Oil passes through a straight circular pipe placed horizontally, where the flow rate is to be measured with a venturi meter mounted on the pipeline. Since the height difference read on the manometer with working fluid water is h=100 mm, calculate the oil flow rate passing through the venturi meter (d =10 mm, D=20 mm, $P_{water}$ = 998 kg/m$^3$, $P_{oil}$ = 800 kg/m$^3$, g = 9.81 m/s$^2$, $C_d$=0.98, A$_2$: the narrow section of the venturi-meter).
$\dot{V} = C_dA_2\sqrt{\frac{2\Delta P}{\rho(1-\beta^4)}}$