This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 11 What is Dispersion? • Dispersion: The act or process to drive off or scatter in different directions • Key parameters: – Diffusion due to concentration gradient – Mean air motion that transport pollutants downwind – Turbulent velocity fluctuations that disperse pollutants in in all directions 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 22 Plume Dispersion H X Y Z u Q 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 33 Gaussian Dispersion Model x Cu z C D y C D x C D t C z y x ∂ ∂ ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ 2 2 2 2 2 2 At any point downwind the emission C : concentration D : diffusion coefficient u : wind velocity 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 44 Assumptions: • Mass transfer due to bulk motion in the x direction far outshadows the contribution due to mass diffusion • Continuous emission • Steady state conditions • u is constant • Conservation of mass Q: So, what will the equation be reduced to? x Cu z C D y C D x C D t C z y x ∂ ∂ ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂ 2 2 2 2 2 2 ~0 ~0 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 55 2 2 2 2 z C D y C D x C u z y ∂ ∂ + ∂ ∂ + = ∂ ∂ ⇒ +  = x u D z D y x K C z y 4 exp 2 2 General solution (from math handbook) B.C.? ∫∫ = uCdydz Q Constant K to be determined by boundary condition Q : (mass) emission rate 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 66 Point source at ground level Boundaries ∞ →∞ ∞ → : : y z Hence, the emission rate is ∫ ∫ ∞ ∞ ∞ +  = 2 2 4 exp dydz x u D z D y x Ku Q z y z y D z z D y y = = * , * Variable transformation * 4 * exp * 4 * exp 2 2 ∫ ∫ ∞ ∞ ∞   = dy x u y dz x u z D D x Ku Q z y 9/13/11 Aerosol & Particulate 9/13/11 Aerosol & Particulate 77 + = x u D z D y D D x Q C z y z y 4 exp 2 2 2 π From standard integral tables, ( 29 a dx x a 2 exp 2 2 π = ∫ ∞ Compare these two equations, z y D D K Q π 2 = z y D D Q K π 2 = 9/13/11...
View
Full
Document
This note was uploaded on 09/11/2011 for the course ENV 6146 taught by Professor Staff during the Spring '11 term at University of Florida.
 Spring '11
 Staff

Click to edit the document details