University of Arizona Department of Hydrology and Water Resources Dr. Marek Zreda. HWR431/531 - Hydrogeology Problem set #1 9 September 1998

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1 University of Arizona Department of Hydrology and Water Resources Dr. Marek Zreda HWR431/531 - Hydrogeology Problem set #1 9 September 1998 Problem 1. Read: Chapter 1 in Freeze & Cherry, McGuiness (1963) predicted that the water needs in the US in the year 2000 will reach 3.36*10 9 m 3 /day. How good was his prediction? Are we close to reaching that value? What is the main source of this water? How much of the total water comes from groundwater sources? Problem 2. Water balance, whether on a global or local scale, is described by a mass conservation equation, whose most general form is: flux in - flux out = change of storage The graph to the right shows evolution of different fluxes to and from an aquifer (underground reservoir). The fluxes into the aquifer include recharge from precipitation and recharge from streams. The fluxes out of the aquifer include evapotranspiration and pumping. Analyze the graph. Explain why the different fluxes have changed. What is the relationship between inflows and outflows. Are they independent? Why or why not? Note: Use less than one page for your analysis. In science, concise writing is better than expansive writing. 1

2 Problem 3. Estimated annual water fluxes and estimated volume of water reservoirs are in the tables below. Water fluxes are related to volumes through the time constant, which is the average time a water molecule spends in the reservoir. It is calculated as the ratio of the volume (V) and the flux (F) out of (or into) this volume: T = V/F Using the data provided in the tables, calculate time constants for different water reservoirs. Use other sources and/or make assumptions if necessary. Discuss the results. Why are they significant? Consider physical and chemical aspects, water quality, contamination, replenishment, travel (transport) time, societal issues, etc. Table 1. Estimated annual water fluxes. Process and reservoir Volume (km 3 ) Evaporation From the ocean 350,000 From continents 70,000 Precipitation Over the ocean 320,000 Over continents 100,000 Runoff to the ocean from rivers 38,000 Groundwater outflow to the ocean 1,600 Table 2. Estimated water volume. Reservoir Volume (km 3 ) Water in land areas Freshwater lakes 125,000 Saline lakes and inland seas 104,000 Rivers 1,250 Soil moisture 67,000 Groundwater (<4,000 m) 8,350,000 Ice caps and glaciers 29,200,000 Total in land areas 37,800,000 Atmosphere 13,000 The ocean 1,320,000,000 2

3 Problem 4. Study topics: hydraulic gradient, piezometers, and aquifers and aquitards. Nest of piezometers consists of the following. Piezometer Piezometer Depth Material depth to water A 35 m 20 m sand B 45 m 15 m clay C 55 m 10 m gravel Surface elevation is 225 m a.s.l. (a) For each piezometer, calculate elevation, pressure and total head (b) What is the direction of water flow? (c) What kind of aquifer is C in? (d) What kind of aquifer is A in? (e) Where is B located? Problem 5. Study topics: hydraulic gradient in two and three dimensions, its representation (symbolic, numerical and graphical), its determination in the field. Three piezometers are located in a horizontal, homogeneous and isotropic aquifer. Their locations (x, y, z at the surface) and depths to water (d), all in meters, are: x y z d Well Well Well Draw the contours of the hydraulic head and determine the direction of groundwater flow through the area. Determine the hydraulic gradient. 3

4 Problem 6. Water at 20 C flows through a sand column shown in the figure below. The median grain size d = 0.5 mm, the hydraulic conductivity K = 5 m/d and the porosity n = 25%. (a) Calculate the specific discharge through the column. (b) Calculate and plot the hydraulic head, elevation head and pressure head along the column length x; set x=0 cm at the left end and x=100 cm at the right end. (c) What is the intrinsic permeability of the soil? What material is it likely to be? (d) How will the answer to (a) change when water temperature drops to 5 C? (e) Is Darcy's law applicable in (a) and (d)? Why or why not? (f) Calculate total water pressure in the middle of the column at x=50 cm. (g) Calculate travel time of a labeled water molecule through the column. 4

5 Problem 7. Show that the fluid potential Φ is an energy term, by carrying out a dimensional analysis on the equation: Φ = gz + p/ρ Do so for both the SI and FPS units. Problem 8. (a) Define and describe in about 100 words hydraulic conductivity and intrinsic permeability. Which of them would you prefer to use and why? (b) Compare and contrast porosity and effective porosity. Use about 100 words. (c) Compare and contrast effective porosity and specific yield. Use about 100 words. Problem 9. (HWR/GEOS 531) For the column in problem 6, assume that the effective porosity, ne, varies linearly with distance, x, along the column as: ne = x/L where x is measured along the column and L is the column length (=100 cm). Calculate travel time of a labeled water molecule through the column. Compare with the answer in problem 6. Discuss. 5