A 300 mm main carries 0.10 m³/s over 1,200 m with f = 0.020. Compute the friction head loss.

Start with the thinking

• Velocity from continuity first.
• The velocity head is squared — a 10% velocity error is a 21% head error.

Step-by-step solution

1. Area

   $$A = \pi(0.30)^{2}/4 = 0.0707 m^{2}$$

2. Velocity

   $$V = Q/A = 0.10/0.0707 = 1.41 m/s$$

3. Velocity head

   $$V^{2}/2g = 1.41^{2}/19.62 = 0.102 m$$

4. Darcy-Weisbach

   $$h_f = f(L/D)(V^{2}/2g)$$

5. Substitute

   $$h_f = 0.020(1,200/0.30)(0.102) = 0.020(4,000)(0.102)$$

6. Result

   $$h_f = 8.15 m$$

Why the other options are there

• 0.82 m (L/D taken as 400)
• 16.3 m (velocity head doubled)

Reference: FE Reference Handbook — Fluid Mechanics — Darcy-Weisbach equation

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0160; pipe length (L) = 630.0 ft; pipe diameter (D) = 2.3000 ft; velocity (V) = 10.6000 ft/s, determine the head loss (hf) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Darcy–Weisbach head loss.
• Everything except hf is given, so isolate hf 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0160, pipe length (L) = 630.0 ft, pipe diameter (D) = 2.3000 ft, velocity (V) = 10.6000 ft/s.

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

5. Step 5 — Evaluate:

   $$hf = 7.6464\ \text{ft}$$

6. Step 6 — Check: returning hf = 7.6464 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 15.2929 — kept a factor of two that cancels in the correct rearrangement.
• 3.8232 — dropped that same factor in the other direction.
• 8.4111 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given pipe length (L) = 1,900 ft; pipe diameter (D) = 1.0000 ft; velocity (V) = 5.9000 ft/s; head loss (hf) = 75.8700 ft, determine the friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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) = 1,900 ft, pipe diameter (D) = 1.0000 ft, velocity (V) = 5.9000 ft/s, head loss (hf) = 75.8700 ft.

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

5. Step 5 — Evaluate:

   $$f = 0.0739$$

6. Step 6 — Check: returning f = 0.0739 to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 0.1478 — kept a factor of two that cancels in the correct rearrangement.
• 0.0369 — dropped that same factor in the other direction.
• 0.0813 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0400; pipe diameter (D) = 2.2000 ft; velocity (V) = 14.4000 ft/s; head loss (hf) = 61.0500 ft, determine the pipe length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0400, pipe diameter (D) = 2.2000 ft, velocity (V) = 14.4000 ft/s, head loss (hf) = 61.0500 ft.

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

5. Step 5 — Evaluate:

   $$L = 1043\ \text{ft}$$

6. Step 6 — Check: returning L = 1,043 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 2,086 — kept a factor of two that cancels in the correct rearrangement.
• 521.4 — dropped that same factor in the other direction.
• 1,147 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0340; pipe length (L) = 2,760 ft; pipe diameter (D) = 1.1000 ft; velocity (V) = 12.9000 ft/s, determine the head loss (hf) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Darcy–Weisbach head loss.
• Everything except hf is given, so isolate hf 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0340, pipe length (L) = 2,760 ft, pipe diameter (D) = 1.1000 ft, velocity (V) = 12.9000 ft/s.

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

5. Step 5 — Evaluate:

   $$hf = 220.4\ \text{ft}$$

6. Step 6 — Check: returning hf = 220.4 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

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

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given pipe length (L) = 2,120 ft; pipe diameter (D) = 2.2000 ft; velocity (V) = 10.3000 ft/s; head loss (hf) = 82.3100 ft, determine the friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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) = 2,120 ft, pipe diameter (D) = 2.2000 ft, velocity (V) = 10.3000 ft/s, head loss (hf) = 82.3100 ft.

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

5. Step 5 — Evaluate:

   $$f = 0.0519$$

6. Step 6 — Check: returning f = 0.0519 to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 0.1037 — kept a factor of two that cancels in the correct rearrangement.
• 0.0259 — dropped that same factor in the other direction.
• 0.0570 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0200; pipe diameter (D) = 1.1500 ft; velocity (V) = 3.8000 ft/s; head loss (hf) = 17.7900 ft, determine the pipe length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0200, pipe diameter (D) = 1.1500 ft, velocity (V) = 3.8000 ft/s, head loss (hf) = 17.7900 ft.

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

5. Step 5 — Evaluate:

   $$L = 4562\ \text{ft}$$

6. Step 6 — Check: returning L = 4,562 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 9,124 — kept a factor of two that cancels in the correct rearrangement.
• 2,281 — dropped that same factor in the other direction.
• 5,018 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0330; pipe length (L) = 1,250 ft; pipe diameter (D) = 0.9500 ft; velocity (V) = 13.6000 ft/s, determine the head loss (hf) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Darcy–Weisbach head loss.
• Everything except hf is given, so isolate hf 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0330, pipe length (L) = 1,250 ft, pipe diameter (D) = 0.9500 ft, velocity (V) = 13.6000 ft/s.

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

5. Step 5 — Evaluate:

   $$hf = 124.7\ \text{ft}$$

6. Step 6 — Check: returning hf = 124.7 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 249.4 — kept a factor of two that cancels in the correct rearrangement.
• 62.3537 — dropped that same factor in the other direction.
• 137.2 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given pipe length (L) = 3,970 ft; pipe diameter (D) = 1.4500 ft; velocity (V) = 7.5000 ft/s; head loss (hf) = 3.0900 ft, determine the friction factor (f).

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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) = 3,970 ft, pipe diameter (D) = 1.4500 ft, velocity (V) = 7.5000 ft/s, head loss (hf) = 3.0900 ft.

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

5. Step 5 — Evaluate:

   $$f = 0.0013$$

6. Step 6 — Check: returning f = 0.0013 to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 0.0026 — kept a factor of two that cancels in the correct rearrangement.
• 0.0006 — dropped that same factor in the other direction.
• 0.0014 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow

A fluid mechanics problem uses Darcy–Weisbach head loss. Given friction factor (f) = 0.0460; pipe diameter (D) = 2.9000 ft; velocity (V) = 9.2000 ft/s; head loss (hf) = 26.6500 ft, determine the pipe length (L) in ft.

Start with the thinking

• The governing relation printed in this handbook section is 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.
• Fluid Mechanics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$h_f = f (L/D) (V^2 / 2g)$$

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

3. Step 3 — List the givens: friction factor (f) = 0.0460, pipe diameter (D) = 2.9000 ft, velocity (V) = 9.2000 ft/s, head loss (hf) = 26.6500 ft.

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

5. Step 5 — Evaluate:

   $$L = 1278\ \text{ft}$$

6. Step 6 — Check: returning L = 1,278 ft to

   $$h_f = f (L/D) (V^2 / 2g)$$

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

Why the other options are there

• 2,557 — kept a factor of two that cancels in the correct rearrangement.
• 639.2 — dropped that same factor in the other direction.
• 1,406 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Fluid Mechanics → Head Loss Due to Flow