If we assume changes in water mass through time ( ρw δℎ proportional to changes in head ( )……… ρ2w𝑛 δ𝑡 ) are δ𝑡 We can re-write the change in water mass through time as Ss Ss δℎ δ𝑡 where Ss represents specific storage (just S is storage) Hydrology Lecture 7b DRIVE Drive Topography Hydraulic Conductivity Topography Groundwater will mimic (when possible) the land surface in flow https://igws.indiana.edu/images/marionCounty/Hydro4.jpg Hydraulic Conductivity Different materials will transmit water faster than others https://lh3.googleusercontent.com/proxy/WnU6sI7bpqWJi1IiVE2e3WZUGZjAoVIGGrtbGJSmVr5c4T_6HWi5qF8WvjkL9U2zBk2YE_VJvaYu5RRHZSrZMMt5rvspb9_tHvk80pHA_5Xwa5dYa5n Hydraulic Conductivity Example: French Drain https://www.lawn-expert.com/wp-content/uploads/2019/11/french-drain.jpg Hydrology Lecture 7c HYDROLOGIC FLOW AND ASSUMPTIONS Assumptions 1. Aquifer bounded on bottom by confining layer 2. Geologic formations are horizontal and extend horizontally indefinity 3. Potentiometric aquifer surface is horizontal prior to pumping 4. Potentiometric aquifer surface is not changing with time prior to pumping 5. All changes to the potentiometric aquifer surface are due to pumping 6. Aquifer is homogenous and isotropic https://livinghistoryfarm.org/farminginthe50s/media/water1201.jpg Assumptions 7. Flow is radial towards well 8. Groundwater flow is horizontal 9. Darcy’s law is valid 10. Groundwater has constant density and viscosity 11. Pumping and observation well are fully penetrating (screened over whole thickness 12. Pumping well has an infinitesimal diameter and is 100% efficient https://livinghistoryfarm.org/farminginthe50s/media/water1201.jpg Flow Steady State Unconfined Confined Unconfined δ 2ℎ Kr δ𝑟2 Assumptions: 1. Aquifer unconfined 2. Vadose zone does not influence drawdown 3. Initial water comes from elastic storage 4. Eventually water comes from gravity drainage 5. Drawdown is negligible compared to saturated aquifer thickness 6. Specific yield is at least 10x elastic storativity 7. Aquifer may be, but does not have to be, anisotropic with radial K different that vertical K + 𝐾𝑟δℎ 𝑟δ𝑟 + δ 2ℎ Kv δ𝑧2 = 𝛿ℎ Ss 𝛿𝑡 Flow Steady State Unconfined Confined Confined δ2ℎ δ𝑥2 + δ2ℎ δ𝑦2 = 𝑆 𝛿ℎ 𝑇 𝛿𝑡 two dimensional version of LaPlace’s equation T is transmissivity (T=K*aquifer thickness) Transmissivity and cone of depression Radial Confined vs. unconfined Drawdown https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSkf_nLLhdE7MYbzJ0EdT4JhbyETLMwO5Qd3g&usqp=CAU Cone of depression https://www.blackforestwater.org/uploads/1/2/6/7/126759640/slide6.jpg Storage https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRq61mQJDRDWogCOOAmkbrY4hqJe_qS10RmKQ&usqp=CAU Theis Equation − ∞𝑒 𝑎 𝑄 𝑑𝑎 4π𝑇 𝑢 𝑎 ho – h = ho – h = Used to find transmissivity and storativity 𝑄
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