A hydraulics problem uses Froude number. Given velocity (V) = 5.6000 ft/s; flow depth (y) = 4.2000 ft, determine the Froude number (Fr).

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except Fr is given, so isolate Fr 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 5.6000 ft/s, flow depth (y) = 4.2000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 0.4815$$

6. Step 6 — Check: returning Fr = 0.4815 to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 0.9631 — kept a factor of two that cancels in the correct rearrangement.
• 0.2408 — dropped that same factor in the other direction.
• 0.5297 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given flow depth (y) = 1.1000 ft; Froude number (Fr) = 2.7200, determine the velocity (V) in ft/s.

Start with the thinking

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

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: flow depth (y) = 1.1000 ft, Froude number (Fr) = 2.7200$$

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

5. Step 5 — Evaluate:

   $$V = 16.1880\ \text{ft/s}$$

6. Step 6 — Check: returning V = 16.1880 ft/s to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 32.3760 — kept a factor of two that cancels in the correct rearrangement.
• 8.0940 — dropped that same factor in the other direction.
• 17.8068 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 11.4000 ft/s; Froude number (Fr) = 0.5500, determine the flow depth (y) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except y is given, so isolate y 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 11.4000 ft/s, Froude number (Fr) = 0.5500$$

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

5. Step 5 — Evaluate:

   $$y = 13.3422\ \text{ft}$$

6. Step 6 — Check: returning y = 13.3422 ft to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 26.6845 — kept a factor of two that cancels in the correct rearrangement.
• 6.6711 — dropped that same factor in the other direction.
• 14.6765 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 13.9000 ft/s; flow depth (y) = 7.0000 ft, determine the Froude number (Fr).

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except Fr is given, so isolate Fr 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 13.9000 ft/s, flow depth (y) = 7.0000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 0.9258$$

6. Step 6 — Check: returning Fr = 0.9258 to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 1.8517 — kept a factor of two that cancels in the correct rearrangement.
• 0.4629 — dropped that same factor in the other direction.
• 1.0184 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given flow depth (y) = 2.0000 ft; Froude number (Fr) = 2.3500, determine the velocity (V) in ft/s.

Start with the thinking

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

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: flow depth (y) = 2.0000 ft, Froude number (Fr) = 2.3500$$

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

5. Step 5 — Evaluate:

   $$V = 18.8587\ \text{ft/s}$$

6. Step 6 — Check: returning V = 18.8587 ft/s to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 37.7173 — kept a factor of two that cancels in the correct rearrangement.
• 9.4293 — dropped that same factor in the other direction.
• 20.7445 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 8.7000 ft/s; Froude number (Fr) = 0.6900, determine the flow depth (y) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except y is given, so isolate y 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 8.7000 ft/s, Froude number (Fr) = 0.6900$$

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

5. Step 5 — Evaluate:

   $$y = 4.9372\ \text{ft}$$

6. Step 6 — Check: returning y = 4.9372 ft to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 9.8745 — kept a factor of two that cancels in the correct rearrangement.
• 2.4686 — dropped that same factor in the other direction.
• 5.4310 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 2.7000 ft/s; flow depth (y) = 7.1000 ft, determine the Froude number (Fr).

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except Fr is given, so isolate Fr 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 2.7000 ft/s, flow depth (y) = 7.1000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 0.1786$$

6. Step 6 — Check: returning Fr = 0.1786 to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 0.3571 — kept a factor of two that cancels in the correct rearrangement.
• 0.0893 — dropped that same factor in the other direction.
• 0.1964 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given flow depth (y) = 5.6000 ft; Froude number (Fr) = 0.4600, determine the velocity (V) in ft/s.

Start with the thinking

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

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: flow depth (y) = 5.6000 ft, Froude number (Fr) = 0.4600$$

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

5. Step 5 — Evaluate:

   $$V = 6.1770\ \text{ft/s}$$

6. Step 6 — Check: returning V = 6.1770 ft/s to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 12.3541 — kept a factor of two that cancels in the correct rearrangement.
• 3.0885 — dropped that same factor in the other direction.
• 6.7947 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 3.3000 ft/s; Froude number (Fr) = 0.8900, determine the flow depth (y) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except y is given, so isolate y 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 3.3000 ft/s, Froude number (Fr) = 0.8900$$

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

5. Step 5 — Evaluate:

   $$y = 0.4270\ \text{ft}$$

6. Step 6 — Check: returning y = 0.4270 ft to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 0.8539 — kept a factor of two that cancels in the correct rearrangement.
• 0.2135 — dropped that same factor in the other direction.
• 0.4697 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy

A hydraulics problem uses Froude number. Given velocity (V) = 6.3000 ft/s; flow depth (y) = 3.2000 ft, determine the Froude number (Fr).

Start with the thinking

• The governing relation printed in this handbook section is Froude number.
• Everything except Fr is given, so isolate Fr 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.
• Hydraulics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_r = V / \sqrt{g y}$$

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

3. Step 3

   $$List the givens: velocity (V) = 6.3000 ft/s, flow depth (y) = 3.2000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 0.6206$$

6. Step 6 — Check: returning Fr = 0.6206 to

   $$F_r = V / \sqrt{g y}$$

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

Why the other options are there

• 1.2413 — kept a factor of two that cancels in the correct rearrangement.
• 0.3103 — dropped that same factor in the other direction.
• 0.6827 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Specific Energy