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Midterm Exam Dr Name: Hydrogeology - HWR/GEOS 431/531 Midterm exam Dr. Marek Zreda 18 October 2010 12:00 - 12:50 Closed books and notes; one “cheat” page allowed The exam contains 6 problems on 3 pages. The total is 100 points. Read the entire exam first. Problem 1. [20 points, 4 points each] Circle the best answer(s); explain your choice briefly: (a) In clay-rich soils (i) specific yield approximately equals total porosity (ii) effective porosity is much larger than specific yield (iii)effective porosity approximately equals total porosity (iv)all of the above (v) none of the above (b) In flow net analysis (i) only homogeneous hydraulic conductivity can be analyzed (ii) no-flow boundary is an equipotential line (iii)prescribed-head boundary is a flow line (iv)aspect ratio of cell width to length must always be unity (v) none of the above (c) Specific yield has the same units (dimensions) as (i) specific storage coefficient (ii) transmissivity (iii)Reynolds number (iv)hydraulic head (v) none of the above (d) In the system in which principal directions of anisotropy are not aligned with x and y (both horizontal), the transmissivity tensor has (i) one non-zero component (ii) three non-zero components (iii)nine non-zero components (iv)none of the above (e) In homogeneous and isotropic aquifer (i) the specific discharge is always in the direction of the hydraulic gradient (ii) the specific discharge may be in the direction of the hydraulic gradient (iii)the specific discharge is never in the direction of the hydraulic gradient (iv)none of the above 1/3 HWR/GEOS 431/531 - Midterm exam - Dr. Marek Zreda - 18 October 2010 Problem 2. [20 points; 4 points each] Describe the following terms (in words, figures and using formulas, where applicable): (a) groundwater residence time. (b) hydraulic conductivity. (c) equipotential line. (d) effective stress. (e) piezometer. Problem 3. [10 points, 5 points each] (a) Define specific storage coefficient and specific yield. In less than half a page compare and contrast the concepts (and parameters) of specific storage coefficient and specific yield. (b) The hydraulic head of a 100-m thick aquifer drops 10 m over the area of 100 km2, yielding 107 m3 for irrigation. What is the specific storage coefficient of the aquifer? Problem 4. [10 points, 5 points each] (a) A horizontal, confined aquifer has a hydraulic conductivity K=10 m/d for water and a porosity n=0.2. Two wells placed 100 m apart on the same flow line measure a head difference dh=1 m. If the upstream well is contaminated, how soon would the first traces of the contaminant appear in the downstream well? (In other words, calculate travel time from one well to the other.) (b) If the aquifer in part a is actually composed of n layers of different hydraulic conductivities K1, K2, ..., Kn, such that the effective K for flow parallel to layers is the same as that in part a (i.e., 10 m/d), is the travel time the same, shorter or longer than that computed in part a? Problem 5. [10 points, 5 points each] (a) What does the following equation describe? Define all variables. Describe each physically meaningful term or group of terms. Remember that terms that physically belong together may be separated by other terms. 2 2 S ∂h ∂ h + ∂ h = ----s ∂x2 ∂y2 K ∂t (b) Write an equation for 3D transient groundwater flow in a heterogeneous, isotropic phreatic aquifer. 2/3 HWR/GEOS 431/531 - Midterm exam - Dr. Marek Zreda - 18 October 2010 Problem 6. [30 points, 10 points each] Equipotentials in the figure are for steady-state flow between an injection well and a pumping well (this is called a closed-cell flow system). The aquifer thickness is 10 m. Do the following: (a) Complete the flow net; use arrows to indicate the direction(s) of flow. (b) If the pumping rate and injection rates are the same and are 1000 m3 d-1, calculate the aquifer transmissivity and the hydraulic conductivity. (c) A chemical tracer injected in the injection well was detected in the pumping well after 1 day. (assume that water leaves injection well at contour 26 m, and enters the pumping well at con- tour 14 m). Determine the porosity of the aquifer. What kind of porosity is this? 60 Contours in meters 50 40 30 14 Y (m) Y 26 15 25 16 24 20 17 23 22 18 21 10 19 20 0 0 102030405060 X (m) 3/3.
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