From Leibniz Integration rule Defining the average head

From Leibniz Integration rule: Defining the average head along the aquifer thickness as Since

Q = -q. B (m/d) It must be recognized that whenever a two dimensional equation in x and y, or a one dimensional equation in x, is used, then the groundwater head is an average value.

for a heterogeneous isotropic confined aquifer for a homogeneous anisotropic confined aquifer For an unconfined aquifer Tx = kx. h and Ty = ky. h. Therefore, above equation for unconfined aquifer is

for a hetero. aniso. unconfined aquifer for a hetero. isotropic unconfined aquifer

for a homogeneous anisotropic unconfined aquifer for a homogeneous isotropic unconfined aquifer

for a confined aquifer for an unconfined aquifer

Governing Equations for Transient Flow Conditions These are also known as time variant, unsteady or non steady state equations. A small control volume element of a confined aquifer is considered. Let there be a decline of the piezometric head by an amount h in a time t in the aquifer. The volume of water released from unit volume of the aquifer due to unit decline of head is termed as the specific storage coefficient. Using this definition,

S

where Ss is specific storage coefficient as defined earlier. Inflow - taken out =out flow Substituting the values of vx, vy and vz from Darcy's law for a hetero. anisotropic aquifer for a heterogeneous isotropic aquifer

for a homogeneous anisotropic aquifer for a homogeneous isotropic aquifer

for a hetero. aniso. Aquifer Radial flow equation for a homo. isotropic aquifer for a homo. anisotropic aquifer for a hetero. isotropic aquifer

Regional Groundwater Flow Equations for Confined Aquifer Dropping the ˜ sign for convenience and using T = k. B, for a heterogeneous confined aquifer

for a homogeneous isotropic confined aquifer for a homo. anisotropic confined aquifer for a hetero. isotropic confined aquifer

Regional Flow in Radial Directions for a heterogeneous confined aquifer for a homogeneous confined aquifer

Regional Flow in an Unconfined Aquifer B of confined aquifer is replaced by variable h and Storage coefficient S is replaced by specific yield Sy Hetr. Aniso. Homog. Iso.

Governing Eq. for a Sloping Confined aquifer

Gov. Eq. for a Sloping Unconfined aquifer Water table Saturated thickness (h-η) η Datum h