Cress Help - Ground water flow - Phreatic water - B26.6

Long parallel channels

This calculation rule calculates the groundwater levels or hydraulic heads of some basic situations in areas with confined and unconfined aquifers and with phreatic water. The theory behind these calculation examples is also examined, by means of which complex situations can be manually calculated. Darcy’s law can also be shown and it is possible to use them to make a calculation. The WATEX and MODUFLOW computer programs can also be used to calculate groundwater flow.

Phreatic water (Unconfined aquifer):

The general differential equation for flow in two directions is:

in which:

h: local hydraulic head (here equal to the height of the place) [m]

Long strip of land with two parallel channels (flowing in the same direction).


     figure 1


This differential equation after the conversion to polar coordinates for radial flow becomes:

    equation 2

The general solution of this is:

    equation 3

The boundary conditions are:

    equation 4

This gives:

    equation 5

and for the total flow:

    equation 6

in which :

  • b: assumed breadth of strip [m]
  • H1 en H2: water levels in the two channels [m]
  • hx: groundwater level at the site x [m]
  • k: permeability [m/s]
  • L: length of strip of land [m]
  • Q: flow though the subsoil [m3/s]

References:

[a] Grondwatermechanica, Handleiding bij het college b90, prof.dr.ir.A. Verruijt, TU Delft, augustus 1992.
[b] Grondmechanica, A. Verruijt, TU-Delft, maart 1990.