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									             FARFIELD.XLS: Far-field dilution of initially diluted effluent plumes using the method of the EPA PLUMES model (EPA/600/R-94/086), with the addition of a
   linear eddy diffusivity algorithm based on the Brooks model as presented by Grace (R.A. Grace. Marine outfall systems: planning, design, and construction. Prentice-Hall, Inc.)

                                                                                                                          INPUT


1. Plume and diffuser characteristics at start of far-field mixing
    Flux-average dilution factor after initial dilution                                                  19.56   (e.g. dilution at end of computations with UDKHDEN)
    Estimated initial width (B) of plume after initial dilution (meters)                                 12.07   (e.g. eqn 70 of EPA/600/R-94/086 for diffuser length and plume diameter)
    Travel distance of plume after initial dilution (meters)                                              5.47   (e.g. "Y" from UDKHDEN or horizontal distance from PLUMES output)

2. Distance from outfall to mixing zone boundary (meters)                                                 65.5   (e.g. distance to the chronic mixing zone boundary)

3. Estimated diffusion parameter "alpha" per equations 66-69 of EPA/600/R-94/086
    Coefficient "alpha" (m^(2/3)/sec), where Eo=(alpha)(width)^(4/3)                                    0.0003   (normal range is 0.0001 to 0.0005 m^(2/3)/sec, 0.0003 is a median value. PLUMES assumes the same initial value
                                                                                                                 of the diffusion coefficient (Eo), calculated as Eo = (alpha)(width)^(4/3), for 4/3 and constant eddy diffusivity algorithms.
                                                                                                                 The same initial value of Eo was assumed for all far-field algorighms as Eo = (alpha)(width)^(4/3).)

4. Horizontal current speed (m/sec)                                                                       0.05   (e.g. same value specified for UDKHDEN or PLUMES)

5. Pollutant initial concentration and decay (optional)                                                          (these inputs do not affect calculated farfield dilution factors)
    Pollutant concentration after initial dilution (any units)                                    5.11E-02       (e.g. effluent volume fraction = 1/initial dilution)
    Pollutant first-order decay rate constant (day^-1)                                            0.00E+00       (e.g. enter 0 for conservative pollutants)

                                                                                                                         OUTPUT


                                                                                        4/3 Power Law                  Linear Eddy Diffusivity              Constant Eddy Diffusivity

                                                                                    (PLUMES equation 69)           (Grace/Brooks equation 7-65)              (PLUMES equation 66)
                                                                                                                            Eo = 8.3061E-03
                                                                                                                          Beta = 1.6516E-01
                                                      Far-field        Far-field                                                                                                              Total
                                                       Travel           Travel                   Pollutant                            Pollutant                              Pollutant       Travel
                                                       Time            Distance     Effluent      conc-               Effluent         conc-                 Effluent         conc-         Distance
                                                      (hours)             (m)       Dilution     entration            Dilution        entration              Dilution        entration         (m)

Dilution along plume trajectory:                     2.63E-02         4.73E+00     1.96E+01      5.11E-02            1.96E+01         5.11E-02              1.96E+01         5.11E-02         10.20
                                                     5.25E-02         9.45E+00     1.96E+01      5.11E-02            1.96E+01         5.11E-02              1.96E+01         5.11E-02         14.92
                                                     7.88E-02         1.42E+01     1.97E+01      5.07E-02            1.97E+01         5.07E-02              1.97E+01         5.08E-02         19.65
                                                     1.05E-01         1.89E+01     2.01E+01      4.98E-02            2.00E+01         4.99E-02              1.99E+01         5.03E-02         24.38
                                                     1.31E-01         2.36E+01     2.06E+01      4.85E-02            2.05E+01         4.88E-02              2.02E+01         4.95E-02         29.10
                                                     1.58E-01         2.84E+01     2.13E+01      4.69E-02            2.11E+01         4.74E-02              2.06E+01         4.86E-02         33.83
                                                     1.84E-01         3.31E+01     2.21E+01      4.53E-02            2.17E+01         4.60E-02              2.10E+01         4.76E-02         38.56
                                                     2.10E-01         3.78E+01     2.30E+01      4.36E-02            2.25E+01         4.45E-02              2.15E+01         4.66E-02         43.28
                                                     2.36E-01         4.25E+01     2.39E+01      4.19E-02            2.32E+01         4.31E-02              2.19E+01         4.56E-02         48.01
                                                     2.63E-01         4.73E+01     2.48E+01      4.03E-02            2.40E+01         4.16E-02              2.24E+01         4.46E-02         52.74
                                                     2.89E-01         5.20E+01     2.59E+01      3.87E-02            2.48E+01         4.03E-02              2.29E+01         4.36E-02         57.46
                                                     3.15E-01         5.67E+01     2.69E+01      3.72E-02            2.57E+01         3.90E-02              2.34E+01         4.27E-02         62.19
                                                     3.41E-01         6.14E+01     2.80E+01      3.58E-02            2.65E+01         3.77E-02              2.39E+01         4.18E-02         66.91
                                                     3.68E-01         6.62E+01     2.91E+01      3.44E-02            2.74E+01         3.65E-02              2.44E+01         4.10E-02         71.64
                                                     3.94E-01         7.09E+01     3.02E+01      3.31E-02            2.82E+01         3.54E-02              2.49E+01         4.02E-02         76.37
                                                     4.20E-01         7.56E+01     3.13E+01      3.19E-02            2.91E+01         3.43E-02              2.54E+01         3.94E-02         81.09
                                                     4.46E-01         8.04E+01     3.25E+01      3.08E-02            3.00E+01         3.33E-02              2.58E+01         3.87E-02         85.82
                                                     4.73E-01         8.51E+01     3.37E+01      2.97E-02            3.09E+01         3.24E-02              2.63E+01         3.80E-02         90.55
                                                     4.99E-01         8.98E+01     3.49E+01      2.87E-02            3.18E+01         3.15E-02              2.68E+01         3.74E-02         95.27
                                                     5.25E-01         9.45E+01     3.61E+01      2.77E-02            3.27E+01         3.06E-02              2.72E+01         3.67E-02          100
                                                     1.08E+00         1.95E+02     6.54E+01      1.53E-02            5.19E+01         1.93E-02              3.57E+01         2.80E-02          200
                                                     1.64E+00         2.95E+02     1.00E+02      9.98E-03            7.12E+01         1.40E-02              4.27E+01         2.34E-02          300
                                                     2.19E+00         3.95E+02     1.40E+02      7.16E-03            9.06E+01         1.10E-02              4.87E+01         2.05E-02          400
                                                     2.75E+00         4.95E+02     1.83E+02      5.46E-03            1.10E+02         9.10E-03              5.40E+01         1.85E-02          500
                                                     5.53E+00         9.95E+02     4.52E+02      2.21E-03            2.07E+02         4.84E-03              7.52E+01         1.33E-02         1000
                                                     1.11E+01         1.99E+03     1.19E+03      8.40E-04            4.00E+02         2.50E-03              1.06E+02         9.48E-03         2000

Dilution at mixing zone boundary:                    3.34E-01         6.00E+01     2.76E+01      3.62E-02            2.63E+01         3.81E-02              2.38E+01         4.21E-02         65.5




                                                                                         607aaa93-a0c0-46aa-bb4a-781a4cf36eeb.xls\PLUMES algorithm, 8/15/2012
         FARFIELD.XLS: Far-field dilution of initially diluted effluent plumes using the 4/3 power law Brooks model
     as presented by Grace (R.A. Grace. Marine outfall systems: planning, design, and construction. Prentice-Hall, Inc.)
                                                                             INPUT

                                                                                                                                        4/3 Power Law
                                                                                                                                   Eo=(alpha)*(width)^(4/3)
                                                                                                                                 (Grace/Brooks equation 7-66)

1. Plume and diffuser characteristics at start of far-field mixing
    Flux-average dilution factor after initial dilution                                                                                 19.56
      (e.g. dilution at end of computations with UDKHDEN)
    Estimated initial width (B) of plume after initial dilution (meters)                                                                12.07 meters
      (e.g. eqn 70 of EPA/600/R-94/086 for diffuser length and plume diameter)
    Travel distance of plume after initial dilution (meters)                                                                             5.47 meters
      (e.g. "Y" from UDKHDEN or horizontal distance from PLUMES output)

2. Distance from outfall to mixing zone boundary (meters)                                                                                65.5 meters
       (e.g. distance to the chronic mixing zone boundary)

3. Diffusion parameter "alpha" per equations 7-62 of Grace, where Eo=(alpha)(width)^(4/3)
    (This sheet differs from the PLUMES approach by assuming different units
    for alpha depending on the far-field algorithm. Initial diffusion coefficients
    (Eo in m^2/sec) are calculated as follows on this sheet: 4/3 power law: Eo =                                                       0.0003 m^(2/3) /sec
    (alpha)(width)^(4/3); linear eddy diffusivity: Eo = (alpha)(width); constant
    eddy diffusivity: Eo = (alpha).)

4. Horizontal current speed (m/sec)                                                                                                      0.05 m/sec
       (e.g. same value specified for UDKHDEN or PLUMES)

5. Pollutant initial concentration and decay (optional)
       (these inputs do not affect calculated farfield dilution factors)
    Pollutant concentration after initial dilution (any units)                                                                      5.11E-02 any units
       (e.g. effluent volume fraction = 1/initial dilution)
    Pollutant first-order decay rate constant (day^-1)                                                                              0.00E+00 day^-1
       (e.g. enter 0 for conservative pollutants)

                                                                            OUTPUT

                                                                                                                                         Eo =    8.3061E-03 m^2/s
                                                                                                                                        Beta =   1.6516E-01 unitless
                                                                                     Far-field      Far-field       Total
                                                                                      Travel         Travel         Travel                        Pollutant
                                                                                      Time          Distance       Distance        Effluent        conc-
                                                                                     (hours)          (m)            (m)           Dilution       entration

Dilution along plume trajectory:                                                     2.63E-02      4.73E+00         10.20         1.96E+01        5.11E-02
                                                                                     5.25E-02      9.45E+00         14.92         1.96E+01        5.11E-02
                                                                                     7.88E-02      1.42E+01         19.65         1.97E+01        5.07E-02
                                                                                     1.05E-01      1.89E+01         24.38         2.01E+01        4.98E-02
                                                                                     1.31E-01      2.36E+01         29.10         2.06E+01        4.85E-02
                                                                                     1.58E-01      2.84E+01         33.83         2.13E+01        4.69E-02
                                                                                     1.84E-01      3.31E+01         38.56         2.21E+01        4.53E-02
                                                                                     2.10E-01      3.78E+01         43.28         2.30E+01        4.36E-02
                                                                                     2.36E-01      4.25E+01         48.01         2.39E+01        4.19E-02
                                                                                     2.63E-01      4.73E+01         52.74         2.48E+01        4.03E-02
                                                                                     2.89E-01      5.20E+01         57.46         2.59E+01        3.87E-02
                                                                                     3.15E-01      5.67E+01         62.19         2.69E+01        3.72E-02
                                                                                     3.41E-01      6.14E+01         66.91         2.80E+01        3.58E-02
                                                                                     3.68E-01      6.62E+01         71.64         2.91E+01        3.44E-02
                                                                                     3.94E-01      7.09E+01         76.37         3.02E+01        3.31E-02
                                                                                     4.20E-01      7.56E+01         81.09         3.13E+01        3.19E-02
                                                                                     4.46E-01      8.04E+01         85.82         3.25E+01        3.08E-02
                                                                                     4.73E-01      8.51E+01         90.55         3.37E+01        2.97E-02
                                                                                     4.99E-01      8.98E+01         95.27         3.49E+01        2.87E-02
                                                                                     5.25E-01      9.45E+01          100          3.61E+01        2.77E-02
                                                                                     1.08E+00      1.95E+02          200          6.54E+01        1.53E-02
                                                                                     1.64E+00      2.95E+02          300          1.00E+02        9.98E-03
                                                                                     2.19E+00      3.95E+02          400          1.40E+02        7.16E-03
                                                                                     2.75E+00      4.95E+02          500          1.83E+02        5.46E-03
                                                                                     5.53E+00      9.95E+02         1000          4.52E+02        2.21E-03
                                                                                     1.11E+01      1.99E+03         2000          1.19E+03        8.40E-04

Dilution at mixing zone boundary:                                                    3.34E-01        60.03          65.5          2.76E+01        3.62E-02




                                              607aaa93-a0c0-46aa-bb4a-781a4cf36eeb.xls\Brooks' four-third power law, 8/15/2012
        FARFIELD.XLS: Far-field dilution of initially diluted effluent plumes using the linear diffusivity Brooks model
     as presented by Grace (R.A. Grace. Marine outfall systems: planning, design, and construction. Prentice-Hall, Inc.)
                                                                                     INPUT

                                                                                                                                     Linear Eddy Diffusivity
                                                                                                                                       Eo=(alpha)(width)
                                                                                                                                  (Grace/Brooks equation 7-65)

1. Plume and diffuser characteristics at start of far-field mixing
    Flux-average dilution factor after initial dilution                                                                                  19.56
      (e.g. dilution at end of computations with UDKHDEN)
    Estimated initial width (B) of plume after initial dilution (meters)                                                                 12.07 meters
      (e.g. eqn 70 of EPA/600/R-94/086 for diffuser length and plume diameter)
    Travel distance of plume after initial dilution (meters)                                                                              5.47 meters
      (e.g. "Y" from UDKHDEN or horizontal distance from PLUMES output)

2. Distance from outfall to mixing zone boundary (meters)                                                                                 65.5 meters
       (e.g. distance to the chronic mixing zone boundary)

3. Diffusion parameter "alpha" per equations 7-62 of Grace, where Eo=(alpha)(width)
    (This sheet differs from the PLUMES approach by assuming different units
    for alpha depending on the far-field algorithm. Initial diffusion coefficients
    (Eo in m^2/sec) are calculated as follows on this sheet: 4/3 power law: Eo =                                                     6.88E-04 m/sec
    (alpha)(width)^(4/3); linear eddy diffusivity: Eo = (alpha)(width); constant
    eddy diffusivity: Eo = (alpha).)

4. Horizontal current speed (m/sec)                                                                                                       0.05 m/sec
       (e.g. same value specified for UDKHDEN or PLUMES)

5. Pollutant initial concentration and decay (optional)
       (these inputs do not affect calculated farfield dilution factors)
    Pollutant concentration after initial dilution (any units)                                                                       5.11E-02 any units
       (e.g. effluent volume fraction = 1/initial dilution)
    Pollutant first-order decay rate constant (day^-1)                                                                               0.00E+00 day^-1
       (e.g. enter 0 for conservative pollutants)

                                                                                     OUTPUT

                                                                                                                                          Eo =    8.3061E-03 m^2/s
                                                                                                                                         Beta =   1.6516E-01 unitless
                                                                                       Far-field      Far-field       Total
                                                                                        Travel         Travel         Travel                       Pollutant
                                                                                        Time          Distance       Distance       Effluent        conc-
                                                                                       (hours)          (m)            (m)          Dilution       entration

Dilution along plume trajectory:                                                      2.63E-02       4.73E+00          10.20       1.96E+01        5.11E-02
                                                                                      5.25E-02       9.45E+00          14.92       1.96E+01        5.11E-02
                                                                                      7.88E-02       1.42E+01          19.65       1.97E+01        5.07E-02
                                                                                      1.05E-01       1.89E+01          24.38       2.00E+01        4.99E-02
                                                                                      1.31E-01       2.36E+01          29.10       2.05E+01        4.88E-02
                                                                                      1.58E-01       2.84E+01          33.83       2.11E+01        4.74E-02
                                                                                      1.84E-01       3.31E+01          38.56       2.17E+01        4.60E-02
                                                                                      2.10E-01       3.78E+01          43.28       2.25E+01        4.45E-02
                                                                                      2.36E-01       4.25E+01          48.01       2.32E+01        4.31E-02
                                                                                      2.63E-01       4.73E+01          52.74       2.40E+01        4.16E-02
                                                                                      2.89E-01       5.20E+01          57.46       2.48E+01        4.03E-02
                                                                                      3.15E-01       5.67E+01          62.19       2.57E+01        3.90E-02
                                                                                      3.41E-01       6.14E+01          66.91       2.65E+01        3.77E-02
                                                                                      3.68E-01       6.62E+01          71.64       2.74E+01        3.65E-02
                                                                                      3.94E-01       7.09E+01          76.37       2.82E+01        3.54E-02
                                                                                      4.20E-01       7.56E+01          81.09       2.91E+01        3.43E-02
                                                                                      4.46E-01       8.04E+01          85.82       3.00E+01        3.33E-02
                                                                                      4.73E-01       8.51E+01          90.55       3.09E+01        3.24E-02
                                                                                      4.99E-01       8.98E+01          95.27       3.18E+01        3.15E-02
                                                                                      5.25E-01       9.45E+01           100        3.27E+01        3.06E-02
                                                                                      1.08E+00       1.95E+02           200        5.19E+01        1.93E-02
                                                                                      1.64E+00       2.95E+02           300        7.12E+01        1.40E-02
                                                                                      2.19E+00       3.95E+02           400        9.06E+01        1.10E-02
                                                                                      2.75E+00       4.95E+02           500        1.10E+02        9.10E-03
                                                                                      5.53E+00       9.95E+02          1000        2.07E+02        4.84E-03
                                                                                      1.11E+01       1.99E+03          2000        4.00E+02        2.50E-03

Dilution at mixing zone boundary:                                                      3.34E-01        60.03           65.5        2.63E+01        3.81E-02




                                                 607aaa93-a0c0-46aa-bb4a-781a4cf36eeb.xls\Brooks' linear diffusivity, 8/15/2012
  FARFIELD.XLS: Far-field dilution of initially diluted effluent plumes using the constant diffusivity Brooks model
as presented by Grace (R.A. Grace. Marine outfall systems: planning, design, and construction. Prentice-Hall, Inc.)
                                                                                      INPUT

                                                                                                                                    Constant Eddy Diffusivity
                                                                                                                                          Eo=(alpha)
                                                                                                                                  (Grace/Brooks equation 7-64)

1. Plume and diffuser characteristics at start of far-field mixing
    Flux-average dilution factor after initial dilution                                                                                  19.56
      (e.g. dilution at end of computations with UDKHDEN)
    Estimated initial width (B) of plume after initial dilution (meters)                                                                 12.07 meters
      (e.g. eqn 70 of EPA/600/R-94/086 for diffuser length and plume diameter)
    Travel distance of plume after initial dilution (meters)                                                                              5.47 meters
      (e.g. "Y" from UDKHDEN or horizontal distance from PLUMES output)

2. Distance from outfall to mixing zone boundary (meters)                                                                                 65.5 meters
       (e.g. distance to the chronic mixing zone boundary)

3. Diffusion parameter "alpha" per equations 7-62 of Grace, where Eo=(alpha)
     (This sheet differs from the PLUMES approach by assuming different units
     for alpha depending on the far-field algorithm. Initial diffusion coefficients
     (Eo in m^2/sec) are calculated as follows on this sheet: 4/3 power law: Eo =                                                    8.31E-03 m^2/sec
     (alpha)(width)^(4/3); linear eddy diffusivity: Eo = (alpha)(width); constant
     eddy diffusivity: Eo = (alpha).)

4. Horizontal current speed (m/sec)                                                                                                       0.05 m/sec
       (e.g. same value specified for UDKHDEN or PLUMES)

5. Pollutant initial concentration and decay (optional)
       (these inputs do not affect calculated farfield dilution factors)
    Pollutant concentration after initial dilution (any units)                                                                       5.11E-02 any units
       (e.g. effluent volume fraction = 1/initial dilution)
    Pollutant first-order decay rate constant (day^-1)                                                                               0.00E+00 day^-1
       (e.g. enter 0 for conservative pollutants)

                                                                                      OUTPUT

                                                                                                                                          Eo =    8.3061E-03 m^2/s
                                                                                                                                         Beta =   1.6516E-01 unitless
                                                                                        Far-field    Far-field       Total
                                                                                         Travel       Travel         Travel                        Pollutant
                                                                                         Time        Distance       Distance        Effluent        conc-
                                                                                        (hours)        (m)            (m)           Dilution       entration

Dilution along plume trajectory:                                                       2.63E-02     4.73E+00         10.20         1.96E+01        5.11E-02
                                                                                       5.25E-02     9.45E+00         14.92         1.96E+01        5.11E-02
                                                                                       7.88E-02     1.42E+01         19.65         1.97E+01        5.08E-02
                                                                                       1.05E-01     1.89E+01         24.38         1.99E+01        5.03E-02
                                                                                       1.31E-01     2.36E+01         29.10         2.02E+01        4.95E-02
                                                                                       1.58E-01     2.84E+01         33.83         2.06E+01        4.86E-02
                                                                                       1.84E-01     3.31E+01         38.56         2.10E+01        4.76E-02
                                                                                       2.10E-01     3.78E+01         43.28         2.15E+01        4.66E-02
                                                                                       2.36E-01     4.25E+01         48.01         2.19E+01        4.56E-02
                                                                                       2.63E-01     4.73E+01         52.74         2.24E+01        4.46E-02
                                                                                       2.89E-01     5.20E+01         57.46         2.29E+01        4.36E-02
                                                                                       3.15E-01     5.67E+01         62.19         2.34E+01        4.27E-02
                                                                                       3.41E-01     6.14E+01         66.91         2.39E+01        4.18E-02
                                                                                       3.68E-01     6.62E+01         71.64         2.44E+01        4.10E-02
                                                                                       3.94E-01     7.09E+01         76.37         2.49E+01        4.02E-02
                                                                                       4.20E-01     7.56E+01         81.09         2.54E+01        3.94E-02
                                                                                       4.46E-01     8.04E+01         85.82         2.58E+01        3.87E-02
                                                                                       4.73E-01     8.51E+01         90.55         2.63E+01        3.80E-02
                                                                                       4.99E-01     8.98E+01         95.27         2.68E+01        3.74E-02
                                                                                       5.25E-01     9.45E+01          100          2.72E+01        3.67E-02
                                                                                       1.08E+00     1.95E+02          200          3.57E+01        2.80E-02
                                                                                       1.64E+00     2.95E+02          300          4.27E+01        2.34E-02
                                                                                       2.19E+00     3.95E+02          400          4.87E+01        2.05E-02
                                                                                       2.75E+00     4.95E+02          500          5.40E+01        1.85E-02
                                                                                       5.53E+00     9.95E+02         1000          7.52E+01        1.33E-02
                                                                                       1.11E+01     1.99E+03         2000          1.06E+02        9.48E-03

Dilution at mixing zone boundary:                                                       3.34E-01      60.03          65.5          2.38E+01        4.21E-02




                                               607aaa93-a0c0-46aa-bb4a-781a4cf36eeb.xls\Brooks' constant diffusivity, 8/15/2012

								
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