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Science of Water : Concepts and Applications

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358 The <strong>Science</strong> <strong>of</strong> <strong>Water</strong>: <strong>Concepts</strong> <strong>and</strong> <strong>Applications</strong><br />

1 mg/L alum reacts with 0.35 mg/L lime<br />

1 mg/L alum reacts with 0.45 mg/L alkalinity<br />

Raw water alkalinity—36 mg/L<br />

Solution:<br />

To calculate the total alkalinity required, you must fi rst calculate the alkalinity that will react with 52<br />

mg/L alum:<br />

0.45 mgL alkalinity x mgL alkalinity<br />

<br />

1 mgL alum 52 mgL alum<br />

(0. 45)( 52)<br />

x<br />

23. 4 mgL alkalinity x<br />

The total alkalinity requirement can now be determined:<br />

Total alkalinity required, mgLalkalinity to react with alum,<br />

mgLresidual alkalinity, mgL 23.4 mgL30mgL 53.4 mg<br />

L total alkalinity required<br />

Next, calculate how much alkalinity must be added to the water:<br />

Alkalinity to be added, mgLtotal alkalinity required, mgLalkalinity<br />

present, mgL 53.4 mgL36mgL 17.4 mgL alkalinity to be added to the water<br />

Finally, calculate the lime required to provide this additional alkalinity:<br />

0.45 mgL alkalinity 17.4 mgL alkalinity<br />

<br />

0.35 mgL lime x mgL lime<br />

0.45 x (17.4)(0.35)<br />

(17.4)(0.35)<br />

x <br />

0.45<br />

x 13.5 mgL lime<br />

DETERMINING LIME DOSAGE, lb/day<br />

After the lime dose has been determined in terms <strong>of</strong> mg/L, it is a fairly simple matter to calculate<br />

the lime dose in lb/day, which is one <strong>of</strong> the most common calculations in water <strong>and</strong> wastewater<br />

treatment. To convert from mg/L to lb/day lime dose, we use the following equation:<br />

Lime, lbday (lime, mgL)(flow, MGD)(8.34 lb gal)<br />

(10.57)

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