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.
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.
SoilMech Ch10 Flow Nets – Soil Mechanics Flow Nets page 1…
The equipotential lines are further extended downward, and one more flow line GHJ is drawn, representing the step (4). Extend the equipotential lines downward forming the sides of the squares. These extensions point out appropriate width of the squares, such as squares marked (1) and (2). The accuracy of the computation of hydraulic quantities, such as discharge and pore water pressure, does not depend much on the exactness of the flow net. Also, let Δq represent the discharge passing through the flow channel, per unit length of structure (perpendicular to paper).
What are the methods of drawing flow net in fluid mechanics?
Methods used for Drawing the Flow Nets:
Analytical Method. Graphical Method. Electrical Analogy Method.
Two sets of lines constitute a flow net, which should be always orthogonal to each
other. The flow lines indicate the direction of groundwater flow and the equipotential lines or head
lines (lines which represent the constant head), indicate the distribution of potential energy. The
flow nets are usually built through a trial and error procedure with sketches. The solution of Laplace equation requires knowledge of complex boundary conditions. Geotechnical problems usually have complex boundary conditions for which it is difficult to
obtain a closed form solution.
Soil Mechanics – Exams (2007-
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.
- These types of points often do make other types of solutions (especially numeric) to these problems difficult, while the simple graphical technique handles them nicely.
- 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. - Calculation of the pore pressure ratio for an embankment is highly important, as this value is
extremely useful in embankment stability analysis problems (Smith, 2006). - Also, the phreatic line is a flow line, and must start perpendicularly to the u/s face AB which is a 100% equipotential line.
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.
Compressive Strength of Concrete -Cube Test , Procedure, Results
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.
- The flow net is an important tool in analysing two-dimensional irrotational flow problems.
- To solve this problem analytically it is difficult, but
flow nets can be used to give a graphical answer (Sachpazis et al, 2005). - The solution of Laplace equation requires knowledge of complex boundary conditions.
- Irregular points (also called singularities) in the flow field occur when streamlines have kinks in them (the derivative doesn’t exist at a point).
- 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.
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).
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.
- The base parabola should also meet the ∂/s filter perpendicular at G.
- The horizontal and vertical component of the hydraulic gradient are, respectively.
- Dams are constructed to impound water for irrigation, water supply, energy generation,
flood control, recreation as well as pollution control. - These extensions point out appropriate width of the squares, such as squares marked (1) and (2).
- 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.
The method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid. First identify the hydraulic boundary conditions. 8.3, the upstream bed level GDA represents 100% potential line and the downstream bed level CFJ, 0% potential line.
What must be the maximum dry density of Granular Sub Base & Wet Mix Macadam used …
For this reason, approximate methods such as graphical methods
and numerical methods are often employed. Flow net technique is a graphical method, which
satisfies Laplace equation. A flow net is a graphical representation of a flow field (Solution of
Laplace equation) and comprises a family of flow lines and equipotential lines, as presented in
previous section. For simple embankment dams such as a homogeneous earthfill dam with simple
configurations, the configuration of a flow net https://accounting-services.net/chapter-5-flow-nets/ is relatively straightforward in the determination
of seepage quantity. However, especially for zoned earthfill dams or embankment dams with
different coefficients of permeability for each zone, the complexity of seepage behaviour
increases dramatically. Therefore, seepage modelling using a drainage and seepage tank as well
as a finite element analysis technique can help to solve the problem promptly, thus saving funds
and time, but immolating a marginal reduction of accuracy.
What is the flow net method?
What are the methods of construction of Flow net? A sheet pile is inserted between the upstream and downstream flow. The path followed by the water along the sheet pile creates a flow line. Impervious boundary creates another flow line.
Flow nets are a graphical way / technique for predicting the quantity of groundwater flow from
a given set of boundary conditions. Flow nets are not a rigorous determination of flow, but they
can give an idea of what head looks like underground. Finally, using the above mentioned procedure the average pore pressure ratio, ru, for the whole
embankment of the earth dam model was calculated equal to 0. Flow lines and equipotentials should always be perpendicular to each other, in a
homogeneous isotropic system, and form curvilinear “squares”.