Flow Rate for Gas Differential Pressure Devices (Orifice, Nozzle and Venturi)

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Flow Rate Equations are provided here for general use which are in accordance with:


  • American Gas Association Report 3
  • American Gas Association Report 5
  • American Gas Association Report 8
  • American Petroleum Institute API MPMS 14.3.1

Following equations can be used for Mass Flow Rate, Volumetric Gross Flow Rate, Volumetric Net Flow Rate and Energy Flow Rate

1.  Mass Flow Rate at Flowing Conditions ‘Qm’ (Klbm/hr)
Q =(C x EV x Y x  ∏/4 x d2 x sqrt(2 x ΔP x Pf) ) x 3600/ 1000

2.  Volumetric Gross Flow Rate at Flowing Conditions ‘Qv’ (MCF/hr)
Qv =  Qm / ρf
3.  Volumetric Net Flow Rate at Base Conditions ‘Qb’ (MSCF/hr)

Qb =  Qm / ρb

4. Energy Flow Rate at Base Conditions ‘Qe’ (MMBTU/hr)

Qe = ( Qb x HV ) / 1000


Nomenclature:
Qm = mass flow rate at flowing (actual) conditions for gas differential
pressure flowmeters, in thousands of pounds mass per hour
(Klbm/hr)

Qv = volume (gross) flow rate at flowing (actual) conditions for gas differential pressure flowmeters, in thousands of cubic feet per
hour (MCF/hr)

Qb = volume (net) flow rate at base (standard/reference) conditions for gas differential pressure flowmeters, in thousands of standard
cubic feet per hour (MSCF/hr)

Qe = energy flow rate at base (standard/reference) conditions for gas differential pressure flowmeters, in millions of British thermal
units per hour (MMBTU/hr)

C = coefficient of discharge
Ev = velocity of approach factor
Y = fluid expansion factor referenced to upstream static pressure
d = orifice plate bore or nozzle/Venturi throat diameter at flowing temperature, in inches
= dr ( 1 + Φ ( Tf - Tr1) ), where
  • d is orifice plate bore or nozzle/Venturi throat diameter at flowing temperature, in inches
  • dr is orifice plate bore or nozzle/Venturi throat diameter at flowing
  • Φ is linear coefficient of thermal expansion of the orifice plate or nozzle/Venturi throat material, in/in⋅°F
  • Tf is temperature of the fluid at flowing conditions, in °F
  • Tr1 is reference temperature for the orifice plate bore or nozzle/Venturi throat diameter, in °F temperature, in inches
ρf = fluid density at upstream flowing conditions (actual temperature and pressure), in pounds mass per cubic foot (lbm/CF)
ΔP = differential pressure, in inches of water at 60°F, which is the static pressure difference measured between the upstream and downstream flange tap holes or in the throat taps.
ρb = fluid density at base conditions (standard/reference temperature and pressure), in pounds mass per cubic foot (lbm/CF)
HV = volumetric heating value at reference conditions, in British thermal units per standard cubic foot (BTU/SCF)

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