Ground engineering · Groundwater & dewatering
Pumping test analysis (Cooper–Jacob straight line) calculator
Fits a straight line to late-time drawdown against log time in an observation well to give transmissivity and storage coefficient, and checks the u < 0.05 validity condition.
Standard: Cooper & Jacob (1946): T = 2.3Q/(4πΔs), S = 2.25Tt0/r², valid for u < 0.05
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Pumping rate | 10 | L/s |
| Distance to observation well | 30 | m |
| Use readings from time ≥ | 20 | min |
| Readings: time (min), drawdown (m) | 1, 0.188 2, 0.321 3, 0.408 5, 0.525 8, 0.638 12, 0.735 20, 0.864 30, 0.965 50, 1.091 80, 1.203 120, 1.301 200, 1.440 300, 1.533 500, 1.665 800, 1.779 1200, 1.876 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Δs per log cycle (slope) | 0.571 | m |
| Intercept | 0.120 | m |
| Fit R² | 1.000 | |
| Transmissivity 2.3Q/(4πΔs) | 0.003 | m²/s |
| Zero-drawdown time t0 | 0.617 | min |
| Storage coefficient 2.25Tt0/r² | 0.000 | |
| Check: u at first fitted time r²S/(4Tt) | 0.017 | |
| Result: transmissivity T | 0.003 | m²/s |
- ✓ u ≤ 0.05 for the fitted data
- ✓ Fit R² ≥ 0.98
Method, formulas and assumptions
- Δs per log cycle (slope) = SLOPE([t.ly],[t.lx]) = 0.57113 m
- Intercept = INTERCEPT([t.ly],[t.lx]) = 0.11985 m
- Fit R² = RSQ([t.ly],[t.lx]) = 0.99989
- Transmissivity 2.3Q/(4πΔs) = 2.3*10/1000/(4*PI()*0.57113) = 0.0032047 m²/s
- Zero-drawdown time t0 = 10^(-0.11985/0.57113) = 0.61681 min
- Storage coefficient 2.25Tt0/r² = 2.25*0.0032047*0.61681*60/30^2 = 2.965e-4
- Check: u at first fitted time r²S/(4Tt) = 30^2*2.965e-4/(4*0.0032047*20*60) = 0.017348
- Result: transmissivity T = 0.0032047 = 0.0032047 m²/s
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.