Darcy Law has many applications in hydrogeology QKi

Darcy Law has many applications • in hydrogeology Q=Ki. A • where • . Q = quantity of water discharged, m 3 • . (K = hydraulic conductivity (constant factor • . i = hydraulic gradient, in meter • A = cross-sectional area, in square meter • . •

Q proportional to the cross-sectional area , A , of the column, proportional to the difference in water level elevations , h 1 and h , 2 in the inflow and outflow reservoirs of the column, respectively, and inversely proportional to the column length , L. When combined, these conclusions give the famous Darcy's formula, or Darcy's law: where K is a coefficient of proportionality called hydraulic conductivity. It will be discussed in detail below. The elevations h 1 and h 2 are measured with respect to some common datum level. The figure below shows how Darcy's experiment is extended to flow through an inclined column of saturated, homogeneous porous medium.

Hydraulic conductivity

Constant head permeameter

Constant head permeameter

Constant head pemeameter Q=Ki. A • --where • . Q = quantity of water discharged, m 3 • . (K = hydraulic conductivity (constant factor • . i = hydraulic gradient, in meter • A = cross-sectional area, in square meter • . •

Falling head permeameter

Falling head permeamter

In(ho/ht) = (KAt)/(a. L) These equations can be used in two ways. 1. If we monitor the water level ht with time, we can plot In(ho/ht) vs t. The resulting slope is (KA)/(a. L), from which the value of K can be determined. 2. If we only have a measurement of h at time 0 and at the end of the experiment, we can calculate K by rearranging the above equation as: K = (a. L)/(At) x In(ho/ht

Groundwater Velocity

V true = V darcy / n

Transmissivity

Hydraulic conductivity &Transmissibilty

Transmissivity T=Kb • Darcy's Law becomes: • A=bw • Q = Kb w dh/ dl • Q = T W (H / L) • where W is the width of the aquifer • T = Q x dl/W x dh • T = m 3 x day. Xm / m x m = m 2/day •

Storage Coefficient

Storage of confined aquifer In confined aquifer, porosity 0. 2 and 15 • o C, the expansion of water alone releases about 3 x 10 -7 m 3 of water per cubic meter of the aquifer per meter of decline in head. To determine the storage coefficient of an aquifer due to expansion of the water , it is necessary to multiply the aquifer thickness (h) X 3 x 10 -7 m 3 Example: S = 3 x 10 -7 m 3 x 100 • (thickness) •

In high pressure, artesian, confined aquifers: S ranges from. 001 to. 00001 Small withdrawals result in large reductions of the potentiometric surface. In unconfined, water table aquifers: S ranges from. 3 to. 01 Much more water can be removed without seriously affecting water table levels.