Multi-stage flash distillation is used to desalinate seawater so it is fit for h

Question

Multi-stage flash distillation is used to desalinate seawater so it is fit for human consumption. A flash distillation tank is composed of small chambers (called "stages"), each at a lower pressure than the previous stage. Salt water enters the first chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, and the process repeats until very salty water is expelled as waste. Brine that is 35,000 ppm salt is desalinated through a 5-stage flash distillation process. The pressure in the stages is such that 8% by mass of the water entering the stage evaporates and leaves as fresh water. If the desalination plant wants to produce 1400.0 gallons of drinking water per day, how many gallons of brine must the plant take in per day? The density of fresh water is 1.000 g/cm3. The density of brine is 1.025 g/cm3.

2. What mass of waste brine is expelled in one day?

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3. What is the ratio of the mass of fresh water produced to the mass of water in the incoming brine?

4. The larger this ratio is, the more fresh water is produced for the given incoming water. If additional stages are added, each removing 8% of the available incoming water, so that the above ratio gets above 0.5, what are the total number of stages in the multi-stage flash distillation tank? (respond with a whole number)

5. The energy requirement of this type of desalination plant is 23.1 kW

Explanation / Answer

let the per day inflow of brine (in gm) be P

(I have already found in my previous answer the input rate of brine, you can check that from there (plz rate it also :D)

P = 15544997.3 gm of brine solution per day.(found in previous answer)

I also found that 34.1% of above leaves as fresh water.

so the rest that is 100-34.1 = 65.9% leaves as waste

so brine left as waste = 0.659(15544997.3) = 10244153.22 gm or 10244.2Kg --- (answer 2)

incoming salt concentration = 35000ppm

35000 gm salt per 1,000,000 gm water

so mass percent of salt = 35000/(35000+1000000) = 3.38%

rest is water,

so mass% of freshwater coming in brine = 100-3.38 = 96.62%

so mass of freshwater in brine = 0.9662P .. (P being total flow rate of brine)

mass of freshwater produced = 0.341P .. (found earlier)

ratio of freshwater produced to water in brine = (0.341P/0.9662P) = 0.353 .....(answer 3)

volume of freshwater produced = 1400 gallons

1 gallon = 0.003785 m3

so,

1400 gallon is equal to 5.3m3

energy requirement per m3 of water = 23.1 kWh

so total energy required = (5.3*23.1) = 122.42 kW.h ..........(answer 5)

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