Water balance (Dilution ratio)

Water is used in mineral processing

1. To transport solids in the circuit
2. To act as a medium for separation

Ball mills use  water for milling and in the discharge water is further added for separation in solids by weight.

Most flotation operations are performed in between  solids by weight.

Some gravity concentration devices operate most efficiently on slurry containing  solids.
Roughly  of water is required for a plant treating 10000 tons of ore. 

 Two product formula is of great use in assessing water balances. In two product formula; feed is divided in two products, namely concentrate and tailing.

Consider a hydrocyclone fed with a slurry containing  solids by weight and producing two products:-
Under flow containing u% solids by wt. and an overflow containing V%  solids by weight.

Consider weight of solids/unit of time in feed, underflow and overflow arc  and  respectively, at equilibrium conditions of operation

(11)

                                                                                               
Dilution ratio is defined as  

Dilution ratio is of feed

Dilution ratio of underflow

(12)

                                                       
Dilution ratio of overflow       

Water balance on the cyclone: weight of water entering the cyclone must equal the weight leaving in  two products output

(13)

By 11 and 13 we get

(14)

 If % solids are unknown, two product balance can be performed by using pulp densities slurry densities.
A balance of slurry weights

(15)

By equation 8 in that  solids and 15 we get after simplification

(16)

On simplifying further we get.

(17)

In equation 17,  is density of slurry of underflow and  is density of slurry of overflow.