atmospheric dispersion modeling of a Gaussian plume from a power plant stack Given emission rate (Q) = 97.0000 g/s; wind speed (u) = 6.2000 m/s; horizontal dispersion coeff (sigma_y) = 73.0000 m; vertical dispersion coeff (sigma_z) = 29.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m, determine the centerline ground concentration (C) in g/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except C is given, so isolate C 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 97.0000 g/s, wind speed (u) = 6.2000 m/s, horizontal dispersion coeff (sigma_y) = 73.0000 m, vertical dispersion coeff (sigma_z) = 29.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m.

4. Step 4 — Substitute the given values:

   $$C = \dfrac{97.0000}{2\pi 6.2000 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   C = 0.0012\ \text{g/m^3}

6. Step 6 — Check: returning C = 0.0012 g/m^3 to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0024 — kept a factor of two that cancels in the correct rearrangement.
• 0.0006 — dropped that same factor in the other direction.
• 0.0013 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

Gaussian dispersion model for a chemical plant emission source Given wind speed (u) = 9.6000 m/s; horizontal dispersion coeff (sigma_y) = 299.0 m; vertical dispersion coeff (sigma_z) = 115.0 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.9293 g/m^3, determine the emission rate (Q) in g/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except Q is given, so isolate Q 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = C\,2\pi u \sigma_y \sigma_z$$

3. Step 3 — List the givens: wind speed (u) = 9.6000 m/s, horizontal dispersion coeff (sigma_y) = 299.0 m, vertical dispersion coeff (sigma_z) = 115.0 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.9293 g/m^3.

4. Step 4 — Substitute the given values:

   $$Q = 0.9293\,2\pi 9.6000 \sigma_0.0000 \sigma_z$$

5. Step 5 — Evaluate:

   $$Q = 1927506\ \text{g/s}$$

6. Step 6 — Check: returning Q = 1,927,506 g/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 3,855,012 — kept a factor of two that cancels in the correct rearrangement.
• 963,753 — dropped that same factor in the other direction.
• 2,120,256 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion Gaussian plume centerline concentration downwind Given emission rate (Q) = 80.0000 g/s; horizontal dispersion coeff (sigma_y) = 98.0000 m; vertical dispersion coeff (sigma_z) = 85.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.9756 g/m^3, determine the wind speed (u) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except u is given, so isolate u 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for u:

   $$u = \dfrac{Q}{2\pi C \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 80.0000 g/s, horizontal dispersion coeff (sigma_y) = 98.0000 m, vertical dispersion coeff (sigma_z) = 85.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.9756 g/m^3.

4. Step 4 — Substitute the given values:

   $$u = \dfrac{80.0000}{2\pi 0.9756 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   $$u = 0.0016\ \text{m/s}$$

6. Step 6 — Check: returning u = 0.0016 m/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0031 — kept a factor of two that cancels in the correct rearrangement.
• 0.0008 — dropped that same factor in the other direction.
• 0.0017 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion modeling of a Gaussian plume from a power plant stack Given emission rate (Q) = 78.0000 g/s; wind speed (u) = 8.6000 m/s; horizontal dispersion coeff (sigma_y) = 238.0 m; vertical dispersion coeff (sigma_z) = 43.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m, determine the centerline ground concentration (C) in g/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except C is given, so isolate C 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 78.0000 g/s, wind speed (u) = 8.6000 m/s, horizontal dispersion coeff (sigma_y) = 238.0 m, vertical dispersion coeff (sigma_z) = 43.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m.

4. Step 4 — Substitute the given values:

   $$C = \dfrac{78.0000}{2\pi 8.6000 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   C = 0.0001\ \text{g/m^3}

6. Step 6 — Check: returning C = 0.0001 g/m^3 to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0003 — kept a factor of two that cancels in the correct rearrangement.
• 0.0001 — dropped that same factor in the other direction.
• 0.0002 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

Gaussian dispersion model for a chemical plant emission source Given wind speed (u) = 4.6000 m/s; horizontal dispersion coeff (sigma_y) = 61.0000 m; vertical dispersion coeff (sigma_z) = 39.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.1419 g/m^3, determine the emission rate (Q) in g/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except Q is given, so isolate Q 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = C\,2\pi u \sigma_y \sigma_z$$

3. Step 3 — List the givens: wind speed (u) = 4.6000 m/s, horizontal dispersion coeff (sigma_y) = 61.0000 m, vertical dispersion coeff (sigma_z) = 39.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.1419 g/m^3.

4. Step 4 — Substitute the given values:

   $$Q = 0.1419\,2\pi 4.6000 \sigma_0.0000 \sigma_z$$

5. Step 5 — Evaluate:

   $$Q = 9758\ \text{g/s}$$

6. Step 6 — Check: returning Q = 9,758 g/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 19,515 — kept a factor of two that cancels in the correct rearrangement.
• 4,879 — dropped that same factor in the other direction.
• 10,733 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion Gaussian plume centerline concentration downwind Given emission rate (Q) = 175.0 g/s; horizontal dispersion coeff (sigma_y) = 50.0000 m; vertical dispersion coeff (sigma_z) = 49.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.9013 g/m^3, determine the wind speed (u) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except u is given, so isolate u 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for u:

   $$u = \dfrac{Q}{2\pi C \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 175.0 g/s, horizontal dispersion coeff (sigma_y) = 50.0000 m, vertical dispersion coeff (sigma_z) = 49.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.9013 g/m^3.

4. Step 4 — Substitute the given values:

   $$u = \dfrac{175.0}{2\pi 0.9013 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   $$u = 0.0126\ \text{m/s}$$

6. Step 6 — Check: returning u = 0.0126 m/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0252 — kept a factor of two that cancels in the correct rearrangement.
• 0.0063 — dropped that same factor in the other direction.
• 0.0139 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion modeling of a Gaussian plume from a power plant stack Given emission rate (Q) = 57.0000 g/s; wind speed (u) = 8.6000 m/s; horizontal dispersion coeff (sigma_y) = 93.0000 m; vertical dispersion coeff (sigma_z) = 103.0 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m, determine the centerline ground concentration (C) in g/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except C is given, so isolate C 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 57.0000 g/s, wind speed (u) = 8.6000 m/s, horizontal dispersion coeff (sigma_y) = 93.0000 m, vertical dispersion coeff (sigma_z) = 103.0 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m.

4. Step 4 — Substitute the given values:

   $$C = \dfrac{57.0000}{2\pi 8.6000 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   C = 0.0001\ \text{g/m^3}

6. Step 6 — Check: returning C = 0.0001 g/m^3 to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0002 — kept a factor of two that cancels in the correct rearrangement.
• 0.0001 — dropped that same factor in the other direction.
• 0.0001 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

Gaussian dispersion model for a chemical plant emission source Given wind speed (u) = 4.1000 m/s; horizontal dispersion coeff (sigma_y) = 41.0000 m; vertical dispersion coeff (sigma_z) = 23.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.4548 g/m^3, determine the emission rate (Q) in g/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except Q is given, so isolate Q 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for Q:

   $$Q = C\,2\pi u \sigma_y \sigma_z$$

3. Step 3 — List the givens: wind speed (u) = 4.1000 m/s, horizontal dispersion coeff (sigma_y) = 41.0000 m, vertical dispersion coeff (sigma_z) = 23.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.4548 g/m^3.

4. Step 4 — Substitute the given values:

   $$Q = 0.4548\,2\pi 4.1000 \sigma_0.0000 \sigma_z$$

5. Step 5 — Evaluate:

   $$Q = 11049\ \text{g/s}$$

6. Step 6 — Check: returning Q = 11,049 g/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 22,098 — kept a factor of two that cancels in the correct rearrangement.
• 5,525 — dropped that same factor in the other direction.
• 12,154 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion Gaussian plume centerline concentration downwind Given emission rate (Q) = 31.0000 g/s; horizontal dispersion coeff (sigma_y) = 212.0 m; vertical dispersion coeff (sigma_z) = 132.0 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m; centerline ground concentration (C) = 0.6298 g/m^3, determine the wind speed (u) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except u is given, so isolate u 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for u:

   $$u = \dfrac{Q}{2\pi C \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 31.0000 g/s, horizontal dispersion coeff (sigma_y) = 212.0 m, vertical dispersion coeff (sigma_z) = 132.0 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m, centerline ground concentration (C) = 0.6298 g/m^3.

4. Step 4 — Substitute the given values:

   $$u = \dfrac{31.0000}{2\pi 0.6298 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   $$u = 0.0003\ \text{m/s}$$

6. Step 6 — Check: returning u = 0.0003 m/s to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0006 — kept a factor of two that cancels in the correct rearrangement.
• 0.0001 — dropped that same factor in the other direction.
• 0.0003 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling

atmospheric dispersion modeling of a Gaussian plume from a power plant stack Given emission rate (Q) = 192.0 g/s; wind speed (u) = 5.5000 m/s; horizontal dispersion coeff (sigma_y) = 28.0000 m; vertical dispersion coeff (sigma_z) = 47.0000 m; crosswind distance (y) = 0.0000 m; effective stack height (H) = 0.0000 m, determine the centerline ground concentration (C) in g/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Atmospheric Dispersion Modeling (Gaussian).
• Everything except C is given, so isolate C 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.
• Atmospheric dispersion modeling with the Gaussian plume equation estimates ground-level concentration downwind of a stack.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

2. Step 2 — Rearrange symbolically for C:

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z}$$

3. Step 3 — List the givens: emission rate (Q) = 192.0 g/s, wind speed (u) = 5.5000 m/s, horizontal dispersion coeff (sigma_y) = 28.0000 m, vertical dispersion coeff (sigma_z) = 47.0000 m, crosswind distance (y) = 0.0000 m, effective stack height (H) = 0.0000 m.

4. Step 4 — Substitute the given values:

   $$C = \dfrac{192.0}{2\pi 5.5000 \sigma_0.0000 \sigma_z}$$

5. Step 5 — Evaluate:

   C = 0.0042\ \text{g/m^3}

6. Step 6 — Check: returning C = 0.0042 g/m^3 to

   $$C = \dfrac{Q}{2\pi u \sigma_y \sigma_z} e^{-\frac{y^2}{2\sigma_y^2}} e^{-\frac{H^2}{2\sigma_z^2}}$$

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

Why the other options are there

• 0.0084 — kept a factor of two that cancels in the correct rearrangement.
• 0.0021 — dropped that same factor in the other direction.
• 0.0046 — rounded an intermediate value before the final step.

Reference: FE Handbook — Atmospheric Dispersion Modeling