Cooper Jacob Equation for Well Drawdown
The Cooper Jacob approximation turns the Theis solution into a straight line on a log time plot, making pumping test analysis fast and visual.
The equation
s = (2.3 Q / 4πT) log(2.25 T t / r² S)
- s is drawdown in meters
- Q is the pumping rate in cubic meters per day
- T is transmissivity in square meters per day
- S is storativity, dimensionless
- r is distance from the well in meters, t is time in days
Worked example
Pumping 1200 cubic meters per day from an aquifer with T of 350 and S of 0.0002 draws the water level down 2.01 meters at an observation well 50 meters away after one day. The drawdown grows by about 0.63 meters for every tenfold increase in time, and that slope is exactly what reveals T from field data.
When to use it
Use it once u = r²S/4Tt drops below about 0.05, which happens quickly near the pumped well. For early times or distant observation wells, fall back on the full Theis solution.
Related Calculators and Reference
- Groundwater Flow Simulator: watch this equation animate a cone of depression.
- Demo Valley Worked Project: a full site project using these methods.
- USGS Water Science School: authoritative background on groundwater.