the friction factor for turbulent flow in a pipe from the Moody chart Given Darcy friction factor (f) = 0.0490; pipe length (L) = 935.0 m; pipe diameter (D) = 0.0500 m; velocity (V) = 3.3500 m/s; gravity (g) = 9.8900 m/s^2, determine the friction head loss (h_f) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except h_f is given, so isolate h_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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0490, pipe length (L) = 935.0 m, pipe diameter (D) = 0.0500 m, velocity (V) = 3.3500 m/s, gravity (g) = 9.8900 m/s^2.

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

5. Step 5 — Evaluate:

   $$h_{f} = 519.9\ \text{m}$$

6. Step 6 — Check: returning h_f = 519.9 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 1,040 — kept a factor of two that cancels in the correct rearrangement.
• 259.9 — dropped that same factor in the other direction.
• 571.9 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor used to compute head loss in a pipeline Given pipe length (L) = 130.0 m; pipe diameter (D) = 0.1200 m; velocity (V) = 2.4000 m/s; gravity (g) = 9.7300 m/s^2; friction head loss (h_f) = 8.1800 m, determine the Darcy friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except f is given, so isolate 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: pipe length (L) = 130.0 m, pipe diameter (D) = 0.1200 m, velocity (V) = 2.4000 m/s, gravity (g) = 9.7300 m/s^2, friction head loss (h_f) = 8.1800 m.

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

5. Step 5 — Evaluate:

   $$f = 0.0255$$

6. Step 6 — Check: returning f = 0.0255 to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 0.0510 — kept a factor of two that cancels in the correct rearrangement.
• 0.0128 — dropped that same factor in the other direction.
• 0.0281 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for a rough concrete pipe carrying water Given Darcy friction factor (f) = 0.0380; pipe diameter (D) = 0.2300 m; velocity (V) = 3.1000 m/s; gravity (g) = 9.8900 m/s^2; friction head loss (h_f) = 5.1900 m, determine the pipe length (L) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except L is given, so isolate L 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0380, pipe diameter (D) = 0.2300 m, velocity (V) = 3.1000 m/s, gravity (g) = 9.8900 m/s^2, friction head loss (h_f) = 5.1900 m.

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

5. Step 5 — Evaluate:

   $$L = 64.6568\ \text{m}$$

6. Step 6 — Check: returning L = 64.6568 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 129.3 — kept a factor of two that cancels in the correct rearrangement.
• 32.3284 — dropped that same factor in the other direction.
• 71.1225 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for turbulent flow in a pipe from the Moody chart Given Darcy friction factor (f) = 0.0220; pipe length (L) = 665.0 m; pipe diameter (D) = 0.3900 m; velocity (V) = 1.9500 m/s; gravity (g) = 9.8300 m/s^2, determine the friction head loss (h_f) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except h_f is given, so isolate h_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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0220, pipe length (L) = 665.0 m, pipe diameter (D) = 0.3900 m, velocity (V) = 1.9500 m/s, gravity (g) = 9.8300 m/s^2.

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

5. Step 5 — Evaluate:

   $$h_{f} = 7.2555\ \text{m}$$

6. Step 6 — Check: returning h_f = 7.2555 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 14.5109 — kept a factor of two that cancels in the correct rearrangement.
• 3.6277 — dropped that same factor in the other direction.
• 7.9810 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor used to compute head loss in a pipeline Given pipe length (L) = 360.0 m; pipe diameter (D) = 0.4000 m; velocity (V) = 1.0000 m/s; gravity (g) = 9.7900 m/s^2; friction head loss (h_f) = 19.1500 m, determine the Darcy friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except f is given, so isolate 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: pipe length (L) = 360.0 m, pipe diameter (D) = 0.4000 m, velocity (V) = 1.0000 m/s, gravity (g) = 9.7900 m/s^2, friction head loss (h_f) = 19.1500 m.

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

5. Step 5 — Evaluate:

   $$f = 0.4166$$

6. Step 6 — Check: returning f = 0.4166 to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 0.8332 — kept a factor of two that cancels in the correct rearrangement.
• 0.2083 — dropped that same factor in the other direction.
• 0.4583 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for a rough concrete pipe carrying water Given Darcy friction factor (f) = 0.0240; pipe diameter (D) = 0.2300 m; velocity (V) = 1.7000 m/s; gravity (g) = 9.7800 m/s^2; friction head loss (h_f) = 2.1100 m, determine the pipe length (L) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except L is given, so isolate L 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0240, pipe diameter (D) = 0.2300 m, velocity (V) = 1.7000 m/s, gravity (g) = 9.7800 m/s^2, friction head loss (h_f) = 2.1100 m.

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

5. Step 5 — Evaluate:

   $$L = 136.9\ \text{m}$$

6. Step 6 — Check: returning L = 136.9 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 273.7 — kept a factor of two that cancels in the correct rearrangement.
• 68.4290 — dropped that same factor in the other direction.
• 150.5 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for turbulent flow in a pipe from the Moody chart Given Darcy friction factor (f) = 0.0180; pipe length (L) = 520.0 m; pipe diameter (D) = 0.2500 m; velocity (V) = 3.9500 m/s; gravity (g) = 9.8000 m/s^2, determine the friction head loss (h_f) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except h_f is given, so isolate h_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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0180, pipe length (L) = 520.0 m, pipe diameter (D) = 0.2500 m, velocity (V) = 3.9500 m/s, gravity (g) = 9.8000 m/s^2.

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

5. Step 5 — Evaluate:

   $$h_{f} = 29.8040\ \text{m}$$

6. Step 6 — Check: returning h_f = 29.8040 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 59.6079 — kept a factor of two that cancels in the correct rearrangement.
• 14.9020 — dropped that same factor in the other direction.
• 32.7844 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor used to compute head loss in a pipeline Given pipe length (L) = 530.0 m; pipe diameter (D) = 0.4500 m; velocity (V) = 1.4000 m/s; gravity (g) = 9.7200 m/s^2; friction head loss (h_f) = 13.8000 m, determine the Darcy friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except f is given, so isolate 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: pipe length (L) = 530.0 m, pipe diameter (D) = 0.4500 m, velocity (V) = 1.4000 m/s, gravity (g) = 9.7200 m/s^2, friction head loss (h_f) = 13.8000 m.

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

5. Step 5 — Evaluate:

   $$f = 0.1162$$

6. Step 6 — Check: returning f = 0.1162 to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 0.2324 — kept a factor of two that cancels in the correct rearrangement.
• 0.0581 — dropped that same factor in the other direction.
• 0.1278 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for a rough concrete pipe carrying water Given Darcy friction factor (f) = 0.0200; pipe diameter (D) = 0.5100 m; velocity (V) = 1.2000 m/s; gravity (g) = 9.7400 m/s^2; friction head loss (h_f) = 18.0400 m, determine the pipe length (L) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except L is given, so isolate L 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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0200, pipe diameter (D) = 0.5100 m, velocity (V) = 1.2000 m/s, gravity (g) = 9.7400 m/s^2, friction head loss (h_f) = 18.0400 m.

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

5. Step 5 — Evaluate:

   $$L = 6223\ \text{m}$$

6. Step 6 — Check: returning L = 6,223 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

• 12,446 — kept a factor of two that cancels in the correct rearrangement.
• 3,112 — dropped that same factor in the other direction.
• 6,845 — rounded an intermediate value before the final step.

Reference: FE Handbook — Friction Factor

the friction factor for turbulent flow in a pipe from the Moody chart Given Darcy friction factor (f) = 0.0500; pipe length (L) = 945.0 m; pipe diameter (D) = 0.0800 m; velocity (V) = 2.6000 m/s; gravity (g) = 9.7300 m/s^2, determine the friction head loss (h_f) in m.

Start with the thinking

• The governing relation printed in this handbook section is Friction factor (Darcy-Weisbach head loss).
• Everything except h_f is given, so isolate h_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.
• The Darcy friction factor governs head loss due to friction in a pipeline of a given length and diameter.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

3. Step 3 — List the givens: Darcy friction factor (f) = 0.0500, pipe length (L) = 945.0 m, pipe diameter (D) = 0.0800 m, velocity (V) = 2.6000 m/s, gravity (g) = 9.7300 m/s^2.

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

5. Step 5 — Evaluate:

   $$h_{f} = 205.2\ \text{m}$$

6. Step 6 — Check: returning h_f = 205.2 m to

   $$h_f = f \dfrac{L}{D} \dfrac{V^2}{2g}$$

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

Why the other options are there

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

Reference: FE Handbook — Friction Factor