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SAME Q T Q t: Q High S Low S different sameTTyields yieldsdifferent same gradient gradient at at well well bore bore different same SSyields yieldssame different volume volume drawdown drawdown cone cone Q S yields Q cone smaller but shape variesproportionally given differentlarger gradient High T Steady state: T differences persist S differences do not Low T SAME S Q t: Hydraulic Diffusivity D = T/S relative rate at which the drawdown cone advances from the well Q Q 2 1 A B High S SAME Q 1 T Q t : Low S Q C High T 2 D SAME S Q t : Low T 1 THINK in 3 Dimensions! … plan view: ?? Explore the influence of pumping andsides the Notice that water comes in from the gradient on the flow field(velocity=0) using a groundand a stagnation zone forms water flow model Fromarea The the contours is surrounded of at a point down gradient of the well. by contours head, how do 42you andknow 44, the head thus heads is must higherbethan 42 in this these between area?values. s vs. log r - is a straight line, if assumptions are met, drawdown decreases logarithmically with distance from the well because gradient decreases linearly with increasing area (2 rh) Theim Eqtn s log r T = transmissivity [L2/T] Q = discharge from pumped well [L3/T] r = radial distance from the well [L] h = head at r [L] and rearranging to get T from field data: Plot before applying equations -WHY to verify you conditions should plotare theappropriate data first? for application of equations - to identify data problems 2 In an unconfined aquifer, T is not constant If drawdown is small relative to saturated thickness, confined equilibrium formulas can be applied with only minor errors Otherwise call on Dupuit assumptions and use: Q pumping well observation well 1 observation well 2 or, to determine K from field measurements of head: s2 s1 r1 r2 Q = pumping rate [L3/T] K = permeability [L/T] hi = head @ a distance ri from well [L] using the aquifer base as datum Why must the aquifer be datum the datum? The aquifer base mustbase be the because the head not only represents the gradient but also reflects the aquifer thickness, hence the flow area. Predict Drawdown Using Theis Equation Class Are these picks: reasonable T and S how do rwe know?t -3 2 1x10 m /s 1x10-5 2m year Take 3 minutes to calculate: s Q 0.01m/s USE table of W(u) from 3 slides back What value did you get for s? ~15m 3