The response curve for a step input in a reactor is designated as the C-curve. In a tanks-in-series model comprising ‘m’ tanks, the variance of the C-curve equals___________________?
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Answer: B. 1/m
Explanation
The tanks-in-series model represents non-ideal flow through a train of equal-sized continuous stirred tank reactors. Mathematical derivation of this dispersion model proves that variance of the C-curve equals one over m. As the number of tanks increases, the variance decreases, reflecting closer approach to plug flow. Residence time distribution analysis helps chemical engineers quantify fluid mixing behaviors inside industrial reactors. The parameter m represents the effective number of equal-sized ideal stirred tanks in the flow model. Variance is a statistical measure of the spread of residence times exiting the reactor system.
Wastewater treatment facilities often use cascading tank systems that approximate the tanks-in-series dispersion model. Chemical processing plants apply this model to predict conversion losses caused by imperfect fluid mixing. Reactor optimization requires accurate variance calculations to ensure uniform product quality and high yields. Option m represents the total number of tanks rather than the inverse proportionality of variance. Square root of m appears in different statistical calculations but does not define C-curve variance. Squared values of m would imply an increasing variance with more tanks, which contradicts fluid dynamics.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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