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##### HONR 297 Environmental Models

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**HONR 297Environmental Models**Chapter 2: Ground Water 2.8: Determining Approximate Flow Direction Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Key Factors for Flow Direction**• From the last section, we saw that the keys to determining flow direction of ground water were hydraulic gradient i = Δh/L and hydraulic contour lines from a given water table contour map. • Using these ideas along with the Key Idea that ground water flows perpendicular to hydraulic head contour lines, we were able to find flow direction and travel time! Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data**• Suppose we are given the scenario illustrated in Figure 2.29 of our text, shown to the right. • In this case, there is a commercial building with three wells drilled into the ground to the east of the building. • Can you guess how one can determine the flow direction of ground water flow from this data? Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data**Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Intermediate**Well • Identify the well head that has a value between the other two. • In this case, Well 1’s head level of 37 feet is between Well 3’s head level (34 feet) and Well 2’s head level (40 feet). Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Intermediate**Point • Since the hydraulic head at Well 1 is between the hydraulic heads of Well 3 and Well 2, there must also be some point along the line segment from Well 3 to Well 2 at which the head value is the same as that for Well 1. • The reason for this is that the hydraulic head must change from Well 3 to Well 2 in a continuous fashion – thus it must hit 37 feet somewhere between these two wells! (Think of contour lines passing through each well …) Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Intermediate**Point • Find the location of this intermediate point P between Wells 3 and 2 – to do so, we can use the idea of proportions! • Since the change in head level from Well 3 to Well 1, relative to the change in head level from Well 3 to Well 2 is (37-34)/(40-34) = 3/6 = 1/2, most likely the distance from Well 3 to the intermediate point P relative to the distance from Well 3 to Well 2 should be the same, i.e. (Distance from Well 3 to point P)/(Distance from Well 3 to Well 2) = 1/2. P Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Intermediate**Point • It follows that Distance from Well 3 to point P = (1/2)(Distance from Well 3 to Well 2) = (1/2)(350 feet) = 175 feet. P Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Contour Line**• Next, we construct our best estimate of the contour line with height 37 feet. • We have two points that are on the 37 – foot contour line, Well 1 and point P. • Since we don’t know any more about the contour line that contains these points, it is standard practice to draw a straight line through these points! P Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Flow**Direction • After we’ve drawn the contour line, we can estimate the groundwater flow direction. • Using the Key Idea, choose a point Q on the 37 – foot contour line so that a perpendicular line segment from Q passes through Well 3 (as shown in Figure 2.30)! Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Flow Directions from Field Data – Flow**Direction Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Determining Hydraulic Gradient from Field Data**• Finally, we can calculate the hydraulic gradient i in the direction of flow! • Using the head levels at point Q and Well 3, we can compute Δh. • The distance L between point Q and Well 3 can be measured off of the map, using the given scale! • We find that i = Δh/L = (37 ft – 34 ft)/(150 ft) = 3/150 = 0.02 Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Additional Example**• Consider the situation shown to the right (Figure 2.31 in Hadlock), which is analogous to the example treated above. Determine the general direction of flow and the corresponding hydraulic gradient.**Additional Example**Courtesy: Charles Hadlock, Mathematical Modeling in the Environment**Resources**• Charles Hadlock, Mathematical Modeling in the Environment, Section 2.8 • Figures 2.29, 2.30, and 2.31 used with permission from the publisher (MAA).