{"id":1349,"date":"2026-05-12T21:47:37","date_gmt":"2026-05-12T21:47:37","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-6\/"},"modified":"2026-05-13T03:33:53","modified_gmt":"2026-05-13T03:33:53","slug":"exercise-6","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-6\/","title":{"raw":"Exercise 6","rendered":"Exercise 6"},"content":{"raw":"
\r\n
\r\n\r\nApply the procedure described in Section\u00a04.3 to Darcy\u2019s law with intrinsic permeability rather than hydraulic conductivity; refer to the following Equation.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]Q = k\\frac{\\rho_{fluid}g}{\\mu_{fluid}}A\\frac{dh}{dl}[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere (parameter dimensions are dark green font with mass as M, length as L, time as T):\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]Q[\/latex]<\/th>\r\n=<\/th>\r\nvolumetric discharge (L3<\/sup>T-1<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]k[\/latex]<\/td>\r\n=<\/td>\r\nintrinsic permeability (L2<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]\\rho_{fluid}[\/latex]<\/td>\r\n=<\/td>\r\ndensity of the fluid (ML-3<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]g[\/latex]<\/td>\r\n=<\/td>\r\ngravitational acceleration (LT-2<\/sup>)<\/td>\r\n<\/tr>\r\n
A<\/em><\/td>\r\n=<\/td>\r\ncross\u2011sectional area perpendicular to flow (L2<\/sup>)<\/td>\r\n<\/tr>\r\n
dh\/dl<\/em><\/td>\r\n=<\/td>\r\nhydraulic gradient ([latex]:[\/latex])<\/td>\r\n<\/tr>\r\n
[latex]\\mu_{fluid}[\/latex]<\/td>\r\n=<\/td>\r\nviscosity of the fluid (ML-1<\/sup>T-1<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\nSolution for Exercise\u00a0<\/span><\/a>6<\/u><\/strong>\u2ba7\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise\u00a06<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Apply the procedure described in Section\u00a04.3 to Darcy\u2019s law with intrinsic permeability rather than hydraulic conductivity; refer to the following Equation.<\/p>\n<\/div>\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]Q = k\\frac{\\rho_{fluid}g}{\\mu_{fluid}}A\\frac{dh}{dl}[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where (parameter dimensions are dark green font with mass as M, length as L, time as T):<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n
[latex]Q[\/latex]<\/th>\n=<\/th>\nvolumetric discharge (L3<\/sup>T-1<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n
[latex]k[\/latex]<\/td>\n=<\/td>\nintrinsic permeability (L2<\/sup>)<\/td>\n<\/tr>\n
[latex]\\rho_{fluid}[\/latex]<\/td>\n=<\/td>\ndensity of the fluid (ML-3<\/sup>)<\/td>\n<\/tr>\n
[latex]g[\/latex]<\/td>\n=<\/td>\ngravitational acceleration (LT-2<\/sup>)<\/td>\n<\/tr>\n
A<\/em><\/td>\n=<\/td>\ncross\u2011sectional area perpendicular to flow (L2<\/sup>)<\/td>\n<\/tr>\n
dh\/dl<\/em><\/td>\n=<\/td>\nhydraulic gradient ([latex]:[\/latex])<\/td>\n<\/tr>\n
[latex]\\mu_{fluid}[\/latex]<\/td>\n=<\/td>\nviscosity of the fluid (ML-1<\/sup>T-1<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Solution for Exercise\u00a0<\/span><\/a>6<\/u><\/strong>\u2ba7<\/p>\n<\/div>\n

\n

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