The equations are as follows
- C is the discharge coefficient. D1 has to be supplied in m
- D1 and D2 are the diameter of the pipe and orifice respectively (m)
- A1 and A2 are the cross sectional areas of the pipe and orifice (m2)
- ΔP is the pressure drop across the orifice (Pa)
- P1 and Pstd are the upstream pressure and standard pressure
- T and Tstd are the gas temperature and standard temperature is the
- ρ is the gas (kg m-3)
- μ is the gas viscosity (Pa s)
- V1 is the liquid velocity in the pipe (m s-1)
- Re1 is the Reynolds Number in the pipe
- β is the diameter ratio
- MW is the molecular weight of the gas (kg mol-1)
- R is the universal gas constant (8314 J kmol-1 K-1)
- γ is the specific heat ratio
- e is the gas expansivity
- Q is the volumetric flowrate (m3s-1)
- Qstd is the volumetric flowrate at standard conditions (m3s-1)
Note these restrictions to the validity of the equations
- Corner Taps: 0.1 < β < 0.8 and 12 mm < D1 < 40 mm
- Flange Taps: 0.15 < β < 0.7 and 25 mm < D1 < 40 mm
- D2 > 6 mm
- Re >1000
You can choose either Corner or Flange taps with a drop-down menu in the spreadsheet, and Excel automatically uses the correct correlation for the discharge coefficient.
These equations (like nearly all orifice flow meter calculations) require an iterative solution. This is easily done with Excel's Goal Seek. All you have to do is click a button.
Goal Seek uses an initial guess value for the Reynolds Number to calculate the discharge coefficients, and uses this to calculate the flowrate. The calculated flowrate is then used to calculate the Reynolds Number. Goal Seek then automatically adjusts the guess and calculated values of the Reynolds number until they are the same.
