In many papers, the flowrate determination has been given as the Bernoulli equation for the determination of brine flowrate however the equation does not remain valid for the last effect because the amount of brine getting out of the last effect gets increased because of this. This is needed for the dynamic simulation of multi-effective desalination systems.
The Bernoulli equation is only valid for a limited subset of problems. Many people don't realize that the Bernoulli equation applies along a single streamline, not across multiple streamlines, which also means that it doesn't apply across phase boundaries or changes in composition. This does not mean, however, that you can't use lumped system analysis and obtain quite accurate results. Google "Crane Technical Paper 410: Flow of Fluids through Valves, Fittings, and Pipes." I was part of a Team that developed the first pipe network solving software to ever meet the stringent quality assurance requirements of the NRC. This type of system (dynamic brine desalination) can be solved but it will take more than the Bernoulli equation and even if you use some commercial code, it will require significant effort.
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