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An inverse hydraulic-conductivity ellipse is then constructed about the point. This ellipse has principal semiaxes and (rather than and , as in Figure 5.7). A line drawn in the direction of the hydraulic gradient intersects the ellipse at the point A. If a tangent is drawn to the ellipse at A, the direction of flow is perpendicular to this tangent line.

- When transforming the y axis, we multiply the y-coordinates of the ellipse by the ratio .
- (5.16) are used for the transformation, but the shape of the region and the resulting flow net are the same in either case.
- We can observe that at any level in the soil sample total head is same for all the points lying in that plane.
- The flow net does not provide precision to the 3 significant figures shown in the contour labels in the diagram.
- Let us consider a small soil element of dimension dx, dy and dz.

Analytical method of obtaining a flow net for a flow of water in a soil mass is a mathematical solution to an equation that is obtained by the flow conditions. It can be used in relatively simple cases of flow, where the boundary conditions are known and can be expressed by equations. Figure Box 5-4 Only a small portion of the field with parallel drains needs to be drawn to develop a flow net. A groundwater divide (no-flow boundary) occurs halfway between two adjacent drains. In addition, flow to the drain from the left is a mirror image of flow from the right. This symmetry enables us to consider the flow to the drain from only one side.

## Dupuit-Forchheimer Theory of Free-Surface Flow

Using knowledge of Darcy’s Law and the fact that flow is parallel to no-flow boundaries, one flow path can be drawn along the concrete dam from the upgradient to the downgradient reservoir (Figure 6). Hydraulic conductivity in an anisotropic aquifer varies with direction. In that case, the https://accounting-services.net/account-balance-definition/ flow lines and equipotential lines of a flow net will not meet at right angles. A rough sketch of the equipotential lines provides an estimate of the number of head drops that will create curvilinear squares. In this case, it is determined that 18 head drops create curvilinear squares.

Because if they cross at any point then the total head at that point will be two values, which is not possible. Let us consider a small soil element of dimension dx, dy and dz. Let’s say water is flowing in the soil because of a hydraulic head h and the hydraulic gradient in the draw flow nets x and z directions are ix and iz respectively. Water is not flowing in y direction as we are analysing flow only in two dimensions. Both of these lines, flow lines and equipotential lines, are crossing each other at right angles and we say they are orthogonal to each other.

## 2 Drawing a Flow Net for a Homogeneous Isotropic System

Hydraulic head is the sum of pressure head in terms of a height of a column of water and elevation. Atmospheric pressure is used as the zero-reference point for quantifying pressure so, at the drain, the pressure is zero and the hydraulic head is equal to the elevation. Consequently, the hydraulic head at the top of the drain is 0.25 m, at the midpoint it is 0.2 m and at the bottom it is 0.15 m.

In homogeneous, isotropic media, the distribution of hydraulic head depends only on the configuration of the boundary conditions. The qualitative nature of the flow net is independent of the hydraulic conductivity of the media. The hydraulic conductivity comes into play only when quantitative discharge calculations are made. The flow nets of Figures 5.2 and 5.3 are equally valid whether the regions of flow are considered to be a few meters square or thousands of meters square.

## How To Draw Flow Net Seepage By Hand

To provide additional practice in visualizing flow nets, this book uses the online computer software, TopoDrive, which simulates groundwater flow in a topographically-driven flow system. If the hydraulic conductivity of the material is known, the volumetric flow rate through the flow domain can be calculated. This book also covers more advanced topics, including treat of a flow domain having a water-table boundary or anisotropic hydraulic conductivity. Second characteristic of the flow net is that flow lines and equipotential lines are orthogonal to each other. So, we can pick up certain points on the different flow lines where total energy lost is equal, or we can say points of same energy level.

- Equations (5.24) through (5.26) are schematically represented, in a self-explanatory way, by the three finite-difference stars of Figure 5.12(c).
- Figure Box 5-6 – An isotropic flow net is drawn in the transformed isotropic system (b) on the right.
- Anisotropy can occur in a horizontal flow net as well as in a vertical one.
- As before, one way to decide if you are creating curvilinear squares is to draw a circle between the intersecting lines.

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