Gaussian differential equation air pollution
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The turbulent diffusion equation (10.10) is a partial differential equation that can be solved with various numerical methods. Assuming a homogenous, steady-state flow and a steady-state point source, equation (10.10) can also be analytically integrated and results the well-known Gaussian plume distribution
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(10.19)
where c is a concentration at a given position, Q is the source term, x is the downwind, y is the crosswind and z is the vertical direction and u is the wind speed at the h height of the release. The σy, σzdeviations describe the crosswind and vertical mixing of the pollutant, thus they are constructed from the Kh, Kz values of equation (10.10). Equation (10.19) describes a mixing process that results a Gaussian concentration distribution both in crosswind and in vertical direction, centered at the line downwind from the source (Figure 10.3). The last term of equation (10.19) expresses a total reflection from the ground, therefore this formula does not count with dry and wet deposition. Adding a third vertical component to the equation, total reflection from an inversion layer can also be computed. Gravitational settling and chemical or radioactive decay are neglected.
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,
(10.19)
where c is a concentration at a given position, Q is the source term, x is the downwind, y is the crosswind and z is the vertical direction and u is the wind speed at the h height of the release. The σy, σzdeviations describe the crosswind and vertical mixing of the pollutant, thus they are constructed from the Kh, Kz values of equation (10.10). Equation (10.19) describes a mixing process that results a Gaussian concentration distribution both in crosswind and in vertical direction, centered at the line downwind from the source (Figure 10.3). The last term of equation (10.19) expresses a total reflection from the ground, therefore this formula does not count with dry and wet deposition. Adding a third vertical component to the equation, total reflection from an inversion layer can also be computed. Gravitational settling and chemical or radioactive decay are neglected.
If the answer is helpful to you mark it as a brainliest answer please
Thank you
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