Question: Residence time distribution in tube flow, define the residence time function F(t) to be that fraction of the fluid flowing in a conduit which flows

Residence time distribution in tube flow, define the residence time function F(t) to be that fraction of the fluid flowing in a conduit which flows completely through the conduit in a time interval t. Also define the mean residence time t_m by the relation

(a) An incompressible Newtonian liquid is flowing in a circular tube of length L and radius R, and the average flow velocity is (v_z,}. Show that

F(t) = 0 for t < (L/2(v_z>)

F(t) = 1 – (L/2(v_z,>t)² for t > (L/2(v_z>)

(b) Show that t_m = (L/z>).

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