## Info FIGURE 10.3 Schematic of the split-treatment mode of softening.

in the finished water. The amount of magnesium removed is then equal to QMgr -QMg f. If qb is the bypassed flow, the amount of magnesium introduced to the second stage from the bypassed flow is qbMg r. The flow coming out of the first stage and flowing into the second stage is Q - qb; the corresponding amount of magnesium introduced into the second stage is (Q - qb)Mg1, where Mg1 is the concentration of magnesium in the effluent of the first stage. The total amount of magnesium introduced into the second stage is then the sum of those coming from the bypassed flow and those coming from the first stage and is equal to qbMg r + (Q - qb) Mg1. No removal of magnesium is effected in the second stage, so this is equal to QMg f. Expressing in terms of an equation,

QMg f = qbMgr + (Q - qb)Mg1 Solving for the fraction of bypassed flow fb, fb =

Example 10.4 For the raw water of Example 10.2, the lime-soda process in the split treatment mode is used to remove the total hardness to 120 mg/L as CaCO3 containing magnesium hardness of 30 mg/L as CaCO3. Calculate the chemical requirements in the first stage.

 Ions Conc. (mg/L) (meq/L) Conc. as CaCO (mg/L) 