Mississippi State University Hydrology Equations Presentation

Mississippi State University Hydrology Equations Presentation

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In this homework, you will be solving and writing about two separate topics:

  1. A mining shaft is sunk into the Earth and passes through an unconfined aquifer. The shaft dimensions are 4m x 4m, and it is continuing to be dug deeper perpendicular to the land surface so we will ignore its depth. The shaft, unsurprisingly, is accumulating water in the bottom, but the owner is trying to avoid paying to fix the problem and instead plans to pump the water out. Since you are in charge, you will have to figure out how to solve the problem. You have a monitoring well dug/installed 30m away from the center of the shaft. Water levels in the well tell you the head here is 14.2 m below a perfectly flat land surface. Workers in the mine report that the water started seeping in at 14.2 m below the surface but have now come in at 14.7 m below the surface. Further details reveal that water seems to seep in for approximately 20 m of the shaft’s length in total. You also injected dye into your monitoring well, and reports came back that it took 10 hours to reach the shaft. Your goals for this project are to identify the aquifer’s transmissivity and the rate at which water is accumulating in the bottom of the shaft. We will continue this fantasy scenario with the belief that all assumptions are met, and equations are valid. To aid you, a worker, who has no sense of scale or ability writing by hand, has drawn you a diagram (see figure).

    Hints: You will not need any advanced equations more difficult than Darcy. Think about what you are given and remember this is a 3D problem. Good luck.



Hydrology Lecture 7a FLOW EQUATIONS: ORIGINS AND BASICS Flow Equations  Rate Law  Conservation of mass (fluid)  LaPlace  Diffusion Rate Law    Developing transport equations: two requirements  Rate law  Conservation statement Rate Law: F = -B grad ϕ  F – flux or flow of something per unit area per unit time  B – conductance or a material property  ϕ – some scalar potential (h, C, T, V) Always has a “-” indicating flow is from where ϕ is high to low. Rate law examples  Darcy: q=-K grad h  Fick: J = -nD’d grad C  Fourier: H = -Ke grad T  Ohm: I = – grad V 1 𝑅 Conservation of Mass  Rate of input – rate of output = rate of accumulation  Movement: ρwqx  Net flux:  If all facies, would have to write more

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