where:

=

fluid density, in (mass/length

3

)

  =

fluid viscosity, in (mass/length time)

v =

specific discharge, in (length/time)

d =

some characteristic dimension of the system, often represented

by the average grain size diameter.

The range of the Reynolds numbers over which Darcy's law is valid depends on the

definition of "d," or diameter of the passageway through which the ground water moves.

When "d" is approximated as average grain size diameter, Darcy's law is only valid for

Reynolds numbers in the range of 1 to 10.

The basic hydraulic principles governing flow through porous media are not applicable

to aquifers where ground water flow is primarily through conduits. Flow through caves

(conduits that can be entered at the earth's surface) and conduits is referred to as conduit

flow. Most conduit flow is turbulent, is analogous to the flow of surface streams, and

resurfaces at a spring or group of springs. Water quality in these springs is usually

representative of the mean water quality of the ground water basin. Aquifers in which

subsurface conduits dominate the flow regime are described in terms of their drainage pattern

rather than by the concept of a water table; these drainage patterns are usually a network of

smaller conduits that contribute their flow to the larger "trunk" conduits. The prediction of

flow paths in such aquifers is not usually possible from wells alone, unlike other aquifers.

Ground water flow in conduits of karst aquifers differs radically from flow in porous

media. Velocities on the order of hundreds of feet per hour may occur in conduits (Quinlan,

1990). Thus, the effects of a release of hazardous material on water quality in an aquifer

dominated by conduit flow can commonly be detected at great distances in less than a day.

In addition, water levels in these aquifers can commonly change rapidly and substantially in

response to heavy rains. Observation wells that intercept conduits in the Mammoth Cave area

of Kentucky typically have water level fluctuations of 60 to 80 feet and at times exceed 100

feet or more.

"Diffuse flow" is a term applied to aquifers in which ground water flow is

predominantly through poorly integrated pores, joints, and tubes. Diffuse flow is intermediate

between flow through fractures and conduits, and flow through porous media. Ground water

flow in aquifers in which diffuse flow predominates is generally laminar and can be described

by Darcy's law (Quinlan, 1989). Many springs in karst terranes are fed by a mixture of both

diffuse and conduit flow, and, in a given region, some springs can be fed by primarily

conduit flow systems, while other nearby springs can be fed by primarily diffuse flow

systems. Although conduit flow is turbulent by definition (and as such, is not described by

Darcy's law), a spring fed by a diffuse flow system may discharge from a conduit and may

have turbulent flow. This is particularly true in structurally and stratigraphically complex

November 1992

4 37