The same 3.0 m channel carries 7.32 m³/s. Find the critical depth and state whether the 1.2 m normal depth is subcritical or supercritical.

Start with the thinking

• For a rectangle y_c = (q²/g)^{1/3}.
• y_n > y_c means subcritical, mild slope.

Step-by-step solution

1. Unit discharge

   $$q = 2.44 m^{2}/s$$

2. Ratio

   $$q^{2}/g = 5.95/9.81 = 0.607$$

3. Critical depth

   $$y_c = 0.607^{1/3} = 0.847 m$$

4. Compare

   $$y_n = 1.2 m > y_c = 0.847 m$$

5. Conclusion — subcritical flow on a mild slope; control is downstream

Why the other options are there

• y_c = 0.607 m (cube root omitted)
• Supercritical (comparison reversed)

Reference: FE Reference Handbook — Hydraulics — Critical flow

A hydraulics problem uses Froude number. Given velocity (V) = 6.7000 ft/s; flow depth (y) = 1.0000 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

   $$List the givens: velocity (V) = 6.7000 ft/s, flow depth (y) = 1.0000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 1.1807$$

6. Step 6 — Check: returning Fr = 1.1807 to

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

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

Why the other options are there

• 2.3614 — kept a factor of two that cancels in the correct rearrangement.
• 0.5904 — dropped that same factor in the other direction.
• 1.2988 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given flow depth (y) = 1.8000 ft; Froude number (Fr) = 2.0900, 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

   $$List the givens: flow depth (y) = 1.8000 ft, Froude number (Fr) = 2.0900$$

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

5. Step 5 — Evaluate:

   $$V = 15.9115\ \text{ft/s}$$

6. Step 6 — Check: returning V = 15.9115 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

• 31.8230 — kept a factor of two that cancels in the correct rearrangement.
• 7.9557 — dropped that same factor in the other direction.
• 17.5026 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given velocity (V) = 13.7000 ft/s; Froude number (Fr) = 0.2700, 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

   $$List the givens: velocity (V) = 13.7000 ft/s, Froude number (Fr) = 0.2700$$

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

5. Step 5 — Evaluate:

   $$y = 79.9572\ \text{ft}$$

6. Step 6 — Check: returning y = 79.9572 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

• 159.9 — kept a factor of two that cancels in the correct rearrangement.
• 39.9786 — dropped that same factor in the other direction.
• 87.9530 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given velocity (V) = 6.6000 ft/s; flow depth (y) = 2.2000 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

   $$List the givens: velocity (V) = 6.6000 ft/s, flow depth (y) = 2.2000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 0.7842$$

6. Step 6 — Check: returning Fr = 0.7842 to

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

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

Why the other options are there

• 1.5683 — kept a factor of two that cancels in the correct rearrangement.
• 0.3921 — dropped that same factor in the other direction.
• 0.8626 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given flow depth (y) = 3.4000 ft; Froude number (Fr) = 1.8600, 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

   $$List the givens: flow depth (y) = 3.4000 ft, Froude number (Fr) = 1.8600$$

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

5. Step 5 — Evaluate:

   $$V = 19.4617\ \text{ft/s}$$

6. Step 6 — Check: returning V = 19.4617 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

• 38.9234 — kept a factor of two that cancels in the correct rearrangement.
• 9.7308 — dropped that same factor in the other direction.
• 21.4078 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given velocity (V) = 9.6000 ft/s; Froude number (Fr) = 1.1700, 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

   $$List the givens: velocity (V) = 9.6000 ft/s, Froude number (Fr) = 1.1700$$

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

5. Step 5 — Evaluate:

   $$y = 2.0908\ \text{ft}$$

6. Step 6 — Check: returning y = 2.0908 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

• 4.1816 — kept a factor of two that cancels in the correct rearrangement.
• 1.0454 — dropped that same factor in the other direction.
• 2.2999 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given velocity (V) = 7.8000 ft/s; flow depth (y) = 1.4000 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

   $$List the givens: velocity (V) = 7.8000 ft/s, flow depth (y) = 1.4000 ft$$

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

5. Step 5 — Evaluate:

   $$Fr = 1.1617$$

6. Step 6 — Check: returning Fr = 1.1617 to

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

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

Why the other options are there

• 2.3234 — kept a factor of two that cancels in the correct rearrangement.
• 0.5809 — dropped that same factor in the other direction.
• 1.2779 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given flow depth (y) = 5.3000 ft; Froude number (Fr) = 2.9600, 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

   $$List the givens: flow depth (y) = 5.3000 ft, Froude number (Fr) = 2.9600$$

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

5. Step 5 — Evaluate:

   $$V = 38.6685\ \text{ft/s}$$

6. Step 6 — Check: returning V = 38.6685 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

• 77.3370 — kept a factor of two that cancels in the correct rearrangement.
• 19.3343 — dropped that same factor in the other direction.
• 42.5354 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump

A hydraulics problem uses Froude number. Given velocity (V) = 11.4000 ft/s; Froude number (Fr) = 1.7800, 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

   $$List the givens: velocity (V) = 11.4000 ft/s, Froude number (Fr) = 1.7800$$

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

5. Step 5 — Evaluate:

   $$y = 1.2738\ \text{ft}$$

6. Step 6 — Check: returning y = 1.2738 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

• 2.5477 — kept a factor of two that cancels in the correct rearrangement.
• 0.6369 — dropped that same factor in the other direction.
• 1.4012 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Hydraulics → Hydraulic Jump