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Ideal fluid flow
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
A line (or a curve) of constant ϕ is called an equipotential line (or curve). Similarly, a line (or curve) of constant ψ is called a streamline. A line of constant ψ is always tangential to the velocity vector and orthogonal to the equipotential lines. The velocity vector is always normal to the equipotential lines. A set of streamlines and equipotential lines with the spacing between streamlines the same as the spacing between equipotential lines is called a Flow Net. There are several methods of obtaining flow nets, such as Freehand drawingPlotting the equations of ψ and ϕConformal mapping in the complex planeNumerical solution of the Laplace equation.
Groundwater Models
Published in Pat M. Cashman, Martin Preene, Groundwater Lowering in Construction, 2020
Flow net analyses are a graphical representation of a solution of a given two-dimensional groundwater flow problem and its associated boundary conditions. A flow net (Figure 5.2) is a network of ‘flow lines’ and ‘equipotentials’ that, when developed correctly, provide a graphical solution to a steady-state groundwater flow regime in two dimensions. Flow lines represent the paths along which water can flow within a two-dimensional cross section. Equipotentials are lines of equal total head.
Groundwater
Published in Duncan C. Wyllie, Rock Slope Engineering, 2017
The following are characteristics of flow nets that are applicable under all conditions and must be used in drawing flow nets. First, equipotential lines must meet impermeable boundaries at right angles and be parallel to constant head boundaries. Second, a uniform head loss occurs between adjacent equipotential lines. Third, equipotential and flow lines intersect at right angles to form curve-linear squares in rock with isotropic hydraulic conductivity. For a flow net such as that shown in Figure 6.6, the equipotential lines illustrate how the ground water pressure varies within the slope, and that flow quantity is equal between the adjacent flow lines.
Investigating reduction of uplift forces by longitudinal drains with underlined canals
Published in ISH Journal of Hydraulic Engineering, 2018
Farzin Salmasi, Rahman Khatibi, Bahram Nourani
The continuity equation embedded in Equation (1) in an isotropic medium represents two orthogonal families of curves: flow lines and equipotential lines. A flow line is a line along which water particles will travel from high upstream to low potential areas in permeable soil media. An equipotential line is a line along which the potential head at all points is equal. Thus, if piezometers are placed at different points along an equipotential line, the water level will rise to the same elevation in all of them. A combination of a number of flow lines and equipotential lines is called a flow net. To complete the graphic construction of a flow net, flow and equipotential lines are drawn subject to: (i) the equipotential lines intersect the flow lines at right angles and (ii) the flow elements formed are approximately squares.
Effect of upstream semi-impervious blanket of embankment dams on seepage
Published in ISH Journal of Hydraulic Engineering, 2019
where H (m) is potential field of water at any point in soil (as porous media), x and y describe the Cartesian coordinates in 2D simulations. The continuity equation embedded in Equation (7) in an anisotropic medium represents two families of curves: flow lines and equipotential lines. A flow line is a line along which water particles will travel from high upstream to low potential areas in permeable soil media. An equipotential line is a line along which the potential head at all points is equal. Thus, if piezometers are placed at different points along an equipotential line, the water level will rise to the same elevation in all of them. A combination of a number of flow lines and equipotential lines is called a flow net.