$($ii$)$ A venturi meter has its axis vertical, the inlet and throat diameters being $150$ mm and $75$ mm respectively. The throat is $225$ mm above the inlet and $Cd=0\mathrm{.}96.$ Petrol of specific gravity $0\mathrm{.}78$ flows up through the meter at a rate of $0\mathrm{.}029$ metre cube per second. Find the pressure difference between the inlet and the throat, and the reading recorded by a mercury U$-$tube manometer. Do you know on which principle this device works?

$(7+3)+(5+4+1)$