Residence time (fluid dynamics)
Residence time, also known as removal time, is the average amount of time spent in a control volume by the particles of a fluid. Since there's more than one way of averaging the time spent by particles inside the volume, there're also more than one definition of residence time. In case the flow is stationary and respects continuity, the definition most usually adopted is:
where
Residence time plays an important role in environmental engineering and chemistry. In these fields, not only the (mean) residence time is of interest, but also the whole residence time distribution. Nevertheless, the simple definition just introduced can be employed to quantify the residence times of specific compounds in a mixture only under the hypothesis that no chemical reaction takes place (otherwise continuity wouldn't be satisfied) and that the compounds concentrations are uniform.
Beyond fluid dynamics and chemistry, the definition(s) of residence time can be applied to any flow network, where the flows of generic "resources" is modeled (e.g.: people, cars, money, products). Most notably, the over-mentioned definition of residence time is extended to stationary random processes by averaging on time (fluid limit), obtaining the so-called Little's Law, which is a prominent relation in queueing theory and supply chain management. In the context of queueing theory, the residence time is addressed as waiting time, while in the context of supply chain management it is most often addressed as lead time.
Fluid dynamic phenomena can be modeled with different degrees of detail. The least detailed and most ubiquitously employed model is that for which we look to just three (functional) variables: the incoming flow , the outcoming flow and the quantity of fluid stored in the system. Unfortunately, in order to quantify the residence time in the non stationary case, we need a higher degree of detail: we need to know the so-called persistence function:
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