Cone Meters

Mass or gross volume flowrate calculation for cone type meters

This is essentially the ISO 5167 standard modified for the geometry and characteristics of a cone meter.



An option is provided to select the primary flowrate calculation method. Typically the McCrometer V-Cone calculation uses gross volume as the primary flowrate.

Gross Volume Flowrate


Gross Volume Flowrate

Symbol Description Units
qg Gross volume flowrate m3/s
ρ1 Upstream density kg/m3
Δp Differential pressure Pa
D0 Internal diameter of the pipe at calibration m
β0 Uncorrected beta ratio -
Cd Coefficient of discharge -
Y Adiabatic expansion factor -
Fa Thermal expansion factor -

Mass Flowrate


Mass Flowrate

Symbol Description Units
qm Mass flowrate kg/s
ρ1 Upstream density kg/m3
Δp Differential pressure Pa
D0 Internal diameter of the pipe at calibration m
β0 Uncorrected beta ratio -
Cd Coefficient of discharge -
Y Adiabatic expansion factor -
Fa Thermal expansion factor -

Corrected Cone Diameter


Corrected Cone Diameter

Symbol Description Units
d Orifice diameter at upstream temperature m
d0 Orifice diameter at calibration temperature m
λd Expansion coefficient of the orifice plate material /°C
t0 Pipe/Cone calibration temperature °C
t1 Upstream temperature °C

Corrected Pipe Diameter


Corrected Pipe Diameter

Symbol Description Units
D Pipe diameter at upstream temperature m
D0 Pipe diameter at calibration temperature m
λD Expansion coefficient of the pipe material /°C
t0 Pipe/Cone calibration temperature °C
t1 Upstream temperature °C

Uncorrected Beta Ratio


Uncorrected Beta Ratio

Symbol Description Units
β0 Beta ratio -
d0 Orifice diameter at calibration temperature m
D0 Pipe diameter at the calibration temperature m

Corrected Beta Ratio


Corrected Beta Ratio

Symbol Description Units
β Beta ratio -
d Orifice diameter at the upstream temperature m
D Pipe diameter at the upstream temperature m

Coefficient of Discharge




An operator selection is provided for the coefficient of discharge. The coefficient of discharge is either derived from an operator entry or from a look-up table. If the look-up table is selected, the coefficient of discharge is obtained from the Reynolds' number to discharge coefficient look-up table (10 entries for the coefficient of discharge and Reynolds' number, with interpolation between points).

Coefficient of Discharge

Symbol Description Units
Cd Interpolated coefficient of discharge -
R Calculated reynold's number -
Rl Curve reynolds number ≤ calculated reynolds number -
Ru Curve reynolds number ≥ calculated reynolds number -
Cl Curve coefficient of discharge corresponding to Rl -
Cu Curve coefficient of discharge corresponding to Ru -

Adiabatic Expansion Factor


In the case of liquids this figure will always be 1.

Lit. #24509-54 Rev 2.5


Adiabatic Expansion Factor1

Lit. #24509-54 Rev 3.2


For option: V-Cone Model - Standard

Adiabatic Expansion Factor1

For option: V-Cone Model - Wafer

Adiabatic Expansion Factor2

Symbol Description Units
Y Adiabatic expansion factor -
β0 Uncorrected beta ratio -
k Isentropic exponent -
R Simplification term -
Δp Differential pressure bar a
p1 Upstream pressure bar a

Thermal Expansion Factor


Thermal Expansion Factor

Symbol Description Units
Fa Thermal expansion factor -
β Corrected beta ratio -
D Internal pipe diameter at working conditions m
β0 Uncorrected beta ratio -
D0 Internal pipe diameter at calibration temperature m

Pipe Reynolds Number


Pipe Reynolds Number

Symbol Description Units
ReD Reynolds number -
qm Mass flowrate kg/s
µ1 Dynamic viscosity Pa.s
D Internal pipe diameter at the upstream temperature m

Permanent Pressure Loss


Permanent Pressure Loss

Symbol Description Units
Δω Permanent pressure loss bar a
β Corrected beta ratio -
Δp Differential pressure bar a

Recovered Pressure


Recovered Pressure

Symbol Description Units
p3 Fully recovered pressure bar a
p1 Upstream pressure bar a
Δω Permanent pressure loss bar a

Upstream Temperature




An option is provided to select the upstream temperature calculation method.


Isentropic Exponent Method


Upstream Temperature

Symbol Description Units
t1 Upstream temperature °C
t3 Temperature at the fully recovered pressure position °C
p1 Upstream pressure bar a
p3 Fully recovered downstream pressure bar a
Y Specific Heat Ratio -


For option: Temperature Transmitter Location - Downstream
-Downstream Pressure is used in the place of Recovery Pressure.


ISO TR 9464


ISO TR 9464

Symbol Description Units
t1 Upstream temperature °C
t3 Temperature at the fully recovered pressure position °C
Δt Difference in temperature °C
Δω Permanent pressure loss bar a
p1 Upstream pressure bar a


For option: Temperature Transmitter Location - Downstream
-Differential Pressure, in bar a, is used in the place of Permanent Pressure Loss.


Alternative Methods




For option: Temperature Transmitter Location - Upstream
-The user inputted value for upstream temperature is used and upstream temperature is no longer an output. The section of the above which calculates the upstream temperature is ommited.



For option: Temperature Exponent Method - User Entered
-The user inputted value for temperature exponent is used in the Upstream temperature(Isentropic Exponent Method) calculation in the place of the calculated value for Temperature Exponent from the Isentropic Exponent using the equation: 1-Y/Y.



For option: Discharge Coefficient - Fixed
-The user inputted value for the dicharge coefficient is used and dicharge coefficient is no longer an output. The section of the above which calculates the discharge coefficient is ommited.

References