CressHelp - A1 - Wind setup

Cress Help - Ground water flow - Phreatic water - B26.7

Radial flow

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]

Well in circular island (radial flow)

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

The final solution is:

equation 5

and if there are more wells or sources close to the centre (superposition principle)

equation 6

Well flow is positive, source flow is negative.

Here also:

equation 7

in which :

H: thickness of uppermost aquifer [m]
hr: remote hydraulic head r [m]
k: permeability of sand layer [m/s]
Q0: pump flow [m3/s]
R: radius of the island [m]
rw: radius of the filter tube [m]
rj: distance between point of interest and spring/well j [m]
xr: x coordinate of point of interest [-]
xj: x coordinate of spring/well j [-]
yr: y coordinate of point of interest [-]
yj: y coordinate of spring/well j [-]

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.