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2.3 Near mixing zone and distant mixing zone

We need to know the place where the plume centerline crosses the water surface or picnocline layer. To calculate this point we will use U_a and the vertical velocity 

Multiport diffuser.- W=1,66(g’q)^1/3 being W the vertical velocity of the effluent (m/s).

Separated ports.- W=6,3(g’Q_b/H)^1/3 .

Single port.- W=6,3(g’Q/H)^1/3.

In the last two cases, H will be replaced by ymax when the water is stratified. The point localization with regard to the place where the plume centerline crosses the surface, gives us the near and distant mixing zone definitions.

2.4 Concentration calculation

The concentration value in a plume point is determined by the X,Y,Z coordinates and is given by the equation:

C(X,Y,Z)=(C₀/S) F₀(t)F₁(t)F₂(Y,t)F₃(Z,t)

C₀=pollutant concentration in the effluent

S=initial dilution

being t=X/U_a. F₀(t) takes into account non-conservative pollutants and is equal to:

F₀(t)=10^-t/T90

The F₀, F₁, F₂ and F₃ functions depend on being in near or distant mixing zone.

(a) Near mixing zone:

In such a case, the equations are

F₁(t)=1

F₂(Y,t)=(1/2)[erf[(B/2+Y)/(σ_y2^1/2)]+ erf[(B/2-Y)/(σ_y2^1/2)]]

F₃(Z,t)=(1/2)[erf[(e+Z)/(σ_z2^1/2)]+ erf[(e-Z)/(σ_z2^1/2)]]

being σ_y=(2K_yt)^1/2 and σ_z=(2K_zt)^1/2. The program calculats erf function by numerical integration. The the precision of integration method depends on the parameter N_int. Increasing N_int value, we increase the numeric convergence but we will need more time of calculation. We should look for an optimized value of N_int.

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