Plume Behaviour and Stack Design Questions and Answers

Q: An effective stack height of \( 120 \) m is needed. If plume rise is \( 40 \) m, the physical stack must be

Correct answer: 80 mEffective height is physical height plus plume rise:\[ H_e = h_s + \Delta h \quad\Rightarrow\quad h_s = 120 - 40 = 80\ \text{m} \]The 40 m of rise is worth 40 m of steelwork, which is why raising exit velocity or gas temperature is often cheaper than building higher.

Q: A stack passes \( 62 \) m\(^3\)/s at \( 18 \) m/s. Its diameter is

Correct answer: 2.09 m\[ A = \frac{Q}{v} = \frac{62}{18} = 3.44\ \text{m}^2 \]\[ d = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4 \times 3.44}{\pi}} = \sqrt{4.38} = 2.09\ \text{m} \]

Q: A plume rise of \( 45 \) m is calculated at a wind speed of \( 4 \) m/s. If rise varies inversely with wind speed, at \( 8 \) m/s it becomes

Correct answer: 22.5 mPlume rise varies inversely with wind speed, so doubling the wind halves the rise:\[ \Delta h_2 = 45 \times \frac{4}{8} = 22.5\ \text{m} \]Physically, a stronger wind bends the plume over and carries it downwind before buoyancy can lift it.

Q: The maximum ground level concentration occurs at \( 1.2 \) km with an effective height of \( 90 \) m. Raising the effective height to \( 135 \) m moves it, other things equal, to roughly

Correct answer: A greater distance downwindA plume released higher must spread further vertically before its edge reaches the ground, and the vertical dispersion coefficient grows with distance - so the point of maximum ground-level concentration moves further downwind, and the maximum itself is lower.

Q: A building \( 24 \) m high and \( 60 \) m wide requires a good engineering practice stack height of

Correct answer: 60 mHere the lesser dimension is the height, 24 m, not the 60 m width:\[ H_{GEP} = 24 + 1.5 \times 24 = 60\ \text{m} \]The 60 m width is the distractor - it is the larger dimension and plays no part.

41.

An effective stack height of \( 120 \) m is needed. If plume rise is \( 40 \) m, the physical stack must be

A.40 m
B.80 m
C.120 m
D.160 m

Answer: B

Correct answer: 80 m

Effective height is physical height plus plume rise:

\[ H_e = h_s + \Delta h \quad\Rightarrow\quad h_s = 120 - 40 = 80\ \text{m} \]

The 40 m of rise is worth 40 m of steelwork, which is why raising exit velocity or gas temperature is often cheaper than building higher.

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42.

A stack passes \( 62 \) m\(^3\)/s at \( 18 \) m/s. Its diameter is

A.1.05 m
B.4.18 m
C.2.09 m
D.3.44 m

Answer: C

Correct answer: 2.09 m

\[ A = \frac{Q}{v} = \frac{62}{18} = 3.44\ \text{m}^2 \]\[ d = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4 \times 3.44}{\pi}} = \sqrt{4.38} = 2.09\ \text{m} \]

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43.

A plume rise of \( 45 \) m is calculated at a wind speed of \( 4 \) m/s. If rise varies inversely with wind speed, at \( 8 \) m/s it becomes

A.90 m
B.45 m
C.11.3 m
D.22.5 m

Answer: D

Correct answer: 22.5 m

Plume rise varies inversely with wind speed, so doubling the wind halves the rise:

\[ \Delta h_2 = 45 \times \frac{4}{8} = 22.5\ \text{m} \]

Physically, a stronger wind bends the plume over and carries it downwind before buoyancy can lift it.

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44.

The maximum ground level concentration occurs at \( 1.2 \) km with an effective height of \( 90 \) m. Raising the effective height to \( 135 \) m moves it, other things equal, to roughly

A.A greater distance downwind
B.The same distance
C.A shorter distance
D.Directly at the stack

Answer: A

Correct answer: A greater distance downwind

A plume released higher must spread further vertically before its edge reaches the ground, and the vertical dispersion coefficient grows with distance - so the point of maximum ground-level concentration moves further downwind, and the maximum itself is lower.

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45.

A building \( 24 \) m high and \( 60 \) m wide requires a good engineering practice stack height of

A.24 m
B.60 m
C.114 m
D.84 m

Answer: B

Correct answer: 60 m

Here the lesser dimension is the height, 24 m, not the 60 m width:

\[ H_{GEP} = 24 + 1.5 \times 24 = 60\ \text{m} \]

The 60 m width is the distractor - it is the larger dimension and plays no part.

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46.

Statement I: A tall stack reduces the total mass of pollutant released.

Statement II: A tall stack releases the same mass where it will be diluted more before reaching anyone.

In the light of the above statements, choose the correct answer.

A.Both Statement I and Statement II are incorrect
B.Statement I is correct but Statement II is incorrect
C.Statement I is incorrect but Statement II is correct
D.Both Statement I and Statement II are correct

Answer: C

Correct answer: Statement I is incorrect but Statement II is correct

A tall stack changes where the pollutant goes, not how much is released - the mass emitted is exactly the same. What it buys is more atmosphere between the release and the nearest receptor, so the material is diluted further before anyone breathes it. That is why tall stacks relieve local concentrations while doing nothing for regional problems such as acid deposition.

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47.

Statement I: Exit velocity is specified above about one and a half times the wind speed.

Statement II: Below that ratio the plume is drawn into the low pressure wake immediately behind the stack.

In the light of the above statements, choose the correct answer.

A.Both Statement I and Statement II are incorrect
B.Statement I is correct but Statement II is incorrect
C.Statement I is incorrect but Statement II is correct
D.Both Statement I and Statement II are correct

Answer: D

Correct answer: Both Statement I and Statement II are correct

Statement II explains statement I. The wind separates round the stack and leaves a low-pressure wake immediately downwind; a plume leaving too slowly is drawn into it instead of rising, and the effective height collapses. Requiring an exit velocity of about 1.5 times the wind speed keeps the jet clear of that wake.

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48.

Statement I: Lofting is the most favourable of the classical plume types.

Statement II: A stable layer beneath the plume prevents downward mixing while unstable air above disperses it.

In the light of the above statements, choose the correct answer.

A.Both Statement I and Statement II are correct
B.Both Statement I and Statement II are incorrect
C.Statement I is correct but Statement II is incorrect
D.Statement I is incorrect but Statement II is correct

Answer: A

Correct answer: Both Statement I and Statement II are correct

Statement II is the reason for statement I. In lofting the stable layer beneath the plume blocks downward mixing while the unstable air above disperses it upward, so very little ever reaches the ground - which makes it the most favourable of the classical plume types.

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49.

Statement I: Reheating flue gas after a wet scrubber is done purely to raise plume rise.

Statement II: Cooled flue gas may fall below its acid dew point and condense sulphuric acid in the stack.

In the light of the above statements, choose the correct answer.

A.Statement I is correct but Statement II is incorrect
B.Statement I is incorrect but Statement II is correct
C.Both Statement I and Statement II are correct
D.Both Statement I and Statement II are incorrect

Answer: B

Correct answer: Statement I is incorrect but Statement II is correct

Reheat is done chiefly to keep the gas above its acid dew point, so that sulphuric acid does not condense in the stack and corrode it. Restoring some buoyant plume rise is a welcome by-product, not the purpose - and it would rarely justify the fuel cost on its own.

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50.

Statement I: Plume rise falls as wind speed increases.

Statement II: A stronger wind bends the plume over and carries it away before it can rise.

In the light of the above statements, choose the correct answer.

A.Statement I is correct but Statement II is incorrect
B.Statement I is incorrect but Statement II is correct
C.Both Statement I and Statement II are correct
D.Both Statement I and Statement II are incorrect

Answer: C

Correct answer: Both Statement I and Statement II are correct

Statement II gives the mechanism for statement I. A stronger wind bends the plume over and carries it downwind before buoyancy has time to lift it, so rise falls roughly as \(1/u\). This is why the worst ground-level concentrations often occur in moderate rather than light winds: the loss of plume rise outweighs the extra dilution.

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