the drag force on a sphere settling through a fluid Given drag coefficient (C_D) = 0.4900; fluid density (rho) = 443.0 kg/m^3; relative velocity (V) = 19.5000 m/s; frontal area (A) = 3.7500 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) = 0.4900, fluid density (rho) = 443.0 kg/m^3, relative velocity (V) = 19.5000 m/s, frontal area (A) = 3.7500 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 154764\ \text{N}$$

6. Step 6 — Check: returning F_D = 154,764 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

• 309,528 — kept a factor of two that cancels in the correct rearrangement.
• 77,382 — dropped that same factor in the other direction.
• 170,241 — 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) = 0.5700; fluid density (rho) = 802.0 kg/m^3; frontal area (A) = 0.8000 m^2; drag force (F_D) = 18,810 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) = 0.5700, fluid density (rho) = 802.0 kg/m^3, frontal area (A) = 0.8000 m^2, drag force (F_D) = 18,810 N.

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

5. Step 5 — Evaluate:

   $$V = 10.1424\ \text{m/s}$$

6. Step 6 — Check: returning V = 10.1424 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

• 20.2848 — kept a factor of two that cancels in the correct rearrangement.
• 5.0712 — dropped that same factor in the other direction.
• 11.1566 — 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) = 1.1700; fluid density (rho) = 7.0000 kg/m^3; relative velocity (V) = 15.5000 m/s; drag force (F_D) = 1,046 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) = 1.1700, fluid density (rho) = 7.0000 kg/m^3, relative velocity (V) = 15.5000 m/s, drag force (F_D) = 1,046 N.

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

5. Step 5 — Evaluate:

   A = 1.0632\ \text{m^2}

6. Step 6 — Check: returning A = 1.0632 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

• 2.1264 — kept a factor of two that cancels in the correct rearrangement.
• 0.5316 — dropped that same factor in the other direction.
• 1.1695 — 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) = 0.6600; fluid density (rho) = 457.0 kg/m^3; relative velocity (V) = 6.0000 m/s; frontal area (A) = 0.6000 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) = 0.6600, fluid density (rho) = 457.0 kg/m^3, relative velocity (V) = 6.0000 m/s, frontal area (A) = 0.6000 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 3257\ \text{N}$$

6. Step 6 — Check: returning F_D = 3,257 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

• 6,515 — kept a factor of two that cancels in the correct rearrangement.
• 1,629 — dropped that same factor in the other direction.
• 3,583 — 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) = 0.4100; fluid density (rho) = 42.0000 kg/m^3; frontal area (A) = 4.9000 m^2; drag force (F_D) = 4,866 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) = 0.4100, fluid density (rho) = 42.0000 kg/m^3, frontal area (A) = 4.9000 m^2, drag force (F_D) = 4,866 N.

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

5. Step 5 — Evaluate:

   $$V = 10.7396\ \text{m/s}$$

6. Step 6 — Check: returning V = 10.7396 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

• 21.4791 — kept a factor of two that cancels in the correct rearrangement.
• 5.3698 — dropped that same factor in the other direction.
• 11.8135 — 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) = 0.6800; fluid density (rho) = 245.0 kg/m^3; relative velocity (V) = 20.5000 m/s; drag force (F_D) = 13,394 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) = 0.6800, fluid density (rho) = 245.0 kg/m^3, relative velocity (V) = 20.5000 m/s, drag force (F_D) = 13,394 N.

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

5. Step 5 — Evaluate:

   A = 0.3826\ \text{m^2}

6. Step 6 — Check: returning A = 0.3826 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

• 0.7652 — kept a factor of two that cancels in the correct rearrangement.
• 0.1913 — dropped that same factor in the other direction.
• 0.4209 — 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) = 1.0000; fluid density (rho) = 950.0 kg/m^3; relative velocity (V) = 15.5000 m/s; frontal area (A) = 2.9000 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) = 1.0000, fluid density (rho) = 950.0 kg/m^3, relative velocity (V) = 15.5000 m/s, frontal area (A) = 2.9000 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 330944\ \text{N}$$

6. Step 6 — Check: returning F_D = 330,944 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

• 661,889 — kept a factor of two that cancels in the correct rearrangement.
• 165,472 — dropped that same factor in the other direction.
• 364,039 — 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) = 0.3200; fluid density (rho) = 846.0 kg/m^3; frontal area (A) = 1.1500 m^2; drag force (F_D) = 17,578 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) = 0.3200, fluid density (rho) = 846.0 kg/m^3, frontal area (A) = 1.1500 m^2, drag force (F_D) = 17,578 N.

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

5. Step 5 — Evaluate:

   $$V = 10.6265\ \text{m/s}$$

6. Step 6 — Check: returning V = 10.6265 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

• 21.2530 — kept a factor of two that cancels in the correct rearrangement.
• 5.3133 — dropped that same factor in the other direction.
• 11.6892 — 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) = 0.7400; fluid density (rho) = 849.0 kg/m^3; relative velocity (V) = 17.0000 m/s; drag force (F_D) = 8,523 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) = 0.7400, fluid density (rho) = 849.0 kg/m^3, relative velocity (V) = 17.0000 m/s, drag force (F_D) = 8,523 N.

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

5. Step 5 — Evaluate:

   A = 0.0939\ \text{m^2}

6. Step 6 — Check: returning A = 0.0939 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

• 0.1878 — kept a factor of two that cancels in the correct rearrangement.
• 0.0469 — dropped that same factor in the other direction.
• 0.1033 — 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) = 0.2800; fluid density (rho) = 805.0 kg/m^3; relative velocity (V) = 6.5000 m/s; frontal area (A) = 2.9000 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) = 0.2800, fluid density (rho) = 805.0 kg/m^3, relative velocity (V) = 6.5000 m/s, frontal area (A) = 2.9000 m^2.

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

5. Step 5 — Evaluate:

   $$F_{D} = 13809\ \text{N}$$

6. Step 6 — Check: returning F_D = 13,809 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

• 27,617 — kept a factor of two that cancels in the correct rearrangement.
• 6,904 — dropped that same factor in the other direction.
• 15,189 — rounded an intermediate value before the final step.

Reference: FE Handbook — Drag Force