1. Consequence Analysis 2.2

2. Dispersion Model
Consider the instantaneous release of a fixed mass of material into an infinite expanse of air. Assuming no reaction or molecular diffusion,

3. Time-Averaged Dispersion Model
Define eddy diffusivity

4. Time-Averaged Dispersion Model
Assume the air is incompressible

5. Time-Averaged Dispersion Model

6. Case 1.1: Steady-State Continuous Point Release with No Wind

7. Case 1.1: Steady-State Continuous Point Release with No Wind
Assume constant release rate
Boundary condition

8. Case 1.2: Unsteady-State Continuous Point Release with No Wind

9. Case 1.3: Steady-State Continuous Point Release with Wind

10. Case 1.3: Steady-State Continuous Point Release with Wind

11. Case 1.3: Steady-State Plume with Source on Ground
Case 1.3: Steady-State Plume with Source at Height H above Ground

12. Case 2.1: Puff with No Wind

13. Case 2.2: Puff with Wind
Case 2.3: Puff with No Wind with Source on Ground

14. Neutral and Positively Buoyant Plume and Puff Models
Neutral and positively buoyant plume and puff models are used to predict concentration and time profiles of flammable or toxic materials downwind of a source based on the concept of Gaussian distribution.
Atmospheric diffusion is a random mixing process driven by turbulence in the atmosphere. The concentration of any point down wind of a source is well approximated by a Gaussian concentration profile in both the horizontal and vertical dimensions.

16. Dispersion Coefficients
The dispersion coefficients represent the standard deviations of concentrations in the downwind, crosswind and vertical directions respectively. They are much easier to obtain experimentally than eddy diffusivities.

17. Dispersion Coefficients
Example formulas as a function of x (meters) in urban D stability conditions are

19. Pasquill-Gifford Model
Case 2.2: Puff. Instantaneous point source at ground level, coordinate fixed at release point. Constant wind in x direction with velocity u.
The total integrated dose

20. Pasquill-Gifford Model
The standard formula for dispersion from an elevated point source assuming no ground absorption or reaction is

21. Gaussian Model for Puff

22. Simplified Approach