CE 394K.2 Hydrology
Homework #4
Spring 1999

The governing equation for onedimensional, 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 crosssection 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 h_{1} and on the right is h_{2}, Q_{x} is the
discharge per unit width of aquifer [L^{2}/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 Q_{x}.
3. Text problems 4.3.3, 4.4.5
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