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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.

(**) Important note for DESCAR 3.2 (or lower versions):

In the approved model, T90 is un hours (this is used by the program). However, and in equation F₀(t)=10^-t/T90  of the approved model(1), time must be in seconds . Following criteria of mathematical coherence and results T90 must be expressed in seconds (multiply by 3600 seconds in one hour). At this point, the user can work following two different ways: using the approved model as is or rectify in the T90 input data. For example, for a T90=2 hours value, the user can introduce as input data:

(a) Following the approved model:

1/T90=0.5 hours^-1 as input data. Then, write 0.5 in the window textbox for a T90=2 hours value .

(b) Following criteria of mathematical coherence and results:

1/T90=1/(2 x 3600)=0,000278 as input data. Then, write 0,000278 in the window textbox for a T90=2 hours value.

(1) Orden del 13 de Julio de 1993 del Ministerio de Obras Públicas y Transportes del Reino de ESPAÑA, B.O.E. Martes 27 de Julio de 1993, página 22861.

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