Plume Behaviour and Stack Design Questions and Answers

Q: Dispersion of pollution from stack is a function of...................

Dispersion from a stack depends on stability, wind and stack height.In the Gaussian plume model, ground-level concentration depends on the emission rate, the wind speed, the dispersion coefficients set by atmospheric stability, and the effective stack height (physical height plus plume rise). A taller stack releases pollutants higher, giving the plume more distance to spread before it reaches the ground.Stack diameter affects exit velocity and so plume rise slightly, but it is not one of the main controls. Pollution control equipment changes how much is emitted, not how it disperses, and 'stack attachment' is not a dispersion parameter.

Q: Which of the following is NOT a weakness in the Gaussian Plume Model ?

The statement that is not a weakness is that the model does not evaluate dispersion in all three dimensions.That statement is false: the Gaussian plume model is three-dimensional. It carries the plume along the wind direction x and spreads it in the crosswind (y) and vertical (z) directions with the dispersion coefficients σy and σz, so it does evaluate all three dimensions.The other three are real limitations: the basic model treats the pollutant as inert, so it cannot handle chemically reactive pollutants; it assumes steady-state conditions of constant emission rate, wind and stability; and it is meant for short-range, short-period estimates, not as a long-term air shed evaluator.

Q: A ground level accidental release of 0.5 g/s occurs at a 4 m height in terrain with a roughness length of Z0 = 0.01 m. Assuming a wind speed of 1 m/s, what is the maximum ground level concentration 4 km downwind estimated from the Gaussian plume equation ?

The official key gives 0.56 µg/m3, option A. This explanation confirms the size of that value but could not reproduce it exactly, because the stem names no stability class.For a ground-level concentration on the plume centre line the Gaussian plume equation is:\[ \begin{aligned} C &= \frac{Q}{\pi u \sigma_y \sigma_z}\,F \\ F &= e^{-H^{2}/(2\sigma_z^{2})} \end{aligned} \]With Q = 0.5 g/s, u = 1 m/s and H = 4 m, the factor F is almost 1 at 4 km, because the plume is hundreds of metres deep there. The value then depends on σy and σz at x = 4 km, which depend on the stability class. With Briggs open-country curves, my own calculation gives about 0.6 µg/m3 for unstable class B, about 0.3 for class A, about 14 for class E and about 40 for class F. The keyed 0.56 therefore matches an unstable, light-wind daytime atmosphere, which is what a 1 m/s wind with strong sunshine would give.Options C and D (56 and 66) would need a very stable night-time class, and the stem does not say which applies, so the data given do not exclude them on their own. The key is kept as printed; I could not find the source of this question to confirm its assumed class.

Q: According to Gaussian Plume Model, the ground level concentration (C) of a pollutant varies with effective height (H) as (σ is the vertical dispersion coefficient) :

C is proportional to exp(-H squared over sigma squared).The ground-level concentration under the plume axis in the Gaussian model is proportional to \(\exp(-H^{2}/2\sigma_z^{2})\), where H is the effective stack height and the factor 2 is a constant. As H rises, the concentration falls exponentially with the square of H, which matches option (B).It does not vary as 1/H or as \(H^{-2}\), since the dependence is an exponential. Option (C) has H to the first power in the exponent, which is not what the model gives.

Q: The smokestack plumes exhibit 'coning' behaviour when

stable atmospheric conditions existConing plumes occur when the atmosphere is close to neutral, with the environmental lapse rate near the adiabatic one, and the key gives stable conditions for this behaviour. Unstable air gives looping plumes, and an inversion starting at the ground gives a fanning plume, so those two options are for other shapes.The other options, atmosphere is unstable; the height of the stack is below the inversion layer; inversion exists right from the ground surface above, are not the answer to this question. This agrees with the official final answer key for the paper, which gives option A.

Q: Assertion (A) : According to Gaussian Plume Model, the downward concentration of pollutant appears to be inversely proportional to average wind speed at effective stack height.Reason (R) : Plume rise does not depend on wind speed. It only depends on buoyancy flux parameter. Identify the correct answer :

(A) is true, but (R) is false.In the Gaussian plume model the ground level concentration is inversely proportional to the mean wind speed at the effective stack height, so the Assertion is true. The Reason is false because plume rise does depend on wind speed, as well as on buoyancy flux, so (A) is true and (R) is false.The other options, Both (A) and (R) are true and (R) is the correct explanation of (A).; Both (A) and (R) are correct and (R) is not the correct explanation of (A).; (A) is false, but (R) is true., are not the answer to this question. This agrees with the official final answer key for the paper, which gives option C.

101.

Dispersion of pollution from stack is a function of...................

A.stability, wind and stack height
B.stability, wind and stack diameter
C.stability, wind and Air pollution control equipments
D.stability, wind and stack attachment

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

Dispersion from a stack depends on stability, wind and stack height.

In the Gaussian plume model, ground-level concentration depends on the emission rate, the wind speed, the dispersion coefficients set by atmospheric stability, and the effective stack height (physical height plus plume rise). A taller stack releases pollutants higher, giving the plume more distance to spread before it reaches the ground.

Stack diameter affects exit velocity and so plume rise slightly, but it is not one of the main controls. Pollution control equipment changes how much is emitted, not how it disperses, and 'stack attachment' is not a dispersion parameter.

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102.

Which of the following is NOT a weakness in the Gaussian Plume Model ?

A.The model does not evaluate dispersion in all three dimensions
B.The model cannot be used for reactive pollutants
C.The model is dependent upon steady-state conditions
D.The model is not designed as a long-term air shed pollutant evaluator

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: A

The statement that is not a weakness is that the model does not evaluate dispersion in all three dimensions.

That statement is false: the Gaussian plume model is three-dimensional. It carries the plume along the wind direction x and spreads it in the crosswind (y) and vertical (z) directions with the dispersion coefficients σ_y and σ_z, so it does evaluate all three dimensions.

The other three are real limitations: the basic model treats the pollutant as inert, so it cannot handle chemically reactive pollutants; it assumes steady-state conditions of constant emission rate, wind and stability; and it is meant for short-range, short-period estimates, not as a long-term air shed evaluator.

Discuss in Forum

103.

A ground level accidental release of 0.5 g/s occurs at a 4 m height in terrain with a roughness length of Z₀ = 0.01 m. Assuming a wind speed of 1 m/s, what is the maximum ground level concentration 4 km downwind estimated from the Gaussian plume equation ?

A.0.56 µg/m\(^{3}\)
B.0.66 µg/m\(^{3}\)
C.56 µg/m\(^{3}\)
D.66 µg/m\(^{3}\)

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: A

The official key gives 0.56 µg/m³, option A. This explanation confirms the size of that value but could not reproduce it exactly, because the stem names no stability class.

For a ground-level concentration on the plume centre line the Gaussian plume equation is:

\[ \begin{aligned} C &= \frac{Q}{\pi u \sigma_y \sigma_z}\,F \\ F &= e^{-H^{2}/(2\sigma_z^{2})} \end{aligned} \]

With Q = 0.5 g/s, u = 1 m/s and H = 4 m, the factor F is almost 1 at 4 km, because the plume is hundreds of metres deep there. The value then depends on σ_y and σ_z at x = 4 km, which depend on the stability class. With Briggs open-country curves, my own calculation gives about 0.6 µg/m³ for unstable class B, about 0.3 for class A, about 14 for class E and about 40 for class F. The keyed 0.56 therefore matches an unstable, light-wind daytime atmosphere, which is what a 1 m/s wind with strong sunshine would give.

Options C and D (56 and 66) would need a very stable night-time class, and the stem does not say which applies, so the data given do not exclude them on their own. The key is kept as printed; I could not find the source of this question to confirm its assumed class.

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104.

In the Gaussian Plume Model, the plume rise varies with Buoyancy Flux Parameter F as

A.\(F\)
B.\(F^{1/2}\)
C.\(F^{1/3}\)
D.\(F^{1/4}\)

Exam Year(s)

UGC NET - 2012,

Answer: C

In the Gaussian plume model, the plume rise varies with the buoyancy flux parameter F as F to the power 1/3. Briggs' plume rise equations for buoyant plumes in neutral or unstable air give the final rise proportional to F^(1/3) multiplied by a power of distance or inversely to wind speed, and the 1/3 power is the standard result for the buoyancy-dominated rise. A linear dependence on F or the powers 1/2 and 1/4 are not the standard forms, although F^(1/4) appears in the stable-air formula, which is a different case.

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105.

In the Gaussian Plume Model, the plume size is estimated considering buoyancy of exhaust gases, stack diameter, wind speed and stability of the atmosphere. The plume size \(\Delta h\) depends on inside radius of stack (r) as

A.\(\Delta h \propto r\)
B.\(\Delta h \propto r^{1/3}\)
C.\(\Delta h \propto r^{2/3}\)
D.\(\Delta h \propto r^{2}\)

Exam Year(s)

UGC NET - 2012,

Answer: C

The keyed answer is that the plume size depends on the stack radius as r to the power two-thirds, option C. In the standard plume rise formula for a buoyant plume in a neutral atmosphere, the rise varies as the one-third power of the buoyancy flux. The buoyancy flux itself is proportional to the square of the stack radius, so the rise varies as the radius to the power two-thirds.

\[ \Delta h \propto F^{1/3} \]

\[ F \propto r^{2} \Rightarrow \Delta h \propto r^{2/3} \]

Option A, a linear dependence, and option D, a square dependence, would need a different power of the buoyancy flux. Option B, r to the power one-third, forgets that the flux itself goes with the square of the radius.

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106.

In Gaussian Plume Model assume \(\sigma_z = cx\) where c is a constant and ratio of \(\sigma_y\) to \(\sigma_z\) to be a constant. If H is the effective height of the stack, the maximum concentration at a distance (x) from the stack is proportional to

A.\(H^{-1}\)
B.\(H^{-2}\)
C.\(\exp(-H^{2})\)
D.\(H^{-3/2}\)

Exam Year(s)

UGC NET - 2013,

Answer: B

In the Gaussian plume model the ground-level centre-line concentration is proportional to \(\frac{1}{\sigma_y \sigma_z}\exp(-H^2/2\sigma_z^2)\). The maximum occurs when \(\sigma_z = H/\sqrt{2}\).

\[ C_{max} \propto \frac{1}{\sigma_y \sigma_z} \]

\[ C_{max} \propto \frac{1}{\sigma_z^2} \propto H^{-2} \]

With the ratio of \(\sigma_y\) to \(\sigma_z\) constant, the maximum concentration is proportional to \(H^{-2}\), option B.

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107.

'Fanning' smokestack plumes are observed when

A.there is an inversion above the ground surface.
B.there is unstable atmosphere.
C.there is neutrally stable atmosphere.
D.the stack height is below an inversion layer.

Exam Year(s)

UGC NET - 2013,

Answer: A

Fanning plumes occur when there is an inversion above the ground surface.

In a fanning plume the smoke spreads sideways but hardly at all vertically, so from above it looks like a fan or a flat ribbon. This happens under a strong, stable inversion, where the air temperature rises with height starting from or near ground level; vertical motion is suppressed, so the plume stays at stack height and drifts along.

An unstable atmosphere gives a looping plume with big eddies. Neutral stability gives a coning plume that spreads in a cone shape. A stack below an inversion layer gives a trapping plume, hemmed in from above, which is a different pattern from fanning.

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108.

According to Gaussian Plume Model, the ground level concentration (C) of a pollutant varies with effective height (H) as (σ is the vertical dispersion coefficient) :

A.\(C \propto \dfrac{1}{H}\)
B.\(C \propto e^{-\frac{H^{2}}{\sigma^{2}}}\)
C.\(C \propto e^{-\frac{H}{\sigma}}\)
D.\(C \propto H^{-2}\)

Exam Year(s)

UGC NET - 2013,

Answer: B

C is proportional to exp(-H squared over sigma squared).

The ground-level concentration under the plume axis in the Gaussian model is proportional to \(\exp(-H^{2}/2\sigma_z^{2})\), where H is the effective stack height and the factor 2 is a constant. As H rises, the concentration falls exponentially with the square of H, which matches option (B).

It does not vary as 1/H or as \(H^{-2}\), since the dependence is an exponential. Option (C) has H to the first power in the exponent, which is not what the model gives.

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109.

The smokestack plumes exhibit 'coning' behaviour when

A.stable atmospheric conditions exist
B.atmosphere is unstable
C.the height of the stack is below the inversion layer
D.inversion exists right from the ground surface above

Exam Year(s)

UGC NET - 2013,

Answer: A

stable atmospheric conditions exist

Coning plumes occur when the atmosphere is close to neutral, with the environmental lapse rate near the adiabatic one, and the key gives stable conditions for this behaviour. Unstable air gives looping plumes, and an inversion starting at the ground gives a fanning plume, so those two options are for other shapes.

The other options, atmosphere is unstable; the height of the stack is below the inversion layer; inversion exists right from the ground surface above, are not the answer to this question. This agrees with the official final answer key for the paper, which gives option A.

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110.

Assertion (A) : According to Gaussian Plume Model, the downward concentration of pollutant appears to be inversely proportional to average wind speed at effective stack height.

Reason (R) : Plume rise does not depend on wind speed. It only depends on buoyancy flux parameter. Identify the correct answer :

A.Both (A) and (R) are true and (R) is the correct explanation of (A).
B.Both (A) and (R) are correct and (R) is not the correct explanation of (A).
C.(A) is true, but (R) is false.
D.(A) is false, but (R) is true.

Exam Year(s)

UGC NET - 2013,

Answer: C

(A) is true, but (R) is false.

In the Gaussian plume model the ground level concentration is inversely proportional to the mean wind speed at the effective stack height, so the Assertion is true. The Reason is false because plume rise does depend on wind speed, as well as on buoyancy flux, so (A) is true and (R) is false.

The other options, Both (A) and (R) are true and (R) is the correct explanation of (A).; Both (A) and (R) are correct and (R) is not the correct explanation of (A).; (A) is false, but (R) is true., are not the answer to this question. This agrees with the official final answer key for the paper, which gives option C.

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