# 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 algor

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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

27b3a456-86cd-4f3f-94cb-91e120fcc7d0.xls\PLUMES algorithm, 4/13/2011
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

27b3a456-86cd-4f3f-94cb-91e120fcc7d0.xls\Brooks' four-third power law, 4/13/2011
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

27b3a456-86cd-4f3f-94cb-91e120fcc7d0.xls\Brooks' linear diffusivity, 4/13/2011
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

27b3a456-86cd-4f3f-94cb-91e120fcc7d0.xls\Brooks' constant diffusivity, 4/13/2011

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