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

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

Transcribed Image Text:

dh Ground surface Water table Infiltration Aquifer Groundwater flow Confining bed