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I have a known flow of Brine (Liter/h) with known concentration (gram/Liter), need to be diluted to defined concentration (gram/Liter), with demineralized water. What Equation should be used to determine flow of water by (Liter/h).

Mahmoud
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1 Answers1

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Given

$F_B$ = Flow of brine

$F_D$ = Flow of demineralized water

$C_B$ = Concentration of minerals in brine

$C_D$ = Concentration of minerals in demineralized water = $0$

$C_F$ = Final concentration of minerals

we have that $$C_F= \frac{F_B*C_B+F_D*C_D}{F_B+F_D}$$ or $$F_D = \frac{F_B*(C_B-C_F)}{C_F}$$

Jens
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  • please, what is the basic for this equation?, can you clear the derivation please. – Mahmoud Apr 01 '17 at 17:51
  • The basis is the conservation of mineral mass. Suppose the two flows are going into an empty tank and run for exactly one hour. Let $F_B = 10$ (L/h), $C_B=2$ (g/L), $F_D =5$ (L/h) and $C_D=0$ (g/L). The mass of minerals in the tank after one hour is then $10$(L/h)$2$(g/L)$1$h $= 20$ g. The volume of liquid in the tank is ($10$(L/h)$+5$(L/h))*$1$h $= 15$ L. The final concentration is thus ($20$g)/($15$L) $= 4$/$3$ (g/L). – Jens Apr 01 '17 at 22:57