A 300.0 mm main (C = 130) carries 0.140 m³/s over 975 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.140/0.07069 = 1.98 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0750 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.01199 m/m$$

5. Head loss

   $$h_f = S L = 0.01199(975) = 11.69 m$$

6. Unit check

   $$11.69 m \times 3.281 = 38.4 ft over 3,199 ft of pipe$$

Why the other options are there

• 18.16 m (U.S. constant used with SI data)
• 3.56 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 200.0 mm main (C = 100) carries 0.090 m³/s over 780 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.090/0.03142 = 2.86 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0500 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.06198 m/m$$

5. Head loss

   $$h_f = S L = 0.06198(780) = 48.35 m$$

6. Unit check

   $$48.35 m \times 3.281 = 158.6 ft over 2,559 ft of pipe$$

Why the other options are there

• 75.06 m (U.S. constant used with SI data)
• 14.74 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 150.0 mm main (C = 130) carries 0.090 m³/s over 264 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.090/0.01767 = 5.09 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0375 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.15480 m/m$$

5. Head loss

   $$h_f = S L = 0.15480(264) = 40.87 m$$

6. Unit check

   $$40.87 m \times 3.281 = 134.1 ft over 866.1 ft of pipe$$

Why the other options are there

• 63.44 m (U.S. constant used with SI data)
• 12.46 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 200.0 mm main (C = 120) carries 0.050 m³/s over 704 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.050/0.03142 = 1.59 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0500 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.01489 m/m$$

5. Head loss

   $$h_f = S L = 0.01489(704) = 10.48 m$$

6. Unit check

   $$10.48 m \times 3.281 = 34.4 ft over 2,310 ft of pipe$$

Why the other options are there

• 16.27 m (U.S. constant used with SI data)
• 3.20 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 200.0 mm main (C = 140) carries 0.030 m³/s over 988 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.030/0.03142 = 0.95 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0500 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.00435 m/m$$

5. Head loss

   $$h_f = S L = 0.00435(988) = 4.29 m$$

6. Unit check

   $$4.29 m \times 3.281 = 14.1 ft over 3,241 ft of pipe$$

Why the other options are there

• 6.67 m (U.S. constant used with SI data)
• 1.31 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 300.0 mm main (C = 140) carries 0.060 m³/s over 1226 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.060/0.07069 = 0.85 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0750 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.00218 m/m$$

5. Head loss

   $$h_f = S L = 0.00218(1226) = 2.67 m$$

6. Unit check

   $$2.67 m \times 3.281 = 8.8 ft over 4,022 ft of pipe$$

Why the other options are there

• 4.14 m (U.S. constant used with SI data)
• 0.81 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 150.0 mm main (C = 120) carries 0.100 m³/s over 696 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.100/0.01767 = 5.66 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0375 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.21822 m/m$$

5. Head loss

   $$h_f = S L = 0.21822(696) = 151.9 m$$

6. Unit check

   $$151.9 m \times 3.281 = 498.3 ft over 2,283 ft of pipe$$

Why the other options are there

• 235.8 m (U.S. constant used with SI data)
• 46.29 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 350.0 mm main (C = 120) carries 0.080 m³/s over 1188 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.080/0.09621 = 0.83 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0875 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.00233 m/m$$

5. Head loss

   $$h_f = S L = 0.00233(1188) = 2.77 m$$

6. Unit check

   $$2.77 m \times 3.281 = 9.1 ft over 3,898 ft of pipe$$

Why the other options are there

• 4.30 m (U.S. constant used with SI data)
• 0.84 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 250.0 mm main (C = 120) carries 0.160 m³/s over 826 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.160/0.04909 = 3.26 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0625 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.04329 m/m$$

5. Head loss

   $$h_f = S L = 0.04329(826) = 35.76 m$$

6. Unit check

   $$35.76 m \times 3.281 = 117.3 ft over 2,710 ft of pipe$$

Why the other options are there

• 55.51 m (U.S. constant used with SI data)
• 10.90 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units

A 300.0 mm main (C = 120) carries 0.170 m³/s over 530 m. Compute the head loss with the SI Hazen-Williams form, then convert the data to U.S. customary units and confirm the loss in feet.

Start with the thinking

• Hazen-Williams uses a different leading constant in each unit system: 0.849 in SI, 1.318 in U.S. customary — the exponents never change.
• Convert the answer, not the constant, when you need the other unit system.

Step-by-step solution

1. Velocity

   $$V = Q/A = 0.170/0.07069 = 2.41 m/s$$

2. Formula (SI)

   $$V = 0.849\,C\,R^{0.63}S^{0.54}$$

3. Hydraulic radius

   $$R = D/4 = 0.0750 m$$

4. Solving for S

   $$S = [V/(0.849 C R^{0.63})]^{1/0.54} = 0.01993 m/m$$

5. Head loss

   $$h_f = S L = 0.01993(530) = 10.56 m$$

6. Unit check

   $$10.56 m \times 3.281 = 34.7 ft over 1,739 ft of pipe$$

Why the other options are there

• 16.40 m (U.S. constant used with SI data)
• 3.22 ft (conversion inverted)

Reference: FE Reference Handbook — Hydraulics → U.S. Customary Units