For the bucket and weir configuration operating isothermally at steady state conditions, derive the following equation for $f_{HW}$ starting with the Bernoulli's

$f_{HW}$ is the fractional height of the weir, which represents the height of the liquid $($in this case, oilwater mixture$)$ above the weir, divided by the total height of the separator.

$f_{HW,\text{w}\text{e}\text{i}\text{r}}$ is the fractional height of the water at the weir.

$f_{HL}$ is the fractional height of the liquid $($oil in this context$)$ in the separator.

${}_w$ is the density of water.

${}_0$ is the density of oil. principle.

$f_{HW}=\frac{f_{HW,\text{w}\text{e}\text{i}\text{r}}{}_w-f_{HL}{}_o}{{}_w-{}_o}$