# Flow-net analyses

a. Flow nets are valuable where irregular configura­tions of the source of seepage or of the dewatering sys­tem make mathematical analyses complex or impossi­ble. However, considerable practice in drawing and studying good flow nets is required before accurate flow nets can be constructed.

b.A flow net is a graphical representation of flow of water through an aquifer and defines paths of seepage (flow lines) and contours of equal piezometric head (equipotential lines). A flow net may be constructed to represent either a plan or a section view of a seepage pattern. Before a sectional flow net can be con­structed, boundary conditions affecting the flow pat – tem must be delineated and the pervious formation transformed into one where kn = к, (app E). In draw­ing a flow net. the following general rules must be ob served:

(1) Flow lines and equipotential lines intersect at right angles and form curvilinear squares or rec­tangles.

(2) The flow between any two adjacent flow lines and the head loss between any two adjacent equipoten­tial lines are equal, except where the plan or section 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 equipotential nor flow line, and the squares at this sur­face are incomplete; the flow and equipotential lines need not intersect such a boundary at right angles.

(4) For gravity flow, equipotential lines intersect the phreatic surface at equal intervals of elevation, each interval being a constant fraction of the total net head.

c. Flow nets are limited to analysis in two dimen­sions; the third dimension in each case is assumed in­finite in extent. An example of a sectional flow net showing artesian flow from two line sources to a par­tially penetrating drainage slot is given in figure 4-27a. An example of a plan flow net showing artesian flow from a river to a line of relief wells is shown in figure 4-27b.

d. The flow per unit length (for sectional flow nets) or depth (for plan flow nets) can be computed by means of equations (1) and (2), and (5) and (6), respec­tively (fig. 4-27). Drawdowns from either sectional or plan flow nets can be computed from equations (3) and (4) (fig. 4-27). In plan flow nets for artesian flow, the equipotential lines correspond to various values of H— h, whereas for gravity flow, they correspond toH2—h2. Since section equipotential lines for gravity flow con­ditions are curved rather than vertical, plan flow nets for gravity flow conditions give erroneous results for large drawdowns and should always be used with cau­tion.

e. Plan flow nets give erroneous results if used to analyze partially penetrating drainage systems, the er­ror being inversely proportional to the percentage of penetration. They give fairly accurate results if the penetration of the drainage system exceeds 80 percent and if the heads are adjusted as described in the fol­lowing paragraph.

f. In previous analyses of well systems by means of flow nets, it was assumed that dewatering or drainage wells were spaced sufficiently close to be simulated by a continuous drainage slot and that the drawdown (H—hD) required to dewater an area equaled the aver­age drawdown at the drainage slot or in the lines of wells (H—he). These analyses give the amount of flow Qt that must be pumped to achieve H—ho but do not give the drawdown at the wells. The drawdown at the wells required to produce H—hD downstream or within a ring of wells can be computed (approximately) for ar­tesian flow from plan flow nets by the equations shown in figure 4-28 if the wells have been spaced proportional to the flow lines as shown in figure 4-27. The drawdown at fully penetrating gravity wells can also be computed from equations given in figure 4-28.