# Equipotential line

```Oleh :
Arwan Apriyono
Sec
Introduction
Flownet is A network of selected streamlines and
equipotential lines to evaluate seepage in water construction.
Sec
Introduction
Stream line is simply the path of a water molecule.
stream line.
Sec
Introduction
Equipotential line is simply a contour of constant
Sec
Theory
1.
2.
3.
4.
Streamlines Y and Equip. lines  are .
Streamlines Y are parallel to no flow
boundaries.
Grids are curvilinear squares, where
diagonals cross at right angles.
Each stream tube carries the same flow.
Flow Net Theory
6
Flow Net in Isotropic Soil
Portion of a flow net is shown below
Y
F
Flow Net in Isotropic Soil

The equation for flow nets originates from
Darcy’s Law.

Flow Net solution is equivalent to solving the
governing equations of flow for a uniform
isotropic aquifer with well-defined boundary
conditions.
8
Flow Net in Isotropic Soil

Flow through a channel between
equipotential lines 1 and 2 per unit width
is:
∆q = K(dm x 1)(∆h1/dl)
m
F1
Dq
Dq
D h1
dm
dl
n
F2
D h2
F3
Flow Net in Isotropic Soil

Flow through equipotential lines 2 and 3 is:
∆q = K(dm x 1)(∆h2/dl)

The flow net has square grids, so the head drop
is the same in each potential drop:∆h1 = ∆h2

If there are nd such drops, then:
∆h = (H/n)
where H is the total head loss between the first
and last equipotential lines.
10
Flow Net in Isotropic Soil

Substitution yields:
 ∆q = K(dm x dl)(H/n)

This equation is for one flow channel. If there
are m such channels in the net, then total
flow per unit width is:
 q = (m/n)K(dm/dl)H
11
Flow Net in Isotropic Soil

Since the flow net is drawn with squares,
then dm  dl, and:
q = (m/n)KH
[L2T-1]
where:





q = rate of flow or seepage per unit width
m= number of flow channels
n= number of equipotential drops
h = total head loss in flow system
K = coefficient of permeability
12
Drawing Method:
1. Draw to a convenient scale the cross
sections of the structure, water elevations,
and aquifer profiles.
2. Establish boundary conditions and draw one
or two flow lines Y and equipotential lines F
near the boundaries.
13
Method:
3. Sketch intermediate flow lines and equipotential
lines by smooth curves adhering to right-angle
intersections and square grids. Where flow
direction is a straight line, flow lines are an equal
distance apart and parallel.
4. Continue sketching until a problem develops. Each
problem will indicate changes to be made in the
entire net. Successive trials will result in a
reasonably consistent flow net.
14
Method:
5.
In most cases, 5 to 10 flow lines are usually
sufficient. Depending on the no. of flow lines
selected, the number of equipotential lines
will automatically be fixed by geometry and
grid layout.
6. Equivalent to solving the governing
equations of GW flow in 2-dimensions.
15
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