Installation — business terrible  1 part
September 8th, 2015
a. The laws governing flow of fluids through porous media and flow of electricity through pure resistance are mathematically similar. Thus, it is feasible to use electrical models to study seepage flows and pressure









SECTIONAL FLOW NET
PLAN FLOW NET
DRAWDOWN AT ANY POINT
N = TOTAL NUMBER OF EQUI POTENTIAL DROPS BETWEEN FULL HEAD, H, AND HEAD AT EXIT, h
e ’ e
ne = NUMBER OF EQUIPOTENTIAL DROPS FROM EXIT TO POINT AT WHICH HEAD, h, IS DESIRED
h_ IS SHOWN IN FIG. 41 О
SEE FIG. 429 FOR HEAD CORRECTION FACTORS,
(Modified from “Foundation Engineering, " G. A. Leonards, ed., 1962, McGrawHill
Book Company. Used with permission of McGrawHill Book Company.)
Figure 427. Flow and drawdown to slots computedfromflow nets.
distribution for various seepage conditions. Both two – and threedimensional models can be used to solve seepage problems.
b. Darcy’s law for twodimensional flow of water
(previously identified as equation (1) in fig. 427) through soil can be expressed for unit length of soil formations as follows:
q = kH’£ (43)
CONSTRUCT PLAN FLOW NET. SPACE WELLS PROPORTIONAL TO FLOW LINES. COMPUTE TOTAL FLOW
tosyStEmFROM EQ 5 FO r ARTESIAN FLOW OR EQ 6 FOR GRAVITY FLOW (FIG. 428). ass U ME IN EQ 5
H’Hh. See fig. 420, b(c; 422, b; AND 426 FOR EXPLANATION OF TERMS.
О
ARTESIAN FLOW
FLOW TO EACH WELL
(5 =*
WHERE П – NUMBER OF WELLS INTHE SYSTEM
DRAWDOWN AT WELLS
FULLYPENETRATING
l w / п і, a
Hh =— 3F+—In——
w bO 277 2777
PARTIALLYPENETRATING
WHERE (7 IS OBTAINED FROM FIG. 421 t
a
HEAD INCREASES MIDWAY BETWEEN AND DOWNSTREAM OF WELLS MAY BE COMPUTED FROM EQUATIONS
GIVEN IN FIG. 420 AND 421.
GRAVITY FLOW
FLOW TO EACH WELL
USE EQ 1
DRAWDOWN AT FULLY PENETRATING WELL
HEAD INCREASES MIDWAY BETWEEN AND DOWNSTREAM OF WELLS MAY BE COMPUTED FROM EQUATIONS GIVEN IN FIG. 422.
t THE AVERAGE WELL SPACING MAY BE USED TO COMPUTE 0 ,0 , AND THE DRAWDOWN AT A N D
a m
BETWEEN WELLS.
U. S. Army Corps of Engineers
Figure 428. Flow and drawdown to wells computed from flownet analyses
where
q = rate of flow к = coefficient of permeability H’ = differential head
f = shape factor dependent on the geometry of the system
C, Ohm’s law expresses the analogous condition for steady flow of electricity through a medium of purere
sistance as follows:
where
I = rate of flow of electricity E = potential difference or voltage p — specific resistance of electrolyte
Since the permeability in fluid flow is analogous to the reciprocal of the specific resistance for geometrically similar mediums, the shape factors for Darcy’s law and Ohm’s law are the same.
d. A twodimensional flow net can be constructed using a scale model of the flow and drainage system made of a conductive material representing the porous media (graphitetreated paper or an electrolytic solution), copper or silver strips for source of seepage and drainage, and nonconductive material representing impervious flow boundaries, The electrical circuit consists of a potential applied across the model and a Wheatstone bridge to control intermediate potentials on the model (fig. 429). The flow net is constructed by tracing lines of constant potential on the model, thus establishing the flownet equipotential lines after which the flow lines are easily added graphically. A
flow net constructed using an electrical analogy model may be analyzed in the same manner as one constructed as in paragraph 43.
e. Equipment for conducting threedimensional electrical analogy model studies is available at the WES. The equipment consists basically of a large plexiglass tank filled with diluted copper sulfate solution and having a calibrated, elevated carrier assembly for the accurate positioning of a point electrode probe anywhere in the fluid medium. A prototype is simulated by fabricating appropriately shaped and sealed source and sink configurations and applying an electrical potential across them. The model is particularly useful for analyzing complex boundary conditions that cannot be readily analyzed by twodimensional techniques.



U. S. Army Corps of Engineers