Groundwater Infiltration into a Lake Problem

One of the primary delivery mechanisms of chemicals into lakes is the discharge of groundwater through lakebed sediments. The transfer of chemicals and nutrients such nitrogen and phosphorus, carbon, etc. affects the biological processes in the lake and helps to control the biochemical characteristics of the lakes and co-dependent ecosystems (including those downstream of the lake). 

Consider the flow of groundwater into a shallow lake as shown below. For groundwater to discharge into the lake, the water table at the shoreline must be higher than the altitude of the lake surface. Determine how much the head in the aquifer will be above that in the lake. Also determine the distance from the shoreline at which 95% of the original aquifer flow has entered the lake.

Given information:

• Aquifer transmissivity, T = 270 m²/d
• Flow in the aquifer measured at the shoreline, Q = 4.5 m³/day
• Lake bed thickness, b’ = 1m
• Lake bed hydraulic conductivity, K’ = 0.06 m/day

Figure 1: Groundwater flow beneath and into a shallow lake.