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(1) Seawater containing 3.5wt% salt and mass flow rate mF is fed into a series of 10 evaporators. Equal mass flow rates of pure water
(1) Seawater containing 3.5wt% salt and mass flow rate mF is fed into a series of 10 evaporators. Equal mass flow rates of pure water are vaporized in each of the 10 units and then condensed and combined to obtain a product stream of fresh water of mass flow rate mW. The brine leaving each evaporator (except for the tenth and final unit) is fed into the next evaporator in series. The brine mass flow rate leaving the first evaporator is m1, leaving the second evaporator is m2, and so on. The brine leaving the tenth evaporator contains 5wt% salt and has a mass flor rate of m10. (a) Draw a flowchart of the process. Label all the necessary streams. Can you draw your flow diagram in such a way as not to need to show all ten units explicitly? (b) Write the set of equations you would solve to determine the fractional yield of fresh water from the process (kgHH2O recovered /kgH2O in feed) and the mass fraction w4S of salt in the solution leaving the fourth evaporator. Each equation you write should contain no more than one previously undetermined variable. In each equation, circle the variable for which you would solve. (c) Solve the equations derived in part (b) for the two specified quantities. Does the problem need a basis? (d) Derive a general expression for the mass fraction of salt leaving the nth evaporator, wns, as a function of n
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