We consider a tandem two-server fluid network with two fluid types. Each server in the network has two buffers, one for each fluid, and the capacity of each server can be shared among the fluids. An initial amount of fluids is to be processed by both servers and drained through the system. We determine the processing rates for which the servers' capacity is optimally shared, with the objective of minimizing the total flow time. Three cases of the optimal strategy are discussed.