{"id":107,"date":"2022-12-30T18:15:40","date_gmt":"2022-12-30T18:15:40","guid":{"rendered":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-6\/"},"modified":"2023-01-08T04:34:15","modified_gmt":"2023-01-08T04:34:15","slug":"solution-exercise-6","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/variable-density-groundwater-flow\/chapter\/solution-exercise-6\/","title":{"raw":"Solution Exercise 6","rendered":"Solution Exercise 6"},"content":{"raw":"
\r\n

K<\/em>f <\/em><\/sub>= <\/em>10\u00a0m\u00a0d\u22121<\/sup>, which is 1.2 \u00d7 10\u22124<\/sup> <\/span>m\u00a0s\u22121<\/sup>, so with<\/p>\r\n

[latex]\\displaystyle K_{f}=\\frac{k\\rho _{f}g}{\\mu _{f}}[\/latex]<\/p>\r\n

The Rayleigh number can be calculated as<\/p>\r\n

[latex]\\displaystyle Ra=\\frac{\\Delta \\rho gkH}{\\mu D_{c}}=\\frac{K_{f}\\Delta \\rho gH}{\\rho _{f}D_{C}}=[\/latex] [latex]\\displaystyle \\frac{1.2\\times 10^{-4}\\times 25\\times 9.81\\times 10}{1000\\times 5.0\\times 10^{-10}}=5.7\\times 10^{5}[\/latex]<\/p>\r\n

Where it was assumed that D<\/em> = D<\/em>C<\/em><\/sub> = 5.0 \u00d7 10\u221210 <\/sup><\/span>m2<\/sup>\u00a0s\u22121<\/sup> and the representative density values for fresh water and seawater were taken as provided in the text of this book.<\/p>\r\n

Return to <\/span>Exercise <\/span>6<\/span><\/a><\/p>\r\n

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

\n

K<\/em>f <\/em><\/sub>= <\/em>10\u00a0m\u00a0d\u22121<\/sup>, which is 1.2 \u00d7 10\u22124<\/sup> <\/span>m\u00a0s\u22121<\/sup>, so with<\/p>\n

\"\displaystyle K_{f}=\frac{k\rho _{f}g}{\mu _{f}}\"<\/p>\n

The Rayleigh number can be calculated as<\/p>\n

\"\displaystyle Ra=\frac{\Delta \rho gkH}{\mu D_{c}}=\frac{K_{f}\Delta \rho gH}{\rho _{f}D_{C}}=\" \"\displaystyle \frac{1.2\times 10^{-4}\times 25\times 9.81\times 10}{1000\times 5.0\times 10^{-10}}=5.7\times 10^{5}\"<\/p>\n

Where it was assumed that D<\/em> = D<\/em>C<\/em><\/sub> = 5.0 \u00d7 10\u221210 <\/sup><\/span>m2<\/sup>\u00a0s\u22121<\/sup> and the representative density values for fresh water and seawater were taken as provided in the text of this book.<\/p>\n

Return to <\/span>Exercise <\/span>6<\/span><\/a><\/p>\n

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