{"id":64,"date":"2021-06-21T21:09:53","date_gmt":"2021-06-21T21:09:53","guid":{"rendered":"https:\/\/books.gw-project.org\/septic-system-impacts-on-groundwater-quality\/chapter\/solution-exercise-1\/"},"modified":"2021-06-22T23:18:42","modified_gmt":"2021-06-22T23:18:42","slug":"solution-exercise-1","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/septic-system-impacts-on-groundwater-quality\/chapter\/solution-exercise-1\/","title":{"raw":"Solution Exercise 1","rendered":"Solution Exercise 1"},"content":{"raw":"
\r\n

Answer<\/strong>:<\/strong> yes<\/strong><\/p>\r\n

Explanation: <\/strong><\/p>\r\n

Drainfield loading:<\/p>\r\n

q<\/em> = wastewater loading<\/em> + net recharge<\/em> (i.e., precipitation - evapotranspiration<\/em>)<\/span><\/p>\r\n

[latex]\\displaystyle q=3.65\\frac{m}{yr}+\\left ( 0.9\\frac{m}{yr}-0.6\\frac{m}{yr} \\right )=3.95\\frac{m}{yr}[\/latex]<\/p>\r\n

Groundwater will reside under the drainfield for:<\/p>\r\n

[latex]\\displaystyle residence\\ time\\ under\\ drainfield=\\frac{width\\ field}{average\\ linear\\ velocity}[\/latex]<\/span><\/p>\r\n

[latex]\\displaystyle =\\frac{30\\ m}{100\\ \\frac{m}{yr}}=0.3\\ yr[\/latex]\r\n<\/span><\/p>\r\n

Plume thickness at the downgradient edge of the drainfield will be:<\/p>\r\n

[latex]\\displaystyle b=\\frac{q\\ast t}{porosity}[\/latex]<\/span><\/p>\r\n

[latex]\\displaystyle b=\\frac{3.95\\frac{m}{yr}\\ 0.3\\ yr}{0.3}=3.95\\ m \\sim 4\\ m[\/latex]\r\n<\/span><\/p>\r\n

Downgradient from the drainfield the average linear vertical velocity will derive from precipitation recharge:<\/p>\r\n

[latex]\\displaystyle average\\ linear\\ vertical\\ velocity=\\frac{net\\ recharge\\ rate}{porosity}[\/latex]<\/span><\/p>\r\n

[latex]\\displaystyle =\\frac{0.9\\frac{m}{yr}-0.6\\frac{m}{yr}}{0.3}=1\\frac{m}{yr}[\/latex]<\/p>\r\n

Given the average linear lateral velocity of 100 m\/yr, the septic system plume will take 3 years to reach the well.<\/p>\r\n

[latex]\\displaystyle time\\ to\\ reach\\ well=\\frac{300\\ m}{100\\frac{m}{yr}}=3\\ yr[\/latex]<\/span><\/p>\r\n

Ignoring dispersion, during those three years, the plume would be driven vertically downward by the net recharge. With the average linear vertical velocity of 1 m\/yr, the 4-m thick plume from the septic field would occur at a depth of 3 to 7 m below the water table at the well location, and could thus pass through the well screen that spans from 5 to 7 m below the water table.<\/p>\r\n

Return to Exercise 1<\/span><\/a><\/p>\r\n

<\/p>\r\n\r\n<\/div>","rendered":"

\n

Answer<\/strong>:<\/strong> yes<\/strong><\/p>\n

Explanation: <\/strong><\/p>\n

Drainfield loading:<\/p>\n

q<\/em> = wastewater loading<\/em> + net recharge<\/em> (i.e., precipitation – evapotranspiration<\/em>)<\/span><\/p>\n

\"\displaystyle q=3.65\frac{m}{yr}+\left ( 0.9\frac{m}{yr}-0.6\frac{m}{yr} \right )=3.95\frac{m}{yr}\"<\/p>\n

Groundwater will reside under the drainfield for:<\/p>\n

\"\displaystyle residence\ time\ under\ drainfield=\frac{width\ field}{average\ linear\ velocity}\"<\/span><\/p>\n

\"\displaystyle =\frac{30\ m}{100\ \frac{m}{yr}}=0.3\ yr\"
\n<\/span><\/p>\n

Plume thickness at the downgradient edge of the drainfield will be:<\/p>\n

\"\displaystyle b=\frac{q\ast t}{porosity}\"<\/span><\/p>\n

\"\displaystyle b=\frac{3.95\frac{m}{yr}\ 0.3\ yr}{0.3}=3.95\ m \sim 4\ m\"
\n<\/span><\/p>\n

Downgradient from the drainfield the average linear vertical velocity will derive from precipitation recharge:<\/p>\n

\"\displaystyle average\ linear\ vertical\ velocity=\frac{net\ recharge\ rate}{porosity}\"<\/span><\/p>\n

\"\displaystyle =\frac{0.9\frac{m}{yr}-0.6\frac{m}{yr}}{0.3}=1\frac{m}{yr}\"<\/p>\n

Given the average linear lateral velocity of 100 m\/yr, the septic system plume will take 3 years to reach the well.<\/p>\n

\"\displaystyle time\ to\ reach\ well=\frac{300\ m}{100\frac{m}{yr}}=3\ yr\"<\/span><\/p>\n

Ignoring dispersion, during those three years, the plume would be driven vertically downward by the net recharge. With the average linear vertical velocity of 1 m\/yr, the 4-m thick plume from the septic field would occur at a depth of 3 to 7 m below the water table at the well location, and could thus pass through the well screen that spans from 5 to 7 m below the water table.<\/p>\n

Return to Exercise 1<\/span><\/a><\/p>\n

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