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Process Calculations
Material Balance
GATE 2009
Hard

Pure water (stream W) is obtained from a feed (F) containing 5 wt% salt using a desalination unit with a recycle (R) taken from the effluent, mixed with F to form a mixed feed (10 wt% salt) entering the unit, which produces pure water W (0% salt) and an effluent. If the overall recovery of pure water (through W) is 0.75 kg/kg feed, then the recycle ratio (R/F) is

  • A0.25
  • 0.5
  • C0.75
  • D1.0

Explanation

Overall (system) balance: W=0.75F, Effluent=0.25F. Salt balance: F(0.05)=Effluent×xeff ⟹ 0.05F=0.25F×xeff ⟹ xeff=0.20. Mixing-point balance (recycle drawn from effluent, so xR=0.20): F(0.05)+R(0.20)=(F+R)(0.10) ⟹ 0.05F+0.20R=0.10F+0.10R ⟹ 0.10R=0.05F ⟹ R/F=0.5.

Source: GATE CH 2009 (2009)

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