CE3354 - Homework 10

CE 3354 – Engineering Hydrology FALL Nohemi Aradillas R11786083 11/17/2023 CE 3354 Engineering Hydrology Required HW 10 Due date Nov 17th and posting date Nov 9th Exercises 1. Figure 1 depicts a cubic meter of material that contains 0.26 cubic meters of liquid when saturated. Figure 1: Cubic meter of saturated geologic material (a) What is the volume of voids in the material? ? ?𝑜𝑖?? = 0.26 ? 3 (b) Write the equation that relates void volume ( V v ), sample volume( V b ), and porosity ( n ). ? = ? ?𝑜𝑖?? ? ???? = 0.26? 3 1.0 ? 3 = 0.26 (c) If the density of the liquid is 9800 N/ m 3 , what would be the weight change of a saturated sample is completely dried (all liquid removed)? Show your arithmetic. ? = ? ????? ? ???? ( 1 𝜌 ????? ) : 0.26 = ? ????? 1.0 ? 3 ( 1 9800 ? ? 3 ) ? ????? = 2548 ?

CE 3354 – Engineering Hydrology FALL 202 3 2. Water flows through the aquifer system shown in Figure 2. The heads in the two monitoring wells are 77.0 m and 71.0 m. Figure 2: Confined aquifer system with three formations in series (a) Write the equation for flow rate through a 1-meter wide (into the figure) portion of aquifer. 𝑄 = −?𝐴 ∆ℎ ∆? (b) Using the equation, estimate flow rate through a 1-meter wide (into the figure) portion of aquifer.

CE 3354 – Engineering Hydrology FALL 202 3 3. Three wells monitor water levels in a confined aquifer. Well MW-A is located 3000 feet south of Well MW-B. Well MW-C is located 2000 feet due west of Well MW-B. The top of casing (TOC) elevations for the three wells are 480 feet, 610 feet, and 545 feet. The depth to water (DTW) in the three wells are 40 feet, 140 feet, and 85 feet. Table 1 is a listing of these values. Table 1: Casing elevations and depth to water in three monitoring wells. Well TOC (feet) DTW (feet) Head (feet) MW-A 480 40 MW-B 610 140 MW-C 545 85 Figure 3 is a sketch that shows the relationship between the top of casing elevation, depth to water, and head in the confined aquifer. Figure 3: Sketch showing the relationship of top of casing (TOC) and depth to water (DTW) (a) Using Figure 3 as a guide, write the formula to convert the depth-to-water (DTW) measurements and top-of-casing (TOC) values into head. 𝑇?? − ?𝑇? = 𝐻??? (b) Using Figure 3 as a guide, compute the head in MW-A. Show your arithmetic. 480 − 40 = 440 (c) Using Figure 3 as a guide, compute the head in MW-B. Show your arithmetic.

CE 3354 – Engineering Hydrology FALL 202 3 610 − 140 = 470 (d) Using Figure 3 as a guide, compute the head in MW-C. Show your arithmetic. 545 − 85 = 460 (e) Complete Table 1 by entering your values computed above into the table. Well TOC (feet) DTW (feet) Head (feet) MW-A 480 40 440 MW-B 610 140 470 MW-C 545 85 460 (f) A sketch of the orientation of the three wells is shown on Figure 4 (Next Page). Write the value of head you computed next to each well on the sketch. (g) Determine the direction of flow using three-well triangulation. Show your arithmetic. 2000? + ? = 440 3000? + ? = 460 2000? + 3000? + ? = 470 460’ 470’ 440'

CE 3354 – Engineering Hydrology FALL 202 3 (j) `Draw and label the equipotential line that passes through well MW-C. (k) Determine the distance along the flowline between the two equipotential lines. (l) Estimate the magnitude of the hydraulic gradient. √ 0.005 2 + 0.015 2 = 0.0158 2000’

CE 3354 – Engineering Hydrology FALL 202 3 Figure 4: Three-wells monitoring a confined aquifer.