CE 394K.2 Hydrology                     Homework #4                         Spring 1999

1. The governing equation for one-dimensional, steady flow in an unconfined aquifer can be written as:
where K is the hydraulic conductivity [L/T], h is the piezometric head [L], w is the recharge rate to the aquifer [L/T] and the equation applies to a vertical cross-section of the aquifer of unit width perpendicular to the flow.

This equation is applied to the flow between two rivers, a distance L apart, in which the water surface elevation of the river on the left is h1 and on the right is h2, Qx is the discharge per unit width of aquifer [L2/T], and d is the location of the maximum water surface elevation in the aquifer (see Handbook of Hydrology p. 6.22 for a diagram of the physical situation). Derive the following results:

2. Two rivers are 50km apart and the rivers have water surface elevations that are at an elevation of 50m. There is an impermeable bed at an elevation of 0m. The conductivity of the aquifer between the two rivers is 1 m/hr and the recharge rate uniformly distributed over the aquifer surface is 0.5 mm/day. Assuming that the recharge has continued long enough for the water surface elevation in the aquifer to be at equilibrium, develop a table and chart showing at 5 km intervals between the two rivers the water surface elevation, h, and the discharge per unit of width Qx.

3. Text problems 4.3.3, 4.4.5