{"id":910,"date":"2020-12-09T05:05:57","date_gmt":"2020-12-09T05:05:57","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/?post_type=chapter&p=910"},"modified":"2020-12-10T17:52:29","modified_gmt":"2020-12-10T17:52:29","slug":"solution-to-exercise-11","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/chapter\/solution-to-exercise-11\/","title":{"raw":"Solution to Exercise 11","rendered":"Solution to Exercise 11"},"content":{"raw":"11) Write the governing equation that describes two-dimensional (x and y), steady-state flow in a confined anisotropic and homogenous aquifer.\r\n\r\nThis can be generated using Equation 68 in this book.\r\n\r\n\r\n\r\n
[latex]\\displaystyle S_s\\frac{\\partial h}{\\partial t}\\ =\\ K_x\\frac{\\partial^2h}{\\partial x^2}+K_y\\frac{\\partial^2h}{\\partial y^2}+K_z\\frac{\\partial^2h}{\\partial z^2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis equation describes three-dimensional flow in a confined aquifer under transient, anisotropic and homogenous conditions. To generate the equation for steady state in two dimensions, set the left-hand side to zero and eliminate the z term.\r\n\r\n\r\n\r\n
[latex]\\displaystyle 0 =\\ K_x\\frac{\\partial^2h}{\\partial x^2}+K_y\\frac{\\partial^2h}{\\partial y^2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Return to Exercise 11<\/a><\/p>","rendered":"

11) Write the governing equation that describes two-dimensional (x and y), steady-state flow in a confined anisotropic and homogenous aquifer.<\/p>\n

This can be generated using Equation 68 in this book.<\/p>\n\n\n\n
\"\displaystyle S_s\frac{\partial h}{\partial t}\ =\ K_x\frac{\partial^2h}{\partial x^2}+K_y\frac{\partial^2h}{\partial y^2}+K_z\frac{\partial^2h}{\partial z^2}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

This equation describes three-dimensional flow in a confined aquifer under transient, anisotropic and homogenous conditions. To generate the equation for steady state in two dimensions, set the left-hand side to zero and eliminate the z term.<\/p>\n\n\n\n
\"\displaystyle 0 =\ K_x\frac{\partial^2h}{\partial x^2}+K_y\frac{\partial^2h}{\partial y^2}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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