Cooper–Jacob: Aquifer Transmissivity

Pump a well at known Q. Measure drawdown s at an observation well versus time and recover T from the late-time slope of s versus log₁₀ t.

University / research· 26 min·Related simulator: Biophysics, Fluids & GeoscienceGroundwater Well Drawdown (Theis)

Goal

Determine transmissivity T from the Cooper–Jacob approximation s ≈ (2.303 Q / 4πT) log₁₀(2.25 T t / r²S). The slope of s versus log₁₀ t is 2.303 Q / (4πT).

Equipment

Pumping well (known Q)
Observation well (known r)
Piezometer
Clock

Experiment

Plan view. Pumping well at the centre, observation well at r = 50 m. No live s on the bench.

Known pumping rate Q = 0.020 m³/s and observation radius r = 50 m. The piezometer reading appears only after you record.

Pumping time tt = 12.0 h

Piezometer: no reading

Record at least 6 late times from 2–72 h, then fit s versus log₁₀ t.

Measurements

№	t h	s m	log₁₀ t
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Cooper–Jacob: Aquifer Transmissivity

Generated: 24 Aug 2026, 22:30

Goal

Determine transmissivity T from the Cooper–Jacob approximation s ≈ (2.303 Q / 4πT) log₁₀(2.25 T t / r²S). The slope of s versus log₁₀ t is 2.303 Q / (4πT).

Measurement table

#	t (h)	s (m)	log₁₀ t
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted transmissivity agrees with the hidden T. Main uncertainties: piezometer noise, using the late-time Jacob line on exact Theis data, and neglecting wellbore storage.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Theis drawdown is s = (Q/4πT) W(u) with u = r²S/(4Tt). At small u (late time) this becomes a straight line on semi-log paper. The bench hides T, S, u and W(u). Q and the observation radius r are known. Storativity S can be estimated from the intercept once T is known; this lab grades T.

Procedure

Q and r are fixed and known. T and S are hidden. You only change pumping time t.
Read the piezometer s and record. Use late times (hours, not seconds) so the Jacob straight line applies.
The notebook computes log₁₀ t. Repeat for at least 6 times from about 2 h to 72 h.
Fit s versus log₁₀ t; T = 2.303 Q / (4π · slope). Compare with the reference.

Conclusion

The fitted transmissivity agrees with the hidden T. Main uncertainties: piezometer noise, using the late-time Jacob line on exact Theis data, and neglecting wellbore storage.