In this paper

the superposition rule of the residence time distribution functions for the general system having multiple inlet and outlet streams

Eq. ( 6 )

has been proved rigorously. For the cascade vessels system where processed material in each stage is not ideally mixed in various degrees and the volumes of different stages may not be equal (Fig. 3)

the overall residence time distribution function E(t) and each Eij(t) of the flow system

Eq. (10)

are derived. If the volumes of different stages are equal

v1 = v2=…=vn

the processed material in each stage is not ideally mixed in the same degree

β1= β2=…=βn and ε1 =ε2=…=εn

the Eq. (10) of this paper can be reduced to Eq. (17) of previous paper[1]. (Please pay attention to some print mistakes in Eq. (17)there

see footnote on page 340 of this paper). The application of Eq. (6) or (10) to the flow system having multiple inlet and outlet streams

the flow system having only one inlet and one outlet stream

as well as the multiple phase system is discussed.