A venturi meter used differential pressure through an orifice in a pipe to determine flow rate. Usually it is used for incompressible fluids and the flow rate calculation assumes that you know several factors, that is pipe diameter, orifice coefficient (usually a function of reynolds number, but generally a constant of the meter) and fluid density. As for flow rate it is fairly easy to modify the manometer scale such that under normal operating conditions, flow rate can be read directly--in the old days this was done using a scale monograph--today if the differential pressure is measured digitally--you let the computer crunch the nomograph directly to flow rate.
Venturi meters can also be used for compressible fluids, however gas conditions are different and choked resulting from Mach effects at sonic throat velocities.
See this web site for a flow calculator, formulae, and a better discussion venturi flow meter