — kept a factor of two that cancels in the correct rearrangement.
• 71,627,593,814 — dropped that same factor in the other direction.
• 157,580,706,391 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane permeate flux for drinking water treatment Given transmembrane pressure (deltaP) = 350.0 kPa; dynamic viscosity (mu) = 0.0013 Pa*s; membrane resistance (R_m) = 940,000,000,000 1/m, determine the ultrafiltration permeate flux (J_w) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except J_w is given, so isolate J_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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for J_w:

   $$J_{w} = \dfrac{\Delta P}{\mu R_m}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 350.0 kPa, dynamic viscosity (mu) = 0.0013 Pa*s, membrane resistance (R_m) = 940,000,000,000 1/m.

4. Step 4 — Substitute the given values:

   $$J_{w} = \dfrac{\Delta P}{0.0013 R_m}$$

5. Step 5 — Evaluate:

   $$J_{w} = 0.0003\ \text{m/s}$$

6. Step 6 — Check: returning J_w = 0.0003 m/s to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 0.0006 — kept a factor of two that cancels in the correct rearrangement.
• 0.0001 — dropped that same factor in the other direction.
• 0.0003 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration flux calculation from transmembrane pressure Given dynamic viscosity (mu) = 0.0015 Pa*s; membrane resistance (R_m) = 688,000,000,000 1/m; ultrafiltration permeate flux (J_w) = 0.0002 m/s, determine the transmembrane pressure (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = J_w \mu R_m$$

3. Step 3 — List the givens: dynamic viscosity (mu) = 0.0015 Pa*s, membrane resistance (R_m) = 688,000,000,000 1/m, ultrafiltration permeate flux (J_w) = 0.0002 m/s.

4. Step 4 — Substitute the given values:

   $$deltaP = J_w 0.0015 R_m$$

5. Step 5 — Evaluate:

   $$deltaP = 212.6\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 212.6 kPa to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

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

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane resistance and flux relationship Given transmembrane pressure (deltaP) = 379.0 kPa; dynamic viscosity (mu) = 0.0011 Pa*s; ultrafiltration permeate flux (J_w) = 0.0002 m/s, determine the membrane resistance (R_m) in 1/m.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except R_m is given, so isolate R_m 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for R_m:

   $$R_{m} = \dfrac{\Delta P}{\mu J_w}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 379.0 kPa, dynamic viscosity (mu) = 0.0011 Pa*s, ultrafiltration permeate flux (J_w) = 0.0002 m/s.

4. Step 4 — Substitute the given values:

   $$R_{m} = \dfrac{\Delta P}{0.0011 J_w}$$

5. Step 5 — Evaluate:

   $$R_{m} = 1479313036690\ \text{1/m}$$

6. Step 6 — Check: returning R_m = 1,479,313,036,690 1/m to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 2,958,626,073,380 — kept a factor of two that cancels in the correct rearrangement.
• 739,656,518,345 — dropped that same factor in the other direction.
• 1,627,244,340,359 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane permeate flux for drinking water treatment Given transmembrane pressure (deltaP) = 369.0 kPa; dynamic viscosity (mu) = 0.0013 Pa*s; membrane resistance (R_m) = 923,000,000,000 1/m, determine the ultrafiltration permeate flux (J_w) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except J_w is given, so isolate J_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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for J_w:

   $$J_{w} = \dfrac{\Delta P}{\mu R_m}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 369.0 kPa, dynamic viscosity (mu) = 0.0013 Pa*s, membrane resistance (R_m) = 923,000,000,000 1/m.

4. Step 4 — Substitute the given values:

   $$J_{w} = \dfrac{\Delta P}{0.0013 R_m}$$

5. Step 5 — Evaluate:

   $$J_{w} = 0.0003\ \text{m/s}$$

6. Step 6 — Check: returning J_w = 0.0003 m/s to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 0.0006 — kept a factor of two that cancels in the correct rearrangement.
• 0.0002 — dropped that same factor in the other direction.
• 0.0003 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration flux calculation from transmembrane pressure Given dynamic viscosity (mu) = 0.0016 Pa*s; membrane resistance (R_m) = 321,000,000,000 1/m; ultrafiltration permeate flux (J_w) = 0.0006 m/s, determine the transmembrane pressure (deltaP) in kPa.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for deltaP:

   $$deltaP = J_w \mu R_m$$

3. Step 3 — List the givens: dynamic viscosity (mu) = 0.0016 Pa*s, membrane resistance (R_m) = 321,000,000,000 1/m, ultrafiltration permeate flux (J_w) = 0.0006 m/s.

4. Step 4 — Substitute the given values:

   $$deltaP = J_w 0.0016 R_m$$

5. Step 5 — Evaluate:

   $$deltaP = 305.3\ \text{kPa}$$

6. Step 6 — Check: returning deltaP = 305.3 kPa to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

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

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane resistance and flux relationship Given transmembrane pressure (deltaP) = 368.0 kPa; dynamic viscosity (mu) = 0.0012 Pa*s; ultrafiltration permeate flux (J_w) = 0.0001 m/s, determine the membrane resistance (R_m) in 1/m.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except R_m is given, so isolate R_m 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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for R_m:

   $$R_{m} = \dfrac{\Delta P}{\mu J_w}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 368.0 kPa, dynamic viscosity (mu) = 0.0012 Pa*s, ultrafiltration permeate flux (J_w) = 0.0001 m/s.

4. Step 4 — Substitute the given values:

   $$R_{m} = \dfrac{\Delta P}{0.0012 J_w}$$

5. Step 5 — Evaluate:

   $$R_{m} = 3046862063256\ \text{1/m}$$

6. Step 6 — Check: returning R_m = 3,046,862,063,256 1/m to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 6,093,724,126,511 — kept a factor of two that cancels in the correct rearrangement.
• 1,523,431,031,628 — dropped that same factor in the other direction.
• 3,351,548,269,581 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration

ultrafiltration membrane permeate flux for drinking water treatment Given transmembrane pressure (deltaP) = 179.0 kPa; dynamic viscosity (mu) = 0.0010 Pa*s; membrane resistance (R_m) = 798,000,000,000 1/m, determine the ultrafiltration permeate flux (J_w) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Ultrafiltration.
• Everything except J_w is given, so isolate J_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.
• Ultrafiltration permeate flux is governed by transmembrane pressure, fluid viscosity, and membrane resistance.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

2. Step 2 — Rearrange symbolically for J_w:

   $$J_{w} = \dfrac{\Delta P}{\mu R_m}$$

3. Step 3 — List the givens: transmembrane pressure (deltaP) = 179.0 kPa, dynamic viscosity (mu) = 0.0010 Pa*s, membrane resistance (R_m) = 798,000,000,000 1/m.

4. Step 4 — Substitute the given values:

   $$J_{w} = \dfrac{\Delta P}{0.0010 R_m}$$

5. Step 5 — Evaluate:

   $$J_{w} = 0.0002\ \text{m/s}$$

6. Step 6 — Check: returning J_w = 0.0002 m/s to

   $$J_w = \dfrac{\Delta P}{\mu R_m}$$

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

Why the other options are there

• 0.0004 — kept a factor of two that cancels in the correct rearrangement.
• 0.0001 — dropped that same factor in the other direction.
• 0.0002 — rounded an intermediate value before the final step.

Reference: FE Handbook — Ultrafiltration