How about this calculator:
http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm#calc
Inputs
Pipe (inlet) diameter upstream of orifice, Di:
Orifice diameter (less than the inlet diameter), Do:
Pressure difference across the orifice, Dp:
Fluid density, r:
Flow Coefficient, Cf:
Answers
Velocity at the inlet, Vi: 2.02 m/s
Volumetric Flowrate, Q: 4.13 ft^3/min
Mass Flowrate: 0.00251 kg/s
Close? I do not know.