V Cone Equation

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3255 WEST STETSON AVENUE HEMET, CALIFORNIA 92545 USA

TEL: 951-652-6811 800-220-2279 FAX: 951-652-3078 Printed In The U.S.A Lit. #24509-54 Rev.3.2/02-08

www.mccrometer.com Copyright 1995-2008 McCrometer, Inc. All printed material should not be changed or altered without permission of McCrometer. Any published pricing, technical data, and instructions are subject to change without notice. Contact your McCrometer representative for current pricing, technical data,and instructions.

Flow Calculations for the V-Cone and Wafer-Cone Flowmeters

Basic flow equation:

English Units:

YCP1

Dg24

Q f psf 4

22ftc

acfs

=

Volume flowrate

YCP1

Dg2

4Q f psf 4

22ft

cslb

=

Mass flowrate

12DD inft = 197.5PP wc psf =

60QQ acfsacfm = 3600QQ acfsacfh =

4805.7QQ acfmgpm = 4805.7QQ acfhgph =

Metric Units:

YCP1

D24

Q f *Pa4

22*m

*

s

m 3

= Volume flowrate

YCP1

D2

4Q f

*Pa4

22*m*

skg

= Mass flowrate

1000

** mmm

DD = 100PP *mbar

*Pa =

60QQs

mminm 33 = 3600QQ

sm

hm 33 =

1000

Q

Q minm

minL

3

= 1000

Q

Q hm

hL

3

=


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Gas Expansion FactorPrecision tube V-Cone and Insertion Top-plate V-Cone Flowmeters (Rev. May 2001)The equation for gas expansion for compressible fluid flow:

NOTE: Y=1 for noncompressible fluids (e.g. water, oil etc.).

P k

P 0.696 (0.6491Y

+= )4

Note that P and P can be in any units as long as they are the same.

Wafer-Cone Flowmeters (Rev. Oct 2001)The equation for gas expansion for compressible fluid flow:

NOTE: Y=1 for non-compressible fluids (e.g. water, oil etc.).

P k

P Y

+= )( 8787.6755.01

The equation to convert from actual to standard / normal volume units: NOTE: This conversion is only used in compressible fluids.

English Units:

=

ZZ

TT

PP

QQ b b b

Lacfsscfs

Metric Units:

=

ZZ

TT

PP

QQ b**

b*

b

*L

s

m

s

Nm 33

The basic equation in terms of C: NOTE: C is used to simplify the flow equation by combining the constant and geometric variables.


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Beta Ratios:

The standard beta ratios for V-Cone flowmeters are: 0.45, 0.55, 0.65, 0.75, and 0.8. Alternative beta ratios can be used if required. Note that differential pressure and/or gas expansion factor may limit the availability of even standard beta ratios. In a liquidapplication, beta ratios should not be used that cause static line pressure minus the differential pressure to be less than the fluidsvapor pressure. In vapor or gas applications, beta ratios should not be used that generate a gas expansion factor less than 0.84.

Reynolds number equation:

English Units:

= in

Dv9.123Re

Metric Units:

***

mm vDRe =

The V-Cone meters discharge coefficient is related to the flows Reynolds number. It is advised that the V-Cone meter be calibratedacross the range of Reynolds numbers for which it is to be used. That is a plot of discharge coefficient to the Reynolds number should

be produced and a line fit relating discharge coefficient to the Reynolds number should then be made.

Flowing density equations:

Liquids : water f Gr =

Steam: .Vol.Sp

1=

Gas: TZ

PS6988.2 Lg

=

Metric units: 0184.16* =

Thermal expansion equation:

When meters are subjected to substantially different temperatures than those at which they were calibrated, there can be an effect onmeter performance due to the expansion of the cone and meter tube materials. Use this equation if the thermal expansion coefficientsfor the pipe and cone are equal:

( )528T21Fa +=


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Use this set of equation if the coefficients are different:

2incone

2in pipe

2in

2in

)d))528T(1(()D))528T(1((dD

Fa

=

To calculate the thermal expansion factor at operating temperature based on beta ratio:

Calculate pipe diameter at operating temperature: ( )( )c pipeininin TTDDD +=

Calculate cone diameter at operating temperature: ( )( )cconeininin TTddd +=

Calculate beta ratio at operating temperature: 2in

2in

Dd

1

=

Calculate thermal expansion factor at operating temperature:

4

22in

4

22

in

a

1

D

1D

F

=

The example below demonstrates the use of this term:

aacfs)temp _ new _ at(acfs FQQ =

Permanent pressure loss equation:Permanent pressure (or total head) loss in differential pressure meters is typically described as a percentage of the differential

pressure created at a particular flowrate. An approximate V-Cone Meter permanent pressure loss can be found by applying thefollowing equation:

( ) 10025.13.1P% loss =


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Nomenclature

C meter constantC * metric meter constant

C d discharge coefficient of the meterDft meter inside diameter in feetDin meter inside diameter in inchesD' in pipe diameter at operating temperature in inchesD* m meter inside diameter in metersD* mm meter inside diameter in millimetersd in cone diameter in inchesd' in cone diameter at operating temperature in inchesd * mm cone diameter in millimetersF a meter thermal expansion factorg c dimensional conversion constant, 32.174 lbm ft / lb f sec

2 k fluid isentropic exponent at flowing conditionsP absolute pressure in same units as P P b base absolute pressure in psi (typically 14.696 psia) P * b base absolute pressure in bars (typically 1.013 bara)P L absolute static line pressure in psi at the meterP * L absolute static line pressure in bars or psi at the meterQ acfs volume flow rate in actual cubic feet per secondQ acfm volume flow rate in cubic feet per minuteQ acfh volume flow rate in cubic feet per hourQ gpm volume flow rate in gallons per minuteQ gph

volume flow rate in gallons per hour

Q kg/s mass flow rate in kilograms per second Q L/min volume flow rate in liters per minuteQ L/h volume flow rate in liters per hourQ lb/s mass flow rate in pounds mass per second Q m3/min volume flow rate in cubic meters per minuteQ m3/h volume flow rate in cubic meters per hourQ m3 /s volume flow rate in actual cubic meters per secondQ Nm3 /h volume flow rate in normal cubic meters per hourQ scfh volume flow rate in standard cubic feet per hourQ scfm volume flow rate in standard cubic feet per minR simplification term used in Y factorRe Reynolds numberS g specific gravity of the gasSp.Vol . specific volume of the vapor


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T flowing temperature in degrees RankineT * flowing temperature in degrees KelvinT b base temperature in degrees Rankine (typically 520 R)T * b base temperature in degrees Kelvin (typically 288.15 K)T c calibration temperature

T' operating temperaturev fluid velocity through the pipe, in feet per secondv * fluid velocity through the pipe, in meters per secondv throat fluid velocity at the throat, in feet per secondv * throat fluid velocity at the throat, in meters per secondY adiabatic expansion factor for contoured elements

note: Y = 1 for liquid flow applicationsZ flowing gas compressibility factorZ b base gas compressibility factor

%P loss

permanent pressure loss across the meter as a percentage of differential pressure

Greek symbols: PE pipe and cone material coefficient of thermal expansion cone thermal expansion coefficient of cone material pipe thermal expansion coefficient of pipe material

meter beta ratio ' beta ratio at operating temperatureP differential pressure in same units as P P * Pa differential pressure in PascalsP * mbar differential pressure in millibarsP wc differential pressure in inches of water column

operating fluid viscosity, in centipoise 3.14159

flowing fluid density in pounds mass per cubic foot * flowing fluid density in kilograms per cubic meter


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V Cone Equation