Point-source diffusion

Diffuse point source Fuel storage Fuel stands, small industries, etc, Mainly groundwater... 

Pit latrines of individual houses should also be taken into account as diffuse point sources... 

For calculating the intensity of the signal at the detector one has to take into account the solid angle of collection for the chromophore embedded into a medium with refractive index n and acting as a non-Lambertian diffuse point source (i.e. the intensity of which in a given direction is not proportional to the cosine of the angle with respect to the direction of maximum irradiance). This solid angle is equal to ... 

Fig. 5. Diffusion of pollutants from a point source. PoUutant concentrations have separate Gaussian distributions in both the horizontal (j) and vertical directions. The spread is parameterized by the standard deviations ( O ) which are related to the diffusivity (fQ.

Strimaitis, D., Hoffnagle, G., and Bass, A., "On-Site Meteorological Instmmentation Requirements to Characterize Diffusion from Point Sources—Workshop Report," EPA-6(X)/9-81-020. U.S. Environmental Protection Agency, Research Triangle Park, NC, 1981. 

It is known that the vertical distribution of diffusing particles from an elevated point source is a function of the standard deviation of the vertical wind direction at the release point. The standard deviations of the vertical and horizontal wind directions are related to the standard deviations of particle concentrations in the vertical and horizontal directions within the plume itself. This is equivalent to saying that fluctuations in stack top conditions control the distribution of pollutant in the plume. Furthermore, it is known that the plume pollutant distributions follow a familiar Gaussian diffusion equation. 

Some researchers (e.g., Abramovich,Baturin,Rajaratnam,- and Nielsen and Moller ) consider x to be the distance from a point located at some distance Xq upstream from the diffuser face. Equations for the jet boundaries and velocity profile used in the centerline velocity derivation assume that the jet is supplied from the point source. Addition of the distance Xq to the distance from the outlet corrects for the influence of the outlet size on the jet geometry. For practical reasons some researchers neglect Xq. 

Another design method uses capture efficiency. There are fewer models for capture efficiency available and none that have been validated over a wide range of conditions. Conroy and Ellenbecker - developed a semi-empirical capture efficiency for flanged slot hoods and point and area sources of contaminant. The point source model uses potential flow theory to describe the flow field in front of a flanged elliptical opening and an empirical factor to describe the turbulent diffusion of contaminant around streamlines. 

RTDM (Rough Terrain Diffusion Model) is a sequential Gaussian plume model designed to estimate ground-level concentrations in rough (or flat) terrain in die vicinity of one or more co-located point sources. 

As point sources of contaminants become more controlled, the problems associated with more diffuse sources such as the residual effects of contaminated... 

The relationship between discharge and metal pollution may differ depending on the type of pollution, whether it originates from point sources or whether it is diffuse. Two hypothetical cases addressing the influence of hydrology on the fate... 

Table 2 Fate and effects of metals in a stream receiving a point-source of metals (upper part of the table) or diffuse input via urban runoff (lower part of the table). Summary of the expected influence of four different hydrological situations base-flow in a rainy period a flood after a rainy period low-flow after a long period of low rainfall (water scarcity) and a flood produced after this drought. Metal concentration (M) metal retention efficiency (measured on the basis of the nutrient spiraling concept) exposure (dose and duration) bioaccumulation (in fluvial biofilms) and metal sensitivity (of biofihns)...

Inputs of organic matter and nutrients, benthic metabolism, and nutrient retention at each stream section depend on diffuse and point sources. Yet, under low flow conditions, water and matter transport downstream becomes impeded or discontinued due to stream contraction and fragmentation during dry periods. Therefore, nutrient export from rivers in semiarid regions will depend, more so than in more humid regions, on the interplay between the spatial configuration of organic matter... 

Environmental contamination, either from diffuse or point sources, may compromise the ability of ecosystems to provide society with those goods and services that we require. Contamination is also linked to other widely recognised anthropogenic threats to sustainable functioning of our planet, such as the loss of biodiversity. As many soil properties and processes are conferred by soil biota, it is currently widely agreed that biological characteristics should be taken into account when evaluating the quality, or health, of soil [13, 16]. 

In comparison with other studies, which reflect either diffusive pollution or sampling sites located relatively far from the pollution point source, the sampling... 

Water resource management strategies need to balance water supply and demand, particularly in the context of droughts or floods, and contend with problems such as diffuse and point source pollution, poor water quality and ecosystem degradation, all within local political and socio-economic frameworks. As water use in one location may influence water quality and availability in another, it is becoming... 

Chemical pollution From a qualitative point of view, an important common issue is the excess of chemicals (fertilisers and pesticides) associated with agrarian and livestock farming diffuse sources and the point-source discharge of (treated and untreated) sewage water. Industrial point-source pollution is not addressed as a relevant issue, but it is assumed that industries operate following the legal rules and only the incomplete elimination of industrial chemicals in urban wastewater treatment plants is perceived as a problem. 

Related to chemical pollution - referring to all kind of contamination (mineral and organic) - there is a clear distinction between point-source pollution and diffuse pollution. It appears that it is easier to take measures for point-source pollution, for instance, the improvement of the wastewater treatment plants, even if the treatments for specific compounds (pesticides, emerging compounds, etc.) still need further research. Measures for diffuse pollution can be more complex because some of them require real political decisions, for instance to interfere on agricultural practices to reduce inorganic and organic fertilisers. 

Case 6 Steady-State Continuous Point Source Release with Wind and Eddy Diffusivity Is a Function of Direction... 

Different techniques are commonly used to solve the diffusion equation (Carslaw and Jaeger, 1959). Analytic solutions can be found by variable separation, Fourier transforms or more conveniently Laplace transforms and other special techniques such as point sources or Green functions. Numerical solutions are calculated for the cases which have no simple analytic solution by finite differences (Mitchell, 1969 Fletcher, 1991), which is the simplest technique to implement, but also finite elements, particularly useful for complicated geometry (Zienkiewicz, 1977), and collocation methods (Finlayson, 1972). 

Figure 8.13 Dispersion of an instantaneous point source [equation (8.5.1)]. A quantity of the diffusing species equivalent to the surface of whatever curve on the diagram is deposited initially at x = 0. The curves are Gauss functions.

From a well-known result of calculus, the definite integral on the right-hand side is s/n so M is just equal to the quantity of diffusing substance. The present solution is therefore applicable to the case where M grams (or moles) per unit surface is deposited on the plane x=x at t=0. In terms of concentration, the initial distribution is an impulse function (point source) centered at x=x which evolves with time towards a gaussian distribution with standard deviation JlQit (Figure 8. 13). Since the standard deviation is the square-root of the second moment, it is often stated that the mean squared distance traveled by the diffusion species is 22t. 

The infinite medium with one-dimensional diffusion and constant diffusion coefficient can be treated easily with the point source theory. Let us first assume that two half-spaces with uniform initial concentrations C0 for x < 0 and 0 for x > 0 are brought into contact with each other. The amount of substance distributed per unit surface between x and x + dx is just C0dx. From the previous result, at time t the effect of the point source C0 dx located at x on the concentration at x will be... 

The exponential term which represents the effect of a point source is sometimes called the influence function or Green function of this diffusion problem. The method of sources and sinks easily produces solutions for an infinite medium or for systems of finite dimension when their boundary is kept at zero concentration. Different boundary conditions require a more elaborate formulation (Carslaw and Jaeger, 1959). 

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