For the conditions of problem 11.2, assume h 1 = 40 m, h 2 = 30 m, L = 5, 000 m, h 0 = 25 m, K = 40.

For the conditions of problem 11.2, assume h1 =
40 m, h2 = 30 m, L = 5, 000 m, h0 = 25 m, K = 40 m/d,  =
0.01 m/d, and b = 5 m

(a) Develop a numerical scheme incorporating linearization
of the basic differential equation and an iterative procedure for the
calculation of the piezometric head distribution in the aquifer. As an
alternative, apply a perturbation approach with another iterative scheme. In
your solution, state clearly which approach you are using.

(b) Apply your numerical scheme and solve the nonlinear
boundary value problem for the distribution of piezometric head in the
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For the conditions of problem 11.2, assume h1 =
40 m, h2 = 30 m, L = 5, 000 m, h0 = 25 m, K = 40 m/d,  =
0.01 m/d, and b = 5 m

(a) Develop a numerical scheme incorporating linearization
of the basic differential equation and an iterative procedure for the
calculation of the piezometric head distribution in the aquifer. As an
alternative, apply a perturbation approach with another iterative scheme. In
your solution, state clearly which approach you are using.

(b) Apply your numerical scheme and solve the nonlinear
boundary value problem for the distribution of piezometric head in the aquifer,
as well as the variation of the aquifer flow rate and the rate of seepage along
the aquifer.

problem 11.2

Flow occurs through a phreatic aquifer in the x-direction as
shown in Fig. 11.11. The length of the aquifer is L and the hydraulic
conductivity is K. The bottom of the aquifer is semipermeable, and it separates
the aquifer from a deeper confined aquifer with constant head h0. The thickness
of the semipermeable bottom layer is b and its hydraulic conductivity is
_. At the left boundary of the phreatic aquifer the piezometric head is h1.
At the right boundary of the aquifer the piezometric head is h2. Apply
the Dupuit approximation to derive the differential equation for the
calculation of the piezometric head and in the aquifer.

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