In the special case shown here, the Gaussian plume model does not predict the location of the maximum concentration in agreement with the experiment, but it is appropriate to determine the concentration decay in downwind direction. That what happens between the point source location and the maximum location is of accademic interest only. A question for practical purpose is how we can get information about the maximum location, where from the model is realistic. From equation (3.13) we can deduct a rough approximation of the location where maximum ground-level concentration occurs. It is argued that the turbulent diffusion acts more and more on the emitted substances, when the distance from the point source increases: therefore the downwind distance dependency of the diffusion coefficients is done afterwards. If we drop this dependency, equation (3.13) leads to Xmax = 34,4 m for AK = I (curve a) and xmax = 87,7 m for AK = V (curve b), what is demonstrated in fig. 11. The interpolated ranges of measured values are lined in. Curve a overestimates the nondimensional concentration maximum, but its location seems to be correct. In the case of curve b the situation is inverted. C urve c is calculated with the data of AK = II. The decay of the nondimen­ sional concentration is predicted well behind the maximum. Curve d is produced with F - 12,1, f = 0,069, G = 0,04 and g = 1,088. The ascent of concentration is acceptable, but that is all, because there is no explana­ tion of plausibility how to alter the diffusivity parameters. Therefore it must be our aim to find a suitable correction in connection with the meteorological input data. o 0

1986 ◽  
pp. 124-124
Keyword(s):  
Point Source ◽  
Diffusion Coefficients ◽  
Input Data ◽  
Ground Level ◽  
Ground Level Concentration ◽  
Concentration Maximum ◽  
Rough Approximation ◽  
Gaussian Plume ◽  
Meteorological Input ◽  
Special Case

scholarly journals An Analytical Simple Formula for the Ground Level Concentration from a Point Source

Atmosphere ◽  
2011 ◽  
Vol 2 (2) ◽  
pp. 21-35 ◽  
Author(s):  
Tiziano Tirabassi ◽  
Alessandro Tiesi ◽  
Marco T. Vilhena ◽  
Bardo E.J. Bodmann ◽  
Daniela Buske
Keyword(s):  
Point Source ◽  
Simple Formula ◽  
Ground Level ◽  
Ground Level Concentration

scholarly journals Maximum ground level concentration Of air pollutant

MAUSAM ◽  
2021 ◽  
Vol 42 (4) ◽  
pp. 381-384
Author(s):  
A. B. MAYHOUB ◽  
AZZA O. EL-SHAL ◽  
A. AZZAM
Keyword(s):  
Ground Level ◽  
Air Pollutant ◽  
Theoretical Treatment ◽  
Illustrative Case ◽  
Effective Height ◽  
Ground Level Concentration ◽  
Gaussian Plume ◽  
Illustrative Case Study ◽  
Semi Empirical

The emission of an air pollutant from an elevated point source according to Gaussian plume model has been presented. Au. elementary theoretical treatment for both the highest possible ground-level concentration and the downwind distance at which this maximum occurs for different stability classes has been constructed. The effective height release modification was taken into consideration. An illustrative case study, namely, the emission from the research reactor in Inchas, has been studied.  The results of these analytical treatments and of the derived semi-empirical formulae are discussed and presented in few  illustrative diagrams.  

AK FfGgmI1,294 0,718 0,241 0,662 0,419 II 0,801 0,754 0,264 0,774 0,369 III-1 0,640 0,784 0,215 0,885 0,282 III-2 0,659 0,807 0,165 0,996 0,223 IV 0,876 0,823 0,127 1,108 0,205 V 1,503 0,833 0,151 1,219 0,089 Ak F F0 f G Go 9m50,25 194 0,72 0,69 48 0,59 0,40 4 1,19 354 0,67 0,60 42 0,74 0,28 3 0,82 198 0,74 0,09 12 1,11 0,22 2 0,94 168 0,76 0,08 12 1,28 0,11 Table 2. Coefficients of diffusivity dependent on stability classes after Klug and Turner; m stands for the exponent in the power law of wind velocity. However, we must keep in mind the limitations of this approach, especially the transfer of consistent sets of dispersion parameters to the propagation of air pollution in the vicinity of a source. The Gaussian plume formula should be used only for those downwind distances for which the empirical diffusion coefficients have been determined by standard diffusion experiments. Because we are interested in emissions near ground level and immissions nearby the source, we use those diffusion parameters which are based on the classification of Klug /12/ and Turner /13/. The parameters are expressible as power functions, Oy(x) = F xf and az(x) = G x9 after Klug (3.6a,b), tfy(x) = (F + Fx)f and az(x) = (GQ + Gx)9 after Turner (3.7a,b). The parameter classification after Klug is determined by six stability classes (with the German abbreviation AK for Ausbreitungsklasse), reaching from extreme stable (AK I) to extreme labile TAK V). In tRe Turner stability scheme AK 5 denotes extreme stable, AK 2 extreme labile, see table 2. An estimate of the stability can be made from synoptical observa­ tions of solar radiation, cloud cover and wind velocity /14/. With the parameters after Klug equation (3.4) becomes C(x,y,z) = ax"(f+9^exp(-bx"2f) [exp(-d0x"2g)+exp(-d1x"2g)] (3.8), wherein - - C0V k ya w (z-H)2 ^ (z+H) a ' TrTOFE • b ■ ■JT • do = -Z IP '- • d1 = ~75*~

1986 ◽  
pp. 120-120
Keyword(s):  
Wind Velocity ◽  
Diffusion Coefficients ◽  
Cloud Cover ◽  
Ground Level ◽  
Power Functions ◽  
Dispersion Parameters ◽  
Diffusion Parameters ◽  
Gaussian Plume ◽  
The Stability

scholarly journals A simple formula for the evaluation of value and position of ground level concentration from a point source

2018 ◽  
Vol 40 ◽  
pp. 69
Author(s):  
Tiziano Tirabassi ◽  
Daniela Buske
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Point Source ◽  
Simple Formula ◽  
Ground Level ◽  
Approximate Expression ◽  
Simple Expression ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Ground Level Concentration

After setting realistic scenarios of the wind and diffusivity parameterizations the Ground Level Concentration is worked out by an analytical solution of the advection-diffusion equation, then an explicit approximate expression is provided for it allowing a simple expression for the position and value of the maximum.

scholarly journals Some characteristic parameters of Gaussian plume model

MAUSAM ◽  
2021 ◽  
Vol 63 (1) ◽  
pp. 123-128
Author(s):  
M. ABDELWAHAB ◽  
KHALEDS.M. ESSA ◽  
M. EMBABY ◽  
SAWSANE.M ELSAID
Keyword(s):  
Concentration Distribution ◽  
Concentration Level ◽  
Ground Level ◽  
Characteristic Parameters ◽  
Gaussian Plume Model ◽  
Ground Level Concentration ◽  
Wind Tunnel Measurements ◽  
Gaussian Plume ◽  
First Four Moments ◽  
Skewness And Kurtosis

The Gaussian solution of the diffusion equation for line source is used to have the first four moments of the vertical concentration distribution (centroid, variance, skewness, and kurtosis). The magnitude and position of maximum concentration level were evaluated. Also the plume advection wind speed is estimated. Equations for the ground level concentration were compared with wind tunnel measurements.

Cation mobilities in liquid and supercritical C1–C4 hydrocarbons

1980 ◽  
Vol 58 (14) ◽  
pp. 1490-1494 ◽  
Author(s):  
Norman Gee ◽  
Gordon R. Freeman
Keyword(s):  
Free Path ◽  
Ion Mobility ◽  
Diffusion Coefficients ◽  
Critical Region ◽  
Mean Free Path ◽  
Liquid Viscosity ◽  
Boiling Points ◽  
Rough Approximation ◽  
The Relationship ◽  
Lower Liquid

The relationship between ion mobility and liquid viscosity is commonly expressed as μ [Formula: see text] η−m. In hydrocarbons the value of m tends to be near 1.0 at η > 5 mP, m > 1.0 at ~5 < η < 1 mP, and m < 1.0 at η < 0.5 mP. Thus there is a maximum in a plot of μη against η−1 and Walden's rule (m = 1.0) is only a rough approximation. The decrease of μη as the critical region is approached is accompanied by an increase in the ratio of diffusion coefficients Dmolec/Dion. Ion mobilities in the liquids well below their normal boiling points are chiefly controlled by the fluidity. At higher temperatures and concomitant lower liquid densities and viscosities μη first increases, due to an increasing ion mean free path, then decreases as the critical region is approached, due to the increasing liquid compressibility and consequent electrostriction about the ion.

AN APPLICATION OF THE TOPOLOGICAL DEGREE TO GRAVITATIONAL LENSES

1998 ◽  
Vol 13 (02) ◽  
pp. 83-86 ◽  
Author(s):  
MARCO LOMBARDI
Keyword(s):  
Point Source ◽  
Mass Distribution ◽  
Topological Degree ◽  
General Theorem ◽  
Gravitational Lens ◽  
Gravitational Lenses ◽  
General Proof ◽  
Special Case

In this letter we provide a new proof of a general theorem on gravitational lenses, first proven by Burke (1981) for the special case of thin lenses. The theorem states that a transparent gravitational lens with non-singular mass distribution produces an odd number of images of a point source. Our general proof shows that the topological degree finds natural and interesting applications in the theory of gravitational lenses.

Sign in / Sign up

Export Citation Format

Share Document