similitude between a spillway model and prototype dam Given prototype velocity (V_p) = 5.6000 m/s; prototype length (L_p) = 31.0000 m; model length (L_m) = 1.0000 m, determine the model velocity (V_m) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_m is given, so isolate V_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 5.6000 m/s, prototype length (L_p) = 31.0000 m, model length (L_m) = 1.0000 m.

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

5. Step 5 — Evaluate:

   $$V_{m} = 1.0058\ \text{m/s}$$

6. Step 6 — Check: returning V_m = 1.0058 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 2.0116 — kept a factor of two that cancels in the correct rearrangement.
• 0.5029 — dropped that same factor in the other direction.
• 1.1064 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude used in a ship-hull towing tank model Given prototype length (L_p) = 47.0000 m; model length (L_m) = 1.3500 m; model velocity (V_m) = 1.5500 m/s, determine the prototype velocity (V_p) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_p is given, so isolate V_p 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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype length (L_p) = 47.0000 m, model length (L_m) = 1.3500 m, model velocity (V_m) = 1.5500 m/s.

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

5. Step 5 — Evaluate:

   $$V_{p} = 9.1456\ \text{m/s}$$

6. Step 6 — Check: returning V_p = 9.1456 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 18.2913 — kept a factor of two that cancels in the correct rearrangement.
• 4.5728 — dropped that same factor in the other direction.
• 10.0602 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude scaling of a scale-model open-channel structure Given prototype velocity (V_p) = 5.5000 m/s; prototype length (L_p) = 11.0000 m; model velocity (V_m) = 3.4000 m/s, determine the model length (L_m) in m.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except L_m is given, so isolate L_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 5.5000 m/s, prototype length (L_p) = 11.0000 m, model velocity (V_m) = 3.4000 m/s.

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

5. Step 5 — Evaluate:

   $$L_{m} = 4.2036\ \text{m}$$

6. Step 6 — Check: returning L_m = 4.2036 m to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 8.4073 — kept a factor of two that cancels in the correct rearrangement.
• 2.1018 — dropped that same factor in the other direction.
• 4.6240 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude between a spillway model and prototype dam Given prototype velocity (V_p) = 4.0000 m/s; prototype length (L_p) = 25.0000 m; model length (L_m) = 0.4000 m, determine the model velocity (V_m) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_m is given, so isolate V_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 4.0000 m/s, prototype length (L_p) = 25.0000 m, model length (L_m) = 0.4000 m.

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

5. Step 5 — Evaluate:

   $$V_{m} = 0.5060\ \text{m/s}$$

6. Step 6 — Check: returning V_m = 0.5060 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 1.0119 — kept a factor of two that cancels in the correct rearrangement.
• 0.2530 — dropped that same factor in the other direction.
• 0.5566 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude used in a ship-hull towing tank model Given prototype length (L_p) = 41.0000 m; model length (L_m) = 1.2000 m; model velocity (V_m) = 0.6500 m/s, determine the prototype velocity (V_p) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_p is given, so isolate V_p 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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype length (L_p) = 41.0000 m, model length (L_m) = 1.2000 m, model velocity (V_m) = 0.6500 m/s.

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

5. Step 5 — Evaluate:

   $$V_{p} = 3.7994\ \text{m/s}$$

6. Step 6 — Check: returning V_p = 3.7994 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 7.5988 — kept a factor of two that cancels in the correct rearrangement.
• 1.8997 — dropped that same factor in the other direction.
• 4.1793 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude scaling of a scale-model open-channel structure Given prototype velocity (V_p) = 2.8000 m/s; prototype length (L_p) = 30.0000 m; model velocity (V_m) = 0.6000 m/s, determine the model length (L_m) in m.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except L_m is given, so isolate L_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 2.8000 m/s, prototype length (L_p) = 30.0000 m, model velocity (V_m) = 0.6000 m/s.

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

5. Step 5 — Evaluate:

   $$L_{m} = 1.3776\ \text{m}$$

6. Step 6 — Check: returning L_m = 1.3776 m to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 2.7551 — kept a factor of two that cancels in the correct rearrangement.
• 0.6888 — dropped that same factor in the other direction.
• 1.5153 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude between a spillway model and prototype dam Given prototype velocity (V_p) = 2.1000 m/s; prototype length (L_p) = 14.0000 m; model length (L_m) = 1.8000 m, determine the model velocity (V_m) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_m is given, so isolate V_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 2.1000 m/s, prototype length (L_p) = 14.0000 m, model length (L_m) = 1.8000 m.

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

5. Step 5 — Evaluate:

   $$V_{m} = 0.7530\ \text{m/s}$$

6. Step 6 — Check: returning V_m = 0.7530 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 1.5060 — kept a factor of two that cancels in the correct rearrangement.
• 0.3765 — dropped that same factor in the other direction.
• 0.8283 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude used in a ship-hull towing tank model Given prototype length (L_p) = 10.0000 m; model length (L_m) = 0.9000 m; model velocity (V_m) = 3.1000 m/s, determine the prototype velocity (V_p) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_p is given, so isolate V_p 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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype length (L_p) = 10.0000 m, model length (L_m) = 0.9000 m, model velocity (V_m) = 3.1000 m/s.

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

5. Step 5 — Evaluate:

   $$V_{p} = 10.3333\ \text{m/s}$$

6. Step 6 — Check: returning V_p = 10.3333 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 20.6667 — kept a factor of two that cancels in the correct rearrangement.
• 5.1667 — dropped that same factor in the other direction.
• 11.3667 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude scaling of a scale-model open-channel structure Given prototype velocity (V_p) = 2.5000 m/s; prototype length (L_p) = 28.0000 m; model velocity (V_m) = 2.2000 m/s, determine the model length (L_m) in m.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except L_m is given, so isolate L_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 2.5000 m/s, prototype length (L_p) = 28.0000 m, model velocity (V_m) = 2.2000 m/s.

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

5. Step 5 — Evaluate:

   $$L_{m} = 21.6832\ \text{m}$$

6. Step 6 — Check: returning L_m = 21.6832 m to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 43.3664 — kept a factor of two that cancels in the correct rearrangement.
• 10.8416 — dropped that same factor in the other direction.
• 23.8515 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude

similitude between a spillway model and prototype dam Given prototype velocity (V_p) = 8.1000 m/s; prototype length (L_p) = 46.0000 m; model length (L_m) = 1.9500 m, determine the model velocity (V_m) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Similitude (Froude number scaling).
• Everything except V_m is given, so isolate V_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.
• Similitude between a scale model and its prototype is maintained by matching the Froude number.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

3. Step 3 — List the givens: prototype velocity (V_p) = 8.1000 m/s, prototype length (L_p) = 46.0000 m, model length (L_m) = 1.9500 m.

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

5. Step 5 — Evaluate:

   $$V_{m} = 1.6677\ \text{m/s}$$

6. Step 6 — Check: returning V_m = 1.6677 m/s to

   $$\dfrac{V_m}{\sqrt{g L_m}} = \dfrac{V_p}{\sqrt{g L_p}}$$

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

Why the other options are there

• 3.3354 — kept a factor of two that cancels in the correct rearrangement.
• 0.8339 — dropped that same factor in the other direction.
• 1.8345 — rounded an intermediate value before the final step.

Reference: FE Handbook — Similitude