(4) For gravity flow, equipotential lines intersect

or

the phreatic surface at equal intervals of elevation,

(4-2a)

each interval being a constant fraction of the total net

with

head.

=

1n(Rrw)

sions; the third dimension in each case is assumed in-

where

finite in extent. An example of a sectional flow net

G = quantity shown in equation (6), figure 4-10

showing artesian flow from two line sources to a par-

tially penetrating drainage slot is given in figure

Figure 4-26 shows some of the results obtained at the

4-27a. An example of a plan flow net showing artesian

flow from a river to a line of relief wells is shown in

inside a circular source. Also presented in figure 4-26

figure 4-27b.

are boundary curves computed for well-screen penetra-

or depth (for plan flow nets) can be computed by

boundary formulas indicates fairly good agreement for

means of equations (1) and (2) and (5) and (6) respec-

well penetrations > 25 percent and values of R/D be-

tively (fig. 4-27). Drawdowns from either sectional or

tween about 5 and 15 where R/rw > 200 to 1000.

plan flow nets can be computed from equations (3) and

Other empirical formulas for flow from a partially

(4) (fig. 4-27). In plan flow nets for artesian flow, the

netrating well suffer from the same limitations.

equipotential lines correspond to various values of H-

(4) *Partially penetrating *wells. The equations for

h, whereas for gravity flow, they correspond to H2-h2.

Since section equipotential lines for gravity flow con-

considered valid for relatively high-percent penetra-

ditions are curved rather than vertical, plan flow nets

tions.

for gravity flow conditions give erroneous results for

large drawdowns and should always be used with cau-

tion.

tions of the source of seepage or of the dewatering sys-

analyze partially penetrating drainage systems, the er-

tem make mathematical analyses complex or impossi-

ror being inversely proportional to the percentage of

ble. However, considerable practice in drawing and

penetration. They give fairly accurate results if the

studying good flow nets is required before accurate

penetration of the drainage system exceeds 80 percent

flow nets can be constructed.

and if the heads are adjusted as described in the fol-

lowing paragraph.

water through an aquifer and defines paths of seepage

(flow lines) and contours of equal piezometric head

flow nets, it was assumed that dewatering or drainage

(equipotential lines). A flow net may be constructed to

wells were spaced sufficiently close to be simulated by

represent either a plan or a section view of a seepage

a continuous drainage slot and that the drawdown

pattern. Before a sectional flow net can be con-

(H-hD) required to dewater an area equaled the aver-

structed, boundary conditions affecting the flow pat-

age drawdown at the drainage slot or in the lines of

tern must be delineated and the pervious formation

wells (H-h,). These analyses give the amount of flow

transformed into one where kn = kv (app E). In draw-

QT that must be pumped to achieve H-hD but do not

ing a flow net, the following general rules must be ob-

give the drawdown at the wells. The drawdown at the

served:

wells required to produce H-ho downstream or within

(1) Flow lines and equipotential lines intersect at

a ring of wells can be computed (approximately) for ar-

right angles and form curvilinear squares or rec-

tesian flow from plan flow nets by the equations

tangles.

shown in figure 4-28 if the wells have been spaced

(2) The flow between any two adjacent flow lines

proportional to the flow lines as shown in figure 4-27.

and the head loss between any two adjacent equipoten-

The drawdown at fully penetrating gravity wells can

tial lines are equal, except where the plan or section

also be computed from equations given in figure 4-28.

cannot be divided conveniently into squares, in which

case a row of rectangles will remain with the ratio of

the lengths to the sides being constant.

(3) A drainage surface exposed to air is neither an

media and flow of electricity through pure resistance

equipotential nor flow line, and the squares at this sur-

are mathematically similar. Thus, it is feasible to use

face are incomplete; the flow and equipotential lines

electrical models to study seepage flows and pressure

need not intersect such a boundary at right angles.

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