Flow nets provide a graphical representation of solutions to the Laplace equation for two-dimensional seepage. A flow net consists of two orthogonal sets of curves: equipotential lines connecting points of equal total head, and flow lines indicating the direction of seepage. The space between adjacent flow lines is called a flow channel. If the fields of a flow net are square (have equal dimensions) it is called a square flow net, where the rate of flow is equal between each channel. The number of flow channels and equipotential line drops determine the total flow rate according to Darcy's law.

1. (two dimensional flow)
LAPLACE EQUATION

3. x

5. Vz
Vx

6. Flow Nets
Graphical form of solutions to Laplace equation for two-dimensional
seepage can be presented as flow nets. Two orthogonal sets of curves
form a flow net:
 Equipotential lines connecting points of equal total head h
 Flow lines indicating the direction of seepage down a hydraulic
gradient
Two flow lines can never meet and similarly, two equipotential lines can
never meet. The space between two adjacent flow lines is known as a flow
channel, and the figure formed on the flownet between any two adjacent
flow lines and two adjacent equipotential lines is referred to as a field
Referring the following field
The curvilinear average distance between the two adjacent equipotential lines =L
and head drop = ∆h, therefore gradient of flow i. = ∆h/L. In the above figure, b is
the average curvilinear distance between two successive flow lines, then rate of
inflow ∆q = k . i. b.1, here the width normal to the bed is considered unity. So, ∆q
= k . ∆h . b/L.
Characteristics of Square Flow Net. If any flow net having its fields square i.e. b =
L then it is called a square flow net. In case of square flownet ∆q = k. ∆h.

7. Now from the equation of continuity of steady flow, the inflow any field = outflow
from that field which implies that for any particular flow channel bounded by two
adjacent flow lines flow is uniform and hence for any successive fields, head drops
at any two equipotential lines are equal.
Thus if in any flownet, there are n number of potential lines, than number of drop
Nd = n-1 and ∆h = h/Nd when h is the total head drop between upstream and
downstream and so, ∆q = k. h /Nd.
Let’s assume there are Nf number of flow channels, and since for any two
successive equipotential lines head drop ∆h = h/Nd is constant, we can draw
inference that flow through each flow channels ∆q = k. h/ Nd are also equal, so
Total flow q = k. h. Nf/Nd.
Note: In any flownet, Nd is always an integer, though Nf does not. As because at
the boundary of the flownet, it is very rare to have all flow fields are square and
hence looking from the graph we have to approximate it to some decimal values.
Characteristics of Flownet: During drawing the flownet on graph-paper we have
to keep following points namely,
1. No two equaipotential lines should intersect or even touch at any point.
2. No two flow lines should intersect or even touch at any point.
3. The equipotential lines and flow lines should intersect at right angle to
each other.
4. Both the lines should be smooth and free of any sharp bend.