a momentum-depth diagram used to locate conjugate depths of a hydraulic jump Given unit discharge (q) = 4.9000 m^2/s; gravity (g) = 9.8700 m/s^2; flow depth (y) = 0.5000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 4.9000 m^2/s, gravity (g) = 9.8700 m/s^2, flow depth (y) = 0.5000 m.

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

5. Step 5 — Evaluate:

   M = 4.9902\ \text{m^2}

6. Step 6 — Check: returning M = 4.9902 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 9.9805 — kept a factor of two that cancels in the correct rearrangement.
• 2.4951 — dropped that same factor in the other direction.
• 5.4893 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

the momentum-depth diagram for flow in a rectangular open channel Given unit discharge (q) = 1.6000 m^2/s; gravity (g) = 9.8500 m/s^2; flow depth (y) = 1.8000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 1.6000 m^2/s, gravity (g) = 9.8500 m/s^2, flow depth (y) = 1.8000 m.

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

5. Step 5 — Evaluate:

   M = 1.7644\ \text{m^2}

6. Step 6 — Check: returning M = 1.7644 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 3.5288 — kept a factor of two that cancels in the correct rearrangement.
• 0.8822 — dropped that same factor in the other direction.
• 1.9408 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram analysis at a stilling basin Given unit discharge (q) = 3.8500 m^2/s; gravity (g) = 9.8500 m/s^2; flow depth (y) = 1.5000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 3.8500 m^2/s, gravity (g) = 9.8500 m/s^2, flow depth (y) = 1.5000 m.

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

5. Step 5 — Evaluate:

   M = 2.1282\ \text{m^2}

6. Step 6 — Check: returning M = 2.1282 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 4.2564 — kept a factor of two that cancels in the correct rearrangement.
• 1.0641 — dropped that same factor in the other direction.
• 2.3410 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram used to locate conjugate depths of a hydraulic jump Given unit discharge (q) = 2.5000 m^2/s; gravity (g) = 9.7700 m/s^2; flow depth (y) = 0.8000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 2.5000 m^2/s, gravity (g) = 9.7700 m/s^2, flow depth (y) = 0.8000 m.

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

5. Step 5 — Evaluate:

   M = 1.1196\ \text{m^2}

6. Step 6 — Check: returning M = 1.1196 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 2.2393 — kept a factor of two that cancels in the correct rearrangement.
• 0.5598 — dropped that same factor in the other direction.
• 1.2316 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

the momentum-depth diagram for flow in a rectangular open channel Given unit discharge (q) = 3.4500 m^2/s; gravity (g) = 9.7500 m/s^2; flow depth (y) = 1.1000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 3.4500 m^2/s, gravity (g) = 9.7500 m/s^2, flow depth (y) = 1.1000 m.

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

5. Step 5 — Evaluate:

   M = 1.7148\ \text{m^2}

6. Step 6 — Check: returning M = 1.7148 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 3.4296 — kept a factor of two that cancels in the correct rearrangement.
• 0.8574 — dropped that same factor in the other direction.
• 1.8863 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram analysis at a stilling basin Given unit discharge (q) = 3.1000 m^2/s; gravity (g) = 9.9000 m/s^2; flow depth (y) = 1.3000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 3.1000 m^2/s, gravity (g) = 9.9000 m/s^2, flow depth (y) = 1.3000 m.

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

5. Step 5 — Evaluate:

   M = 1.5917\ \text{m^2}

6. Step 6 — Check: returning M = 1.5917 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 3.1834 — kept a factor of two that cancels in the correct rearrangement.
• 0.7958 — dropped that same factor in the other direction.
• 1.7509 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram used to locate conjugate depths of a hydraulic jump Given unit discharge (q) = 4.0500 m^2/s; gravity (g) = 9.9000 m/s^2; flow depth (y) = 2.4000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 4.0500 m^2/s, gravity (g) = 9.9000 m/s^2, flow depth (y) = 2.4000 m.

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

5. Step 5 — Evaluate:

   M = 3.5703\ \text{m^2}

6. Step 6 — Check: returning M = 3.5703 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 7.1407 — kept a factor of two that cancels in the correct rearrangement.
• 1.7852 — dropped that same factor in the other direction.
• 3.9274 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

the momentum-depth diagram for flow in a rectangular open channel Given unit discharge (q) = 0.6500 m^2/s; gravity (g) = 9.8500 m/s^2; flow depth (y) = 1.0000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 0.6500 m^2/s, gravity (g) = 9.8500 m/s^2, flow depth (y) = 1.0000 m.

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

5. Step 5 — Evaluate:

   M = 0.5429\ \text{m^2}

6. Step 6 — Check: returning M = 0.5429 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 1.0858 — kept a factor of two that cancels in the correct rearrangement.
• 0.2714 — dropped that same factor in the other direction.
• 0.5972 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram analysis at a stilling basin Given unit discharge (q) = 4.1500 m^2/s; gravity (g) = 9.8100 m/s^2; flow depth (y) = 1.1000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 4.1500 m^2/s, gravity (g) = 9.8100 m/s^2, flow depth (y) = 1.1000 m.

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

5. Step 5 — Evaluate:

   M = 2.2010\ \text{m^2}

6. Step 6 — Check: returning M = 2.2010 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 4.4020 — kept a factor of two that cancels in the correct rearrangement.
• 1.1005 — dropped that same factor in the other direction.
• 2.4211 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram

a momentum-depth diagram used to locate conjugate depths of a hydraulic jump Given unit discharge (q) = 3.4000 m^2/s; gravity (g) = 9.7400 m/s^2; flow depth (y) = 1.3000 m, determine the specific force (momentum function) (M) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Momentum Depth Diagram (specific force).
• Everything except M is given, so isolate M 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 momentum-depth diagram plots specific force against depth to find conjugate depths across a hydraulic jump.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

3. Step 3 — List the givens: unit discharge (q) = 3.4000 m^2/s, gravity (g) = 9.7400 m/s^2, flow depth (y) = 1.3000 m.

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

5. Step 5 — Evaluate:

   M = 1.7580\ \text{m^2}

6. Step 6 — Check: returning M = 1.7580 m^2 to

   $$M = \dfrac{q^2}{g y} + \dfrac{y^2}{2}$$

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

Why the other options are there

• 3.5159 — kept a factor of two that cancels in the correct rearrangement.
• 0.8790 — dropped that same factor in the other direction.
• 1.9338 — rounded an intermediate value before the final step.

Reference: FE Handbook — Momentum Depth Diagram