For each of three water samples $($Problems $1-3),$ calculate the amount of generated sludge $($a$)$ report in

$l\frac{b}{?}$ day $($mass of solids in sludge$)$; and $($b$)$ in gallon$/$day $($volume of the sludge$)$ if the sludge contains $11\%$

solids, specific gravity of the sludge is $1\mathrm{.}0.$ The total residual hardness is $40m\frac{g}{L}$ as $CaC{O}_3$ that include

$30m\frac{g}{L}$ as $CaC{O}_3$ of $CaC{O}_3(s)$ and $10m\frac{g}{L}$ as $CaC{O}_3$ of $Mg(OH{)}_2(s).$ An excess of $35m\frac{g}{L}$ as CaO of

lime is added for softening. Both of added lime and soda ash are $100\%$ pure. Treated flow rate is $1$ MGD$.$

Problem $1($Water Sample #$1)$

Problem $2($Water Sample #$2)$

Problem $3($Water Sample #$3)$

Problem $4($Ion Exchange$).$ A water softener has $0\mathrm{.}15m^3$ of ion exchange resin with an exchange

capacity of $60k\frac{g}{m^3}$ as $CaC{O}_3.$ The occupants use $400$ gallons of water per day. If the water contains

$323m\frac{g}{L}$ as $CaC{O}_3$ of hardness and it is desired to soften it to $80m\frac{g}{L}$ as $CaC{O}_3,($a$)$ how much

water should bypass the system? $($b$)$ how long will it take that the resin is completely saturated and

needs to be regenerated?