Handbook of Civil Engineering Calculations

(a) Flow net

FIGURE 2

In Fig. 2a, where water flows under a dam under a head H 9 lines AB and CD are flow
lines and EF and GH are equipotential lines.

2. Discuss the relationship of flow and equipotential lines
   Since a water particle flowing from one equipotential line to another of smaller head will
   traverse the shortest path, it follows that flow lines and equipotential lines intersect at
   right angles, thus forming a system of orthogonal curves. In a flow net, the equipotential
   lines should be so spaced that the difference in head between successive lines is a con-
   stant, and the flow lines should be so spaced that the discharge through the space between
   successive lines is a constant. A flow net constructed in compliance with these rules illus-
   trates the basic characteristics of the flow. For example, a close spacing of equipotential
   lines signifies a rapid loss of head in that region.


3. Write the velocity equation
   Let h denote the head on the water at a given point. Equation 2 can be written as

dh

v = -k—- (2a)

dL

where dL denotes an elemental distance along the flow line.

4. State the particular form of the general Laplace equation
   Let jc and z denote a horizontal and vertical coordinate axis, respectively. By investigating
   the two-dimensional flow through an elemental rectangular prism of homogeneous, isen-
   tropic soil, and combining Eq. Ia with the equation of continuity, the particular form of
   the general Laplace equation

#h ^h

^

+

^=°

(4)

is obtained.
This equation is analogous to the equation for the flow of an electric current through a
conducting sheet of uniform thickness and the equation of the trajectory of principal
stress. (This is a curve that is tangent to the direction of a principal stress at each point
along the curve. Refer to earlier calculation procedures for a discussion of principal
stresses.)
The seepage of moisture through soil may be investigated by analogy with either the
flow of an electric current or the stresses in a body. In the latter method, it is merely nec-

(b) Relaxation grid

Water

Dam,