## Interface Flow

The flow of groundwater in coastal aquifers, as shown in Figure 9.10.1, can be treated as an interface flow problem in which two fluids of different densities, fresh and salt water, have a clear interface rather than a transition zone. This flow problem assumes that the fresh water flows over the salt water which is at rest. These flows are denoted as the Ghyben-Duipint approximations.

The pressure distribution in the salt water ps is ps = psgfa - z) 9.10(1)

and the pressure distribution in the fresh water pf is pf = Agfa - z) 9.10(2)

where <j)s and ^ are the head in the salt and fresh water respectively, and z is the distance from the reference plane to the interface. The pressure at any point of the interface must be a single value, that is pf = ps. Therefore, with Equations 9.10(1) and 9.10(2) and with z = Hs — hs, then

Psgfa — Hs + hs) = ftgfa — Hs + hs) 9.10(3) If = Hs and ^ = Hs + hf, Equation 9.10(3) yields hs = —— hf = ahf 9.10(4)

This equation is known as the Ghyben-Herzberg equation. This equation is also valid for confined aquifers, in which the upper boundary of the aquifer is a horizontal impermeable boundary rather than a phreatic surface and hf represents the piezometric head with respect to sea level. The ratio between the densities of salt and fresh water is of the order of 1.025. Then, Equation 9.10(4) shows that groundwater table interface

FIG. 9.10.1 Interface flow in coastal aquifers. (Reprinted from O.D.L. Strack, 1989, Groundwater mechanics, Vol. 3, Pt. 3, Prentice-Hall, Inc.)

hs is about 40 times h. Therefore, in coastal aquifers, storage of 40 m of fresh water exists below sea level for every meter of fresh water above sea level.