Problem $4$:

a$)$ A continuous gravity decanter is to separate the light organic liquid $(SG=0\mathrm{.}8)$ from a dilute solution of wash water $(SG=1\mathrm{.}3).$ If the total depth in the separator is $7\mathrm{.}5ft$ and the interface is to be $1\mathrm{.}1ft$ from the vessel floor, what should the height $($in ff$)$ of the heavy$-$liquid overflow leg be$?$

b$)$ What should be the volume $($in ftis$)$ of the separator to separate $13\mathrm{.}000l\frac{b}{h}r$ light organic liquid from $35,000lb\frac{m}{h}r$ of wash water? The light organic liquid is the continuous phase and at the operating temperature has a viscosity of $2\mathrm{.}83cP.$

c$)$ The liquids described in $($a$)$ are to be separated in a tubular centrifuge bowl with an inside diameter of $180in,$ rotating at $3,000re\frac{v}{m}in.$ The free liquid sufface inside the bowl is $30$ in from the axis of rotation. If the mass ratio of the petroleum liquid to wash water in the centrifuge is $2$:$1,$ what should be the radial distance from the rotational axis to the top of the Overflow dam for the heavy liquid $($in in$)?$