A phreatic aquifer is defined as the aquifer where water table is considered as the upper boundary of the aquifer. In case of phreatic aquifer, the phreatic surface is never horizontal and the equipotential lines are not vertical. As such, the hydraulic head (φ) is a function of spatial coordinates x, y , z   and time t. Further on the phreatic surface, a non-linear boundary condition has to be specified. At the same time, the location of the phreatic surface is also not known. Fig. 8.1 (a) shows the actual phreatic surface with streamline. At point p, specific discharge is in a direction tangent to the

Fig. 8.1 Pressure distribution

streamline. The specific discharge can be expressed as,

(8.1)

At phreatic surface, pressure is zero, hence φ = z.  As per the observation made by Dupuit (1863), the slope of the phreatic surface is very small and is in the range of 1 in 1000 to 10 in 1000. As such, Dupuit suggested that sinθ can be replaced by tanθ. Thus the equation (8.1) can be written as

(8.2)

It may be noted that assumption of small θ is equivalent to the following assumptions

1. Equipotential lines are vertical, and
2. The flow is essentially horizontal

For the Fig. 8.2, if we consider Dupuit assumption, the hydraulic head is a function of x and y only, i.e. h(x,y).

Fig. 8.2 Flow in phreatic aquifer

Thus

(8.3)