the Hazen-Williams equation for a water distribution pipeline Given Hazen-Williams coefficient (C_HW) = 116.0; hydraulic radius (R_H) = 0.2100 m; slope of energy grade line (S) = 0.0161 m/m, determine the velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except V is given, so isolate V 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: Hazen-Williams coefficient (C_HW) = 116.0, hydraulic radius (R_H) = 0.2100 m, slope of energy grade line (S) = 0.0161 m/m.

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

5. Step 5 — Evaluate:

   $$V = 3.9632\ \text{m/s}$$

6. Step 6 — Check: returning V = 3.9632 m/s to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 7.9265 — kept a factor of two that cancels in the correct rearrangement.
• 1.9816 — dropped that same factor in the other direction.
• 4.3596 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation applied to a ductile-iron pipe Given hydraulic radius (R_H) = 0.1800 m; slope of energy grade line (S) = 0.0153 m/m; velocity (V) = 2.4000 m/s, determine the Hazen-Williams coefficient (C_HW).

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except C_HW is given, so isolate C_HW 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: hydraulic radius (R_H) = 0.1800 m, slope of energy grade line (S) = 0.0153 m/m, velocity (V) = 2.4000 m/s.

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

5. Step 5 — Evaluate:

   $$C_{HW} = 79.5698$$

6. Step 6 — Check: returning C_HW = 79.5698 to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 159.1 — kept a factor of two that cancels in the correct rearrangement.
• 39.7849 — dropped that same factor in the other direction.
• 87.5268 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation to size a municipal pipe Given Hazen-Williams coefficient (C_HW) = 97.0000; hydraulic radius (R_H) = 0.2500 m; slope of energy grade line (S) = 0.0197 m/m, determine the velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except V is given, so isolate V 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: Hazen-Williams coefficient (C_HW) = 97.0000, hydraulic radius (R_H) = 0.2500 m, slope of energy grade line (S) = 0.0197 m/m.

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

5. Step 5 — Evaluate:

   $$V = 4.1247\ \text{m/s}$$

6. Step 6 — Check: returning V = 4.1247 m/s to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 8.2494 — kept a factor of two that cancels in the correct rearrangement.
• 2.0624 — dropped that same factor in the other direction.
• 4.5372 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation for a water distribution pipeline Given hydraulic radius (R_H) = 0.0300 m; slope of energy grade line (S) = 0.0181 m/m; velocity (V) = 0.8000 m/s, determine the Hazen-Williams coefficient (C_HW).

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except C_HW is given, so isolate C_HW 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: hydraulic radius (R_H) = 0.0300 m, slope of energy grade line (S) = 0.0181 m/m, velocity (V) = 0.8000 m/s.

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

5. Step 5 — Evaluate:

   $$C_{HW} = 74.8944$$

6. Step 6 — Check: returning C_HW = 74.8944 to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 149.8 — kept a factor of two that cancels in the correct rearrangement.
• 37.4472 — dropped that same factor in the other direction.
• 82.3839 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation applied to a ductile-iron pipe Given Hazen-Williams coefficient (C_HW) = 139.0; hydraulic radius (R_H) = 0.1200 m; slope of energy grade line (S) = 0.0021 m/m, determine the velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except V is given, so isolate V 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: Hazen-Williams coefficient (C_HW) = 139.0, hydraulic radius (R_H) = 0.1200 m, slope of energy grade line (S) = 0.0021 m/m.

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

5. Step 5 — Evaluate:

   $$V = 1.1112\ \text{m/s}$$

6. Step 6 — Check: returning V = 1.1112 m/s to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 2.2225 — kept a factor of two that cancels in the correct rearrangement.
• 0.5556 — dropped that same factor in the other direction.
• 1.2224 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation to size a municipal pipe Given hydraulic radius (R_H) = 0.1900 m; slope of energy grade line (S) = 0.0113 m/m; velocity (V) = 0.5500 m/s, determine the Hazen-Williams coefficient (C_HW).

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except C_HW is given, so isolate C_HW 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: hydraulic radius (R_H) = 0.1900 m, slope of energy grade line (S) = 0.0113 m/m, velocity (V) = 0.5500 m/s.

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

5. Step 5 — Evaluate:

   $$C_{HW} = 20.7576$$

6. Step 6 — Check: returning C_HW = 20.7576 to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 41.5153 — kept a factor of two that cancels in the correct rearrangement.
• 10.3788 — dropped that same factor in the other direction.
• 22.8334 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation for a water distribution pipeline Given Hazen-Williams coefficient (C_HW) = 126.0; hydraulic radius (R_H) = 0.1800 m; slope of energy grade line (S) = 0.0112 m/m, determine the velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except V is given, so isolate V 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: Hazen-Williams coefficient (C_HW) = 126.0, hydraulic radius (R_H) = 0.1800 m, slope of energy grade line (S) = 0.0112 m/m.

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

5. Step 5 — Evaluate:

   $$V = 3.2113\ \text{m/s}$$

6. Step 6 — Check: returning V = 3.2113 m/s to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 6.4226 — kept a factor of two that cancels in the correct rearrangement.
• 1.6056 — dropped that same factor in the other direction.
• 3.5324 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation applied to a ductile-iron pipe Given hydraulic radius (R_H) = 0.2900 m; slope of energy grade line (S) = 0.0098 m/m; velocity (V) = 1.3500 m/s, determine the Hazen-Williams coefficient (C_HW).

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except C_HW is given, so isolate C_HW 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: hydraulic radius (R_H) = 0.2900 m, slope of energy grade line (S) = 0.0098 m/m, velocity (V) = 1.3500 m/s.

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

5. Step 5 — Evaluate:

   $$C_{HW} = 42.1554$$

6. Step 6 — Check: returning C_HW = 42.1554 to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 84.3108 — kept a factor of two that cancels in the correct rearrangement.
• 21.0777 — dropped that same factor in the other direction.
• 46.3709 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation to size a municipal pipe Given Hazen-Williams coefficient (C_HW) = 116.0; hydraulic radius (R_H) = 0.0300 m; slope of energy grade line (S) = 0.0122 m/m, determine the velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except V is given, so isolate V 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: Hazen-Williams coefficient (C_HW) = 116.0, hydraulic radius (R_H) = 0.0300 m, slope of energy grade line (S) = 0.0122 m/m.

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

5. Step 5 — Evaluate:

   $$V = 1.0014\ \text{m/s}$$

6. Step 6 — Check: returning V = 1.0014 m/s to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 2.0027 — kept a factor of two that cancels in the correct rearrangement.
• 0.5007 — dropped that same factor in the other direction.
• 1.1015 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation

the Hazen-Williams equation for a water distribution pipeline Given hydraulic radius (R_H) = 0.1800 m; slope of energy grade line (S) = 0.0045 m/m; velocity (V) = 0.7000 m/s, determine the Hazen-Williams coefficient (C_HW).

Start with the thinking

• The governing relation printed in this handbook section is Hazen-Williams equation.
• Everything except C_HW is given, so isolate C_HW 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 Hazen-Williams equation estimates flow velocity in a pipeline given its roughness coefficient and slope.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

3. Step 3 — List the givens: hydraulic radius (R_H) = 0.1800 m, slope of energy grade line (S) = 0.0045 m/m, velocity (V) = 0.7000 m/s.

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

5. Step 5 — Evaluate:

   $$C_{HW} = 44.9401$$

6. Step 6 — Check: returning C_HW = 44.9401 to

   $$V = 0.849\, C_{HW} R_H^{0.63} S^{0.54}$$

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

Why the other options are there

• 89.8802 — kept a factor of two that cancels in the correct rearrangement.
• 22.4700 — dropped that same factor in the other direction.
• 49.4341 — rounded an intermediate value before the final step.

Reference: FE Handbook — Hazen-Williams Equation