# Under a number of simplifying assumptions, the steady-state height of the water table in a…

Under a number of simplifying assumptions, the steady-state height of the water table in a one-dimensional, unconfined groundwater aquifer (Fig. P28.30) can be modeled with the following second-order ODE,

wherex = distance (m),K = hydraulic conductivity (m/d),h = height of the water table (m),

= the average height of the water table (m), and N = infiltration rate (m/d).

Solve for the height of the water table for x = 0 to 1000 m where h(0) = 10 m and h(1000) = 5 m. Use the following parameters for the calculation: K = 1 m/d and N = 0.0001 m/d. Set the average height of the water table as the average of the boundary conditions. Obtain your solution with (a) the shooting method and (b) the finite-difference method (?x = 100 m).

FIGURE P28.30

An unconfined or “phreatic” aquifer.

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