Calculation of Cumulative Residence Time Distribution

The derivation of the residence time behavior of the single streamlines now allows the formulation of the cumulative residence-time distribution function F(t) according to the following formula  

The exit-age distribution function E(t) is approximately obtained by following the experimentally often used method of backward differencing  

The division of the flow area into individual channels forces a discretization of the distribution function. The integration will be replaced by the sum of the contributions of every channel i  

The amount of the exit flow Fi with the respective residence time t can be calculated if the cross-section of the respective streamline and their mean velocity V is known. This is the case inside the channels (values given above)  

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