A venturi meter with an $8in.$ diameter throat is installed in a $12in.$ water line.

The venturi meter is perfectly smoth, coefficient of velocity is $1\mathrm{.}00.$ An attached mercury

manometer registers a $4$ in$.$ differential. The specific weight of mercury is $0\mathrm{.}491\frac{lbf}{i{n}^3},$ the

specific weight of water is$.0\mathrm{.}0361\frac{lbf}{i{n}^3}.$ Volumetric flow rate? I have the solution, what I dont understand $is$ the conversion $of$ the equation $to$ include the specifid weights $of$ mercury and water outlined below.

$Q=\frac{C{A}_2}{\sqrt[\phantom{2}]{1-(\frac{A_2}{A_1}{)}^2}}\sqrt[\phantom{2}]{2g(\frac{P_1}{}+z_1-\frac{P_2}{}-z_2)}$

$2g(\frac{P_1}{}+z_1-\frac{P_2}{}-z_2)=>2g{}_{\text{m}\text{e}\text{r}\text{c}\text{u}\text{r}\text{y}}(\frac{h_1-h_2}{{}_{\text{w}\text{u}\text{t}\text{e}\text{r}}})$

how?