As mentioned earlier the main application of flow net is that it is employed in estimating
quantity of seepage. If H is the net hydraulic head of flow (i. the difference in total head between
the first and last equipotential), the quantity of seepage due to flow may be estimated by drawing
the flow net, which is shown in Figure 15. With reference to Figures 15 & 17, the following terms
may be defined in order to estimate the quantity of seepage through the earth dam model. It has been noticed from experiments on homogeneous earth dam models that the line of
seepage assumes more or less the shape of a parabola. Also, assuming that hydraulic gradient i is
equal to the slope of the free surface and is constant with depth (Dupit’s theory), the resulting
solution of the phreatic surface is parabola. In some sections a little divergence from a regular
parabola is required particularly at the surfaces of entry and discharge of the line of seepage.
The appearance of the entire flow net should be watched and not that of a part of it. Small details can be adjusted after the entire flow net has been roughly drawn. Let us consider an element of soil of size dx, dz through which flow is taking place. Dams are constructed to impound water for irrigation, water supply, energy generation,
flood control, recreation as well as pollution control. Moreover, disastrous effects of water are
significant on them.
Electrical Analogy Method:
The pressure drop from one side of the embankment to the other,
The seepage flow rate in each flow “channel”,
The total seepage flow rate, and
The pore pressure ratio, ru, for the embankment. A Flow net is a graphical representation of flow of water
through a soil mass. It is a curvilinear net formed by the combination of flow
lines and equipotential lines. Properties and application of flow net are
explained in this article.
What are the rules of flow nets?
- The angle of intersection between each flow line and an equipotential line must be 90o which means they should be orthogonal to each other.
- Two flow lines or two equipotential lines can never cross each other.
- quantity of seepage occurs in each flow channel.
The
properties of the regular parabola which are essential to obtain phreatic line are depicted in Figure
6. Mathematically, the process of making out a flownet consists of contouring the two
harmonic or analytic functions of potential and flow line function. These functions both satisfy
the Laplace equation and the contour lines represent lines of constant head, i.
Various Methods of Drawing Flow Nets
Many researches indicated that
failure of embankment dams due to seepage alone stands for about 25% of the total failure
cases, apart from overtopping, piping, internal erosion, etc (Singh, 1995). Darcy’s law describes the flow of water through the flow net. Since the head drops are uniform by construction, the gradient is inversely proportional to the size of the blocks. Big blocks mean there is a low gradient, and therefore low discharge (hydraulic conductivity is assumed constant here).
- A flow net is a graphical representation of two-dimensional steady-state groundwater flow through aquifers.
- Mathematically, the process of constructing a flow net consists of contouring the two harmonic or analytic functions of potential and stream function.
- Starting from the upstream end, divide the first flow channel into approximate squares.
- A flow net represents the graphical solution of the equations of the steady / continuous flow of
groundwater. - Phreatic line is a seepage line as the line within a dam section below which there are positive hydrostatic pressures in the dam.
- With reference to Figures 15 & 17, the following terms
may be defined in order to estimate the quantity of seepage through the earth dam model.
These functions both satisfy the Laplace equation and the contour lines represent lines of constant head (equipotentials) and lines tangent to flowpaths (streamlines). Together, the potential function and the stream function form the complex potential, where the potential is the real part, and the stream function is the imaginary part. Historically, Stelzer et al, 1987, presented an introductory scheme for plotting contours that
are traced along paths of constant function values. Desai et al, 1988, presented a detailed
theoretical development of Residual Flow Procedure (R.F.) for three dimensional seepage,
and a scheme for locating of the three dimensional free surface. Fan et al, 1992, presented a
simple and unique method for generating flow nets based on nodal potentials and bilinear shape
functions. The method reduces the work of performing a second FEM to compute the stream
potentials at the nodes.
Properties of Flow Net
With F as the centre and QH as the radius, draw an arc to cut vertical line through Q in point P. Now join all the points G, S, P, B to get parabola. The phreatic line must start from B and not from C.
An equivalent amount of flow is passing through each streamtube (defined by two adjacent blue lines in diagram), therefore narrow streamtubes are located where there is more flow. Draw a trial flow line ABC adjacent to boundary line. The line must be at right angles to the upstream and downstream beds. The size of the square in a flow channel should change gradually from the upstream to the downstream.
The equation is used in the construction of flow net. Phreatic line is a seepage line as the line within a dam section below which https://accounting-services.net/chapter-5-flow-nets/ there are positive hydrostatic pressures in the dam. The hydrostatic pressure on the phreatic line itself is atmospheric.
- (Coefficient of permeability is same in all directions)
During flow, the volume of soil & water remains constant. - The following diagram in figure 18 shows a static ground water level within the earth dam
model as derived from the Flow Net shown in Figure 15. - It is a curvilinear net formed by the combination of flow
lines and equipotential lines. - Since the head drops are uniform by construction, the gradient is inversely proportional to the size of the blocks.
- Historically, Stelzer et al, 1987, presented an introductory scheme for plotting contours that
are traced along paths of constant function values.
Construction of a flow net is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical. The method is often used in civil engineering, hydrogeology or soil mechanics as a first check for problems of flow under hydraulic structures like dams or sheet pile walls. As such, a grid obtained by drawing a series of equipotential lines is called a flow net. The flow net is an important tool in analysing two-dimensional irrotational flow problems. Flow net technique is a graphical representation method. A flow net represents the graphical solution of the equations of the steady / continuous flow of
groundwater.
Laplace’s equation governs the flow of an incompressible fluid, through an incompressible
homogeneous soil medium. Continuity equation for
steady state and Darcy’s equations and for the case of isotropic soil, the permeability coefficient is
independent of direction (Craig, 2004). Irregular points (also called singularities) in the flow field occur when streamlines have kinks in them (the derivative doesn’t exist at a point).
A photograph of the experiment set up of the earth dam model was taken as shown in
Figure 2, where the seepage flow lines through the earth dam model and the boundary
conditions are also shown. These seepage flow lines were used as a rough guide for the
flow net construction. Flow lines represent the path of flow along which the water will seep through the soil. Equipotential lines are formed by connecting the points of equal total head.