# Principles of groundwater flow

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3 gradient (i is the same thing as dh/dl, height difference over length difference). Fetter goes on at some length about the inapplicability of Darcy s law under conditions of turbulent flow, but then finally concludes with the statement that: Under most natural ground-water conditions the velocity is sufficiently low for Darcy s law to be valid. We ll stick with that. If we want to use Darcy to estimate flow volume then we would use the equation: Q = AKi or Q = AK dh/dl Where Q is the discharge and A is the cross-sectional area of the aquifer in question. Groundwater will flow down the hydraulic gradient. When we look at flow over the area of an aquifer we are typically interested in two-dimensional flow. In most cases the X and Y dimensions (100s to 10,000s of m) are much greater than the Z dimension (depth: m to 10s of m), and we tend to ignore the vertical component of the flow. When we contour the water table surface on a map, and then draw in flow lines, we are only considering the horizontal component of the flow. Of course there is a vertical component to groundwater flow and to visualize it we need to look at the problem in cross section. Flow nets A flow net is a diagrammatic representation of the groundwater flow within an area either in plan view (map) or cross-section. Flow nets Consider the map area shown to the right where the various numbers represent elevation of the water table, either from observation wells or from measurements of the creek elevation. We can contour the water-table surface as shown below, and then construct flow lines, which are drawn perpendicular to the contours.

4 Equipotential lines and flow lines in plan view This gives us some idea of directions in which the groundwater is likely to be flowing, not surprisingly towards the creek, where it is contributing to the baseflow. The water table contour lines are lines of constant hydraulic head. Lines of constant head are also known as equipotential lines. A flow net for cross-section from the SW to the NE corners of this area is depicted in the following diagram. As for the plan-view diagrams, the equipotential lines are dashed-red and flow lines are dotted-black. The water table is the dashed blue line. The heavy orange lines are no-flow boundaries situated at the two drainage basin divides and at the creek. Groundwater does not flow across these boundaries, at least not the relatively shallow groundwater depicted here. There are some rules for constructing flow nets as follows: (1) flow lines and equipotential lines must cross at right angles, (2) equipotential lines must meet impermeable boundaries and other no-flow boundaries at right angles (3) equipotential lines must be parallel to constant head boundaries. Rules for constructing flow nets Equipotential lines and flow lines in cross section Not all groundwater boundaries are no-flow boundaries. There are four types of boundaries possible: 1) No-flow boundaries. These include boundaries between aquifers and impermeable layers, and drainage divide boundaries as shown Types of groundwater boundaries

5 above. Flow is always parallel to no-flow boundaries. 2) Constant-head boundaries, which are the same as equipotential lines. Flow is always perpendicular to constant head boundaries. 3) Water-table boundaries. The water table is a surface of varying head along which the head is known. Flow is normally at an oblique angle to a water-table boundary. 4) Hydraulic conductivity boundaries. These are boundaries between two layers of differing permeability. Flow paths change direction at conductivity boundaries. The change in direction of a flow path at a hydraulic conductivity boundary can be determined from the formula: K 1 /K 2 = tan 1 / tan 2 Where the symbols are defined as shown to the right. Flow-line refraction at a conductivity boundary Typically 1 will be known and the two K values will be known, so it makes sense to rearrange the formula as follows: tan 2 = tan 1 /( K 1 /K 2 ) Two examples are given in the table below. If the conductivity of the second layer is less than that for first layer, the flow lines will steepen. If the conductivity in the second layer is greater than in the first, the flow lines will flatten. K 1 K Flow-lines for high to low conductivity boundaries and for low to high conductivity boundaries We will do a number of manual flow net exercises in class, but we will also be using some software to help us understand groundwater flow behaviour and rates. The software is Visual Modflow, which is provided on the CD in Fetter. Modflow and Visual Modflow Visual Modflow, which was developed by Waterloo Hydrogeologic in Waterloo Ontario, is an industry-standard program for studying groundwater flow. The version that we have is a student one, not the professional

6 version, but it will do for our purposes, and learning how to use it will be good experience if you ever do work in Hydrogeology. Visual Modflow is actually just a front end program for the program Modflow, which was developed by the U.S. Geological Survey.

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