Residence Time Distribution Calculator
The pulse-tracer curve gives a mean residence time of 4.70213 min.
4.70212765957447 min
Full answer, then cut to fewer decimals (not rounded):
- 4.70212765957447 min
- 4.7021276595744 min
- 4.702127659574 min
- 4.70212765957 min
- 4.7021276595 min
- 4.702127659 min
- 4.70212765 min
- 4.7021276 min
- 4.702127 min
- 4.70212 min
- 4.7021 min
- 4.702 min
- 4.70 min
- 4.7 min
- Variance σ²
- 3.826165686 min²
- Dimensionless variance σ²/t̄²
- 0.1730513298
- Equivalent tanks in series N = t̄²/σ²
- 5.778632276
- Area under the C curve
- 47
Step-by-step solution
- E(t) = C/∫C dt; ∫C dt = 47 (trapezoidal rule)
- t̄ = ∫tC dt / ∫C dt = 4.70212766 min
- σ² = ∫t²C dt / ∫C dt − t̄² = 3.826165686 min²
Residence Time Distribution Formula
t̄ = ∫tC dt / ∫C dt, σ² = ∫t²C dt / ∫C dt − t̄²
tanks-in-series N = t̄²/σ²
Worked Example
A pulse tracer read every minute for 10 minutes:
- E(t) = C/∫C dt; ∫C dt = 47 (trapezoidal rule)
- t̄ = ∫tC dt / ∫C dt = 4.70212766 min
- σ² = ∫t²C dt / ∫C dt − t̄² = 3.826165686 min²
Dimensionless variance σ²/t̄²: 0.1730513298 · Equivalent tanks in series N = t̄²/σ²: 5.778632276 · Area under the C curve: 47
GATE tip
Compare t̄ with V/v₀: a smaller measured t̄ means dead volume, a larger one usually means tracer tailing or adsorption.
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Frequently asked questions
What does N tell me?
N = 1 is a perfectly mixed tank; large N approaches plug flow. It sets the conversion of a non-ideal reactor.
Should the tracer data be evenly spaced?
No: the trapezoidal rule here handles any increasing times.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Residence Time Distribution Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/residence-time-distribution-calculator/
IEEE
Scientific Converters, "Residence Time Distribution Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/residence-time-distribution-calculator/