the drag force on a sphere settling through a fluid Given drag coefficient (C_D) = 0.5300; fluid density (rho) = 1,152 kg/m^3; relative velocity (V) = 4.0000 m/s; frontal area (A) = 2.3500 m^2, determine the drag force (F_D) in N.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except F_D is given, so isolate F_D 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.5300, fluid density (rho) = 1,152 kg/m^3, relative velocity (V) = 4.0000 m/s, frontal area (A) = 2.3500 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 11479\ \text{N}$$

6. Step 6 — Check: returning F_D = 11,479 N to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 22,957 — kept a factor of two that cancels in the correct rearrangement.
• 5,739 — dropped that same factor in the other direction.
• 12,626 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on an automobile modeled with a drag coefficient Given drag coefficient (C_D) = 0.2500; fluid density (rho) = 1,081 kg/m^3; frontal area (A) = 4.6500 m^2; drag force (F_D) = 14,843 N, determine the relative velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.2500, fluid density (rho) = 1,081 kg/m^3, frontal area (A) = 4.6500 m^2, drag force (F_D) = 14,843 N.

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

5. Step 5 — Evaluate:

   $$V = 4.8603\ \text{m/s}$$

6. Step 6 — Check: returning V = 4.8603 m/s to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 9.7207 — kept a factor of two that cancels in the correct rearrangement.
• 2.4302 — dropped that same factor in the other direction.
• 5.3464 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a piling exposed to river flow Given drag coefficient (C_D) = 0.4100; fluid density (rho) = 453.0 kg/m^3; relative velocity (V) = 15.5000 m/s; drag force (F_D) = 9,856 N, determine the frontal area (A) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except A is given, so isolate A 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.4100, fluid density (rho) = 453.0 kg/m^3, relative velocity (V) = 15.5000 m/s, drag force (F_D) = 9,856 N.

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

5. Step 5 — Evaluate:

   A = 0.4418\ \text{m^2}

6. Step 6 — Check: returning A = 0.4418 m^2 to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 0.8835 — kept a factor of two that cancels in the correct rearrangement.
• 0.2209 — dropped that same factor in the other direction.
• 0.4859 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a sphere settling through a fluid Given drag coefficient (C_D) = 0.6400; fluid density (rho) = 17.0000 kg/m^3; relative velocity (V) = 28.0000 m/s; frontal area (A) = 2.4500 m^2, determine the drag force (F_D) in N.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except F_D is given, so isolate F_D 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.6400, fluid density (rho) = 17.0000 kg/m^3, relative velocity (V) = 28.0000 m/s, frontal area (A) = 2.4500 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 10449\ \text{N}$$

6. Step 6 — Check: returning F_D = 10,449 N to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 20,898 — kept a factor of two that cancels in the correct rearrangement.
• 5,225 — dropped that same factor in the other direction.
• 11,494 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on an automobile modeled with a drag coefficient Given drag coefficient (C_D) = 0.3400; fluid density (rho) = 703.0 kg/m^3; frontal area (A) = 4.1500 m^2; drag force (F_D) = 11,156 N, determine the relative velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.3400, fluid density (rho) = 703.0 kg/m^3, frontal area (A) = 4.1500 m^2, drag force (F_D) = 11,156 N.

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

5. Step 5 — Evaluate:

   $$V = 4.7427\ \text{m/s}$$

6. Step 6 — Check: returning V = 4.7427 m/s to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 9.4855 — kept a factor of two that cancels in the correct rearrangement.
• 2.3714 — dropped that same factor in the other direction.
• 5.2170 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a piling exposed to river flow Given drag coefficient (C_D) = 0.4500; fluid density (rho) = 1,156 kg/m^3; relative velocity (V) = 2.0000 m/s; drag force (F_D) = 14,883 N, determine the frontal area (A) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except A is given, so isolate A 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.4500, fluid density (rho) = 1,156 kg/m^3, relative velocity (V) = 2.0000 m/s, drag force (F_D) = 14,883 N.

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

5. Step 5 — Evaluate:

   A = 14.3051\ \text{m^2}

6. Step 6 — Check: returning A = 14.3051 m^2 to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 28.6101 — kept a factor of two that cancels in the correct rearrangement.
• 7.1525 — dropped that same factor in the other direction.
• 15.7356 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a sphere settling through a fluid Given drag coefficient (C_D) = 0.1100; fluid density (rho) = 699.0 kg/m^3; relative velocity (V) = 6.0000 m/s; frontal area (A) = 0.4000 m^2, determine the drag force (F_D) in N.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except F_D is given, so isolate F_D 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.1100, fluid density (rho) = 699.0 kg/m^3, relative velocity (V) = 6.0000 m/s, frontal area (A) = 0.4000 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 553.6\ \text{N}$$

6. Step 6 — Check: returning F_D = 553.6 N to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 1,107 — kept a factor of two that cancels in the correct rearrangement.
• 276.8 — dropped that same factor in the other direction.
• 609.0 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on an automobile modeled with a drag coefficient Given drag coefficient (C_D) = 0.5900; fluid density (rho) = 446.0 kg/m^3; frontal area (A) = 2.2000 m^2; drag force (F_D) = 14,001 N, determine the relative velocity (V) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 0.5900, fluid density (rho) = 446.0 kg/m^3, frontal area (A) = 2.2000 m^2, drag force (F_D) = 14,001 N.

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

5. Step 5 — Evaluate:

   $$V = 6.9549\ \text{m/s}$$

6. Step 6 — Check: returning V = 6.9549 m/s to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 13.9098 — kept a factor of two that cancels in the correct rearrangement.
• 3.4774 — dropped that same factor in the other direction.
• 7.6504 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a piling exposed to river flow Given drag coefficient (C_D) = 1.0800; fluid density (rho) = 698.0 kg/m^3; relative velocity (V) = 15.5000 m/s; drag force (F_D) = 4,326 N, determine the frontal area (A) in m^2.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except A is given, so isolate A 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 1.0800, fluid density (rho) = 698.0 kg/m^3, relative velocity (V) = 15.5000 m/s, drag force (F_D) = 4,326 N.

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

5. Step 5 — Evaluate:

   A = 0.0478\ \text{m^2}

6. Step 6 — Check: returning A = 0.0478 m^2 to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 0.0955 — kept a factor of two that cancels in the correct rearrangement.
• 0.0239 — dropped that same factor in the other direction.
• 0.0525 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force

the drag force on a sphere settling through a fluid Given drag coefficient (C_D) = 1.1400; fluid density (rho) = 559.0 kg/m^3; relative velocity (V) = 22.0000 m/s; frontal area (A) = 3.2500 m^2, determine the drag force (F_D) in N.

Start with the thinking

• The governing relation printed in this handbook section is Drag force.
• Everything except F_D is given, so isolate F_D 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 drag force on a body moving through a fluid depends on the drag coefficient, velocity, and frontal area.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

3. Step 3 — List the givens: drag coefficient (C_D) = 1.1400, fluid density (rho) = 559.0 kg/m^3, relative velocity (V) = 22.0000 m/s, frontal area (A) = 3.2500 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 501205\ \text{N}$$

6. Step 6 — Check: returning F_D = 501,205 N to

   $$F_D = C_D \dfrac{\rho V^2}{2} A$$

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

Why the other options are there

• 1,002,410 — kept a factor of two that cancels in the correct rearrangement.
• 250,602 — dropped that same factor in the other direction.
• 551,325 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force