Examples
Examples
Try the starting example
- Tracer times (minutes)
- 0,1,2,3,4
- Blank-corrected tracer concentrations
- 0,1,2,1,0
- Normalized sampled E(t) (1/minute)
- [0,0.25,0.5,0.25,0]
- Mean residence time (minutes)
- 2
- Residence-time variance (minutes²)
- 0.5
Try another scenario
- Tracer times (minutes)
- [0, 1, 2, 3, 4]
- Blank-corrected tracer concentrations
- [0, 1, 3, 2, 0]
- Normalized sampled E(t) (1/minute)
- [0,0.166666666667,0.5,0.333333333333,0]
- Mean residence time (minutes)
- 2.166667
- Residence-time variance (minutes²)
- 0.472222
Calculation method
Calculation method
Normalized sampled E(t) (1/minute)
Concentration divided by trapezoidal concentration-time integral.
Mean residence time (minutes)
Trapezoidal integral t C(t) / integral C(t).
Residence-time variance (minutes²)
Trapezoidal integral (t−mean)² C / integral C.
Symbols and units
- a
- Tracer times (minutes)
- b
- Blank-corrected tracer concentrations
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Tracer concentration-time samples. Returns Normalized distribution and mean residence. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Tracer times (minutes): minimum 0, maximum 1000000000000.0. Blank-corrected tracer concentrations: minimum 0, maximum 1000000000000.0.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.