7. If the fluid is gas then calculate the expansion factor
HN Y = 1- 0.41+ 0.35β 4O 27.73KPf
(
)
8. Repeat from step 4 until the beta ratio value changes less than 0.000001 9. Calculate orifice bore
d = β O .D Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. For complete details of all formula and techniques refer to the AGA Report #3 and The Flow Measurement Engineering Handbook By R.W.Miller. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information. Nomenclature
WM
Flowrate upper range variable
lb/h
WN
Flowrate normal flow
lb/h
HM
Differential upper range variable
inches of water
HN
Differential normal
inches of water
SM
Orifice sizing factor
dimensionless
M1
Correction for pipe sizes less than 1.8 inches
see AGA Report #3
Pipe inside diameter at flowing temperature
inches
Orifice inside diameter
inches
Density at flow conditions
lb/ft3
µ CP
Absolute Viscosity
centipoise
RD
Reynolds Number
dimensionless
βO
D d γn
Beta Ratio
dimensionless
C C INF
Orifice discharge coefficient
dimensionless
Orifice discharge coefficient for infinite Reynolds Number
dimensionless
Y Pf
Gas expansion factor
dimensionless
Upstream pressure
psia
k
Ratio of specific heats TapTerm Correction for tap location
dimensionless see AGA Report #3
Fixed Geometry1 Calculation Routines Annubar Liquid Flow 1 Calculate the differential range
Wm Hm = 2 2834.717KD FA G f
2
Inches of water
2 Calculate velocity
V=
Wn 19.65 γ nFAD 2
feet per second 3 Calculate Rod Velocity. There is a minimum rod Reynolds Number below which the flowing fluid will not separate properly from the edges of the Annubar.
RD = 1487
PW vγ n µ CP
Annubar Gas Flow 1. Calculate the differential range 2
Wm Hm = 2 . γ KD F 358 94 A n Inches of water 2. Calculate the expansion factor 2 Hm 1273 . d Y = 1 − 0.011332 1 − − 0.00342 D Pf k
3. Apply the expansion factor -
Hm =
Hm Y2 .
Repeat steps 2 and 3 again Nomenclature
D γN
Pipe inside diameter
inches
Density at flow conditions
lb/cubic foot
FA
Thermal expansion factor
dimensionless
Gf
Specific gravity at flow temperature
dimensionless
Hm
Differential range
inches of water
Ratio of specific heats
dimensionless
Flow coefficient
dimensionless
Inlet pressure
psia
PW
Annubar width
feet
RD
Rod Reynolds Number
dimensionless
V Wm
Fluid velocity
feet per second
Flow rate
lb/h
Y µ CP
Expansion factor
dimensionless
k K Pf
Viscosity centipoises Reference The Annubar Flow Handbook Dover Industries Inc Annubar Is a registered trademark of Dover Industries Inc
Elbow Flowmeter 1.. Calculate the Reynolds Number -
RD =
6.31533.WM D. µ CP
2.. Calculate the discharge coefficient -
K SM =
rb + 2D
6.5
rb 2D
RD0.5
3.. Calculate the differential range 2
Wm HM = 2 358.9268K SMFA D γ n inches of water Nomenclature
Nomenclature BT Target ratio (Target diameter/Bore diameter) (Supplied by manufacturer)
D γN
FA
dimensionless
Pipe inside diameter
inches
Density
lb/cubic foot
Thermal expansion factor
dimensionless
K
Discharge coefficient (Supplied by manufacturer)
dimensionless
W µ CP
Flow rate
lb/h
Viscosity
centipoises
Integral Flow Orifice Assemblies 1. Calculate the Reynolds Number -
Rd =
6.31533.W d. µ CP
2. Calculate the discharge coefficient -
C∞ = A + Dβ 2 + Eβ 4 + Fβ 8 B = G + Hβ 2 + Jβ 4 C = C∞ + BRd−0.5 (Values of A,D,E,F,G,H and J vary with design and size. See manufacturers data) (C for Jewel insert is 0.995) 3. Calculate the expansion factor -
(
Y1 = 1 − 0.41 + 0.35β 4
H ) 27.73 Pk f
4. Calculate flow rate -
W=
358.9268CFA Y1d2 Hγ n 1− β 4
lb/h
Nomenclature
d D γn
FA C H k Pf
Rd W β
Orifice bore diameter
inches
Pipe inside diameter
inches
Density
lb/cubic foot
Thermal expansion factor
dimensionless
Discharge coefficient
dimensionless
Differential range
inches water
Ratio of specific heats (Gas only)
dimensionless
Inlet pressure
psia
Orifice Reynolds Number
dimensionless
Flow rate
lb/h
Beta ratio
µ CP
Viscosity
(d/D)
dimensionless centipoises
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. For complete details of all formula and techniques refer to The Flow Measurement Engineering Handbook By R.W.Miller and Foxboro Technical Information T! 037 087. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information.
Control Valve Calculation Routines Liquid 1 Calculate the vena-contracta pressure drop -
P PVC = P1 − 0.96 − 0.28 VAP PVAP PC 2 Calculate the critical drop -
4 34.6Fd W FL2 C 2V = + 1 2 µ CP FL C V 890d
5. Calculate Reynolds Number Factor -
C FR = 1044 . − 0.358 VS C VT
0.655
Where -
C VS =
1 W µ CP FS 23500G f ∆P
0.6667
and -
F 0.6667 F 2 C 2 FS = d .333 L V2 + 1 FL 890d
0.1667
6. Calculate the pressure recovery and piping geometry factors
K B1
d = 1− D1 FLP
4
K B2
d = 1− D2
(K 1 + K B1 )FL2 C 2v = FL + 1 890d4
4
−0.5
(K 1 + K 2 + K B1 − K B 2 )C 2v Fp = + 1 890d4 7 Calculate the final valve size Turbulent flow -
CV = or
or
Pr e lim inaryC V FP
Transitional flow -
CV =
Pr e lim inaryC V FR
Laminar flow -
C V = C VS or
Choked or flashing flow -
CV =
d2 K 1 = 0.5 1 − 2 D1
W 500FLP ∆PCRIT G f
−0 .5
2
d2 K 2 = 1 − 2 D2
2
8 Calculate the noise level
SL = 10LogC V + 20Log∆P − 30Log( t) + 5 For incipient cavitation add --
∆P −Kc P − P Log(P2 + 1 − PVAP ) 5 1 2 VAP FL − K c For full cavitation subtract from incipient cavitation --
5Log( ∆P + 1 − ∆PCrit )
Gas 1 Calculate the pressure drop ratio factors
∆P P1
X1 =
K 14 .
Fk =
2 Calculate the minimum size for sonic velocity
dmin = 0.0454
T1 M
W P2
inches
3 Calculate the preliminary valve size
CV =
W 63.3 X 1P1γ N
4 Calculate the piping geometry factor
K B1
d = 1− D1
4
K B2
d = 1− D2
4
d2 K 1 = 0.5 1 − 2 D1
(K 1 + K 2 + K B1 − K B 2 )C 2v Fp = + 1 4 890d
2
−0 .5
5 Calculate the pressure drop ratio factor
X TP
X = 2T FP
X T (K 1 + K B1 )C 2v + 1 4 1000d
−1
6 Calculate the expansion factor
Y = 1−
X1 3Fk X T
7 Calculate the final size
FinalC V =
Pr e lim inaryC V FP Y
8 Calculate the valve sound pressure level Gas
T SL 1 = 10Log 28C vFLP1P2D 2 η 31 + SL G t Steam
(
SL1 = 10Log 11000C vFLP1P2D 2 η(1 + 0.0007 TSH ) / t 3 9 Calculate the outlet noise
(
6
)
SL 2 = 10Log 0.18P22 d2D 22Ms T1 + SL G
)
d2 K 2 = 1 − 2 D2
2
10. If
SL 1 − SL 2 ≥ 7 then
SL = SL 1 Else
SL = SL 1 + SL 2 Two Phase Flow 1 Calculate the vena-contracta pressure drop
P PVC = P1 − 0.96 − 0.28 VAP PVAP PC 2 Calculate the critical drop
PCRIT = FL2PVC 3 Calculate the specific volumes of the gas and liquid
vg =
1 γN
vl =
0.016033 Gf
4 Calculate the volume fraction and the weight fraction of the gas
Vg =
w gvg
fg =
w gvg + wf vf
wg wg + wf
5 Calculate the pressure drop ratio factors
X1 =
∆P P1
Fk =
K 14 .
6 Calculate the expansion factor
Y = 1−
X1 3Fk X T
7 Calculate the effective specific volume for the mixture
ve =
fg v g 2
Y Y
+
(1 − f ) g
63.3G f
8 Calculate the preliminary valve size
Cv =
(w
f
+ wg
)
63.3
ve X 1P1
9 Calculate the piping geometry factor
K B1
d = 1− D1
4
K B2
d = 1− D2
4
(K 1 + K 2 + K B1 − K B 2 )C 2v Fp = + 1 4 890d
d2 K 1 = 0.5 1 − 2 D1
2
d2 K 2 = 1 − 2 D2
2
−0 .5
10 Calculate the final size
Cv =
Pr e lim inaryC V FP
11 Sound level calculated using the liquid calculations above.
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical
calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.
Nomenclature
CV
Valve sizing coefficient
dimensionless
Nominal valve size
inches
Inside diameter of inlet piping
inches
D2
Inside diameter of outlet piping
inches
γn
Fluid density at operating temp and pressure
pounds per cubic foot
Fd
Valve style modifier
dimensionless
Ratio of specific heats
dimensionless
d D1
k FK
Ratio of specific heats factor
dimensionless
FL
Rated pressure recovery factor
dimensionless
FLP
Combined liquid pressure recovery factor
dimensionless
FP
Piping geometry factor
dimensionless
FR
Reynolds number factor
dimensionless
Gf
Specific gravity at flow temperature
dimensionless
Molecular weight
dimensionless
Mach number at flow conditions
dimensionless
P1
Upstream absolute pressure
psia
P2
Downstream absolute pressure
psia
Pc
Critical pressure
psia
PVAP
Vapor pressure
psia
Valve pressure drop
psi
Sound pressure level
dBA
Gas property factor
dBA
Pipe wall thickness
inches
M MS
∆P SL SL G t T1
Absolute upstream temperature
degR
TSH
Steam superheat temperature
degF
REV
Reynolds number
dimensionless
ve
Effective two phase specific volume
ft3/lb
vf
Specific volume of liquid
ft3/lb
vg
Specific volume of gas
ft3/lb
Vg
Volume fraction of gas
dimensionless
Total rate of flow
lb/h
Rate of liquid flow
lb/h
Rate of gas flow
lb/h
W wf
wg
X1
Pressure drop ratio
dimensionless
XT
Rated pressure drop ratio factor
dimensionless
X TP
Value of XT for valve/reducer assembly
dimensionless
Y η
Expansion factor
dimensionless
Acoustic efficiency
dimensionless
References Control Valve Sizing Equations ANSI/ISA S75.01 Masoneilan Noise Control Manual Masoneilan - Dresser ISA Handbook of Control Valves. J. W. Hutchison
ISO Flow Element Calculation Routines Routines are similar all devices except that the discharge coefficient formulas vary. The gas restriction orifice is checked for critical flow, see RO Sonic Gas Routine. Set initial values. C=0.6:Y=1 1. Calculate the Normal Differential Range
W HN = HM . N WM
2
2. Calculate the SM Factor
WN
SM =
358.9628.D 2 .FA . γ n .HN
3. Calculate Reynolds Number
RD =
6.31533.WN D. µ p
4. Calculate the beta ratio 2 C β O = 1 + Y. S M
−0 .25
5. Calculate the discharge coefficient at infinite Reynolds Number Typical for corner taps
b = 91.71β 2.5 O and n = 0.75 for corner taps 7. If the fluid is gas then calculate the expansion factor
HN Y = 1- 0.41+ 0.35β 4O 27.73KPf
(
)
8. Repeat from step 4 until the value of the beta ratio changes less than 0.000001 9. Calculate orifice bore
d = β O .D R. O. Sonic Gas Routine 1. Check for sonic velocity
PSONIC
2 = Pf k + 1
k
k k −1
2. If the discharge pressure is more than -
PSONIC then use pipe tap calculation Else
YT SP =
WM 359D .FA γ N .Pf 2
3. Calculate Beta Ratio
β O = 0.6991YT SP
0.4919
4. Calculate orifice bore
d = β O .D Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. For complete details of all formula and techniques refer to the ISO 5167 and The Flow Measurement Engineering Handbook By R.W.Miller. These describe the development of the formulas, the application limitations and installation requirements for predictable results as well as a large amount of other valuable information. Nomenclature
WM
Flowrate upper range variable
lb/h
WN
Flowrate normal flow
lb/h
HM
Differential upper range variable
HN
Differential normal
inches of water
SM
Orifice sizing factor
dimensionless
Pipe inside diameter at flowing temperature
inches
Orifice inside diameter
inches
D d γn
inches of water
Density at flow conditions
lb/ft3
µ CP
Absolute Viscosity
centipoise
RD
Reynolds Number
dimensionless
βO
Beta Ratio
dimensionless
C C INF
Orifice discharge coefficient
dimensionless
Orifice discharge coefficient for infinite Reynolds Number
dimensionless
Y Pf
Gas expansion factor
dimensionless
Upstream pressure
psia
k FA
Ratio of specific heats
dimensionless
Thermal expansion factor
dimensionless
PSONIC Downstream pressure for sonic velocity
psia
Fixed Geometry2 Calculation Routines Rotameters Liquid Calculation 1. Calculate the equivalent flow in US gallons per minute of water -
Wm
Qm =
188.814 G f (GF − G f )
US gallons per minute -
2. Calculate the sizing viscosity -
2.6496µ CP
µ CS =
G f ( GF − G f )
centistokes 3. Calculate the Maximum allowable viscosity -.
µ CP = µ CS G f centipoises Gas calculation 1. Calculate the equivalent flow -
Qm =
Wm 5.862 GF γ n
Standard cubic feet of air equivalent.
Nomenclature
Qm
Calculated equivalent water flow US gallons per minute
Wm
Desired quantity of flowing fluid
lb/h
γn
Gas density
lb per cubic foot
Gf
Specific gravity of flowing fluid
dimensionless
GF
Specific gravity of float
dimensionless
µ CS
Rotameter viscosity immunity ceiling
centistokes
µ CP
Viscosity of flowing fluid
centipoises
Vortex meters 1. Calculate the flow area -
A=
Wm 3600 Vγ n square feet
2. Calculate the maximum and minimum flowrate -
WMAX = 3600 A SEL VMAX γ n lb/h
WMIN = 3600 A SEL VMin γ n lb/h
3. For liquids callculate the Reynolds Number -
RD =
6.31533 Wm Dµ CP
Nomenclature
A Flow area for required flow A SEL Cross section area of selected meter
square feet square feet
Supplied by manufacturer (Bore area - Element area)
D γn
Pipe inside diameter at flowing temperature
Inches
Density at flow conditions
lb/ft3
RD
Reynolds Number
dimensionless
Wm
Required flowrate
lb/h
WMAX Flowrate upper range variable
lb/h
WMIN Flowrate lower range variable V Velocity at Wm VMAX Velocity at WMAX
lb/h feet per second feet per second
(Supplied by the manufacturer)
VMIN
µ CP
Velocity at WMIN (Supplied by the manufacturer)
feet per second
Absolute Viscosity
centipoise
Wedge Flowmeter 1. Set Y = 1 2. Calculate the differential range -
Wm h m = 358 . 9626 γ F YK 2 a n d
2
inches of water 3. If fluid is gas then calculate the expansion factor -
h β Y = 1 − 0.012 n P1 0.54
0 .3
4. Repeat from 2 until error is less than 0.00001 Nomenclature
Wm
Desired quantity of flowing fluid
lb/h
γn
Fluid density
lb per cubic foot
Hm
Differential range
inches of water
K d2
Wedge coefficient
dimensionless
P1
Inlet pressure
psia
Gas expansion factor
dimensionless
Wedge ratio ( Supplied by the manufacturer )
dimensionless
Y β
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation.
Relief Valve Calculation Routines Fire size Liquid Vaporization 1. Calculate the wetted area -
A W = ΣXπD V (D V + L V )
square feet
2. Calculate vaporized liquid -
Wm =
21000FA 0W.82 L HV lb/h
3. Calculate the pressure ratio -
r=
P2 P1
Limited to a minimum of k
2 k −1 k + 1 4. Calculate the specific heat ratio coefficient k +1
2 k −1 C = 520 k k + 1 5. Calculate the back pressure correction factor Standard valves
Kb =
735F2 1− r C
Where k −1 2 k − 1 k r k F2 = r k − 1 1 − r
Bellows valves 2
60 + OV K b = 16 . − 0.3 ε −0.04PIN − 118 . r P 70 IN (Typical)
(
)
6. Calculate the required area
A=
Wm K d CP1K b
Tf Z M square inches
7. Calculate maximum allowable back pressure -
K bMAX =
A CALC Kb A VALVE
Standard valves Iterate to find r Maximum back pressure -
= rP1 − 14.7 psig Bellows valves Maximum back pressure -
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. Nomenclature
A AW
Relief area
square inches
Wetted area
square feet
C DV
Specific heat ratio coefficient
dimensionless
Vessel diameter
feet
F/ Kd
Relief valve factor
dimensionless
Coefficient of discharge
dimensionless
Gas back pressure correction factor
dimensionless
Ratio of specific heats
dimensionless
Kb k Kp
Overpressure correction factor
dimensionless
L HV
Latent heat of vaporization at flow temp.
Btu per pound
LV
Vessel length, tangent to tangent
feet
% overpressure Molecular weight
dimensionless dimensionless
Maximum back pressure factor
dimensionless
Pin
Set pressure
psig
Pn
Operating pressure
psig
P1
Relieving pressure
psia
Back pressure Pressure ratio
psia dimensionless
Relief temperature
degR
Operating temperature
degF
OV M Pbmax
P2 r Tf Tn
Wm
Flow rate
lb/h
X1
Vessel wetted portion
dimensionless
Z
Compressibility factor
dimensionless
Relief Valve Calculation Routines Liquid Relief Known flow 1. Calculate the back pressure factor Standard valves -
KW = 1 Bellows valves.-
P KW = 117 . − IN POUT 2. Calculate the relief area -
A=
Wm
19008.4K dK pK w G f (P1 − POUT )
3. Calculate viscosity correction factor
RD = Kv =
5.6 Wm µ cp A 1892 . ln.ln.ln.RD − RD−0.6 RD0.047
If the Reynolds Number is greater than 50000 then -
Kv = 1 If the Reynolds Number is less than 100 then -
K v = 0.26.Ln.RD − 0.6 If the Reynolds Number is less than 15 then -
Kv =
RD 15
4. Calculate the viscosity corrected area -
A Kv
A=
5. Calculate the maximum allowable back pressure.Standard valves
PBMAX
2 Wm 19008.4K dK pK w K v A = PIN − Gf
Bellows valves Calculate
P KW = 117 . − IN POUT Calculate A in formula 2 Increment POUT until A equals the selected valve area Gas Relief Known Flow 1. Calculate the pressure ratio -
r=
P2 P1
Limited to a minimum of -
k
2 k −1 k + 1 2. Calculate the specific heat ratio coefficient k +1
2 k −1 C = 520 k k + 1 3. Calculate the back pressure correction factor Standard valves
Kb =
735F2 1− r C
Where k −1 2 k k 1− r k F2 = r k − 1 1 − r
Bellows valves (Typical) --
(
K b = 16 . − 0.3 ε
−0.04PIN
2
60 + OV − 118 . r P 70 IN
)
4. Calculate the required area -
A=
Wm K d CP1K b
Tf Z M square inches
5. Calculate maximum allowable back pressure -
K bMAX =
A CALC Kb A VALVE
Standard valves Iterate to find r Maximum back pressure
= rP1 − 14.7 psig Bellows valves Maximum back pressure -
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. Nomenclature
Entrapped liquid - pipeline 1. Calculate the flow rate.-
Wm = 13.62D 2LBG f lb/h (for a temperature rise of 5 degF per hour) Both are common from here 2 Calculate the back pressure factor Standard valves -
KW = 1 Bellows valves -
P KW = 117 . − IN POUT 3 Calculate the relief area -
A=
Wm
19008.4K dK pK w G f (P1 − POUT )
square inches
4 Calculate viscosity correction factor -
RD = Kv =
5.6 Wm µ cp A 1892 . ln.ln.ln.RD − RD−0.6 RD0.047
If the Reynolds Number is greater than 50000 then -
Kv = 1 If the Reynolds Number is less than 100 then -
K v = 0.26.Ln.RD − 0.6 If the Reynolds Number is less than 15 then -
Kv =
RD 15
5. Calculate the viscosity corrected area -
A=
A Kv
6 Calculate the maximum allowable back pressure Standard valves -
PBMAX
2 Wm 19008.4K dK pK w K v A = PIN − Gf psig
Bellows valves Calculate
P KW = 117 . − IN POUT
Calculate A in formula 3 Increment POUT until A equals the selected valve area Heat Exchanger Tube Failure -
A=
A TUBE Kd
PTUBE − 15 . (PSHELL − P bMAX
)
185 . PSHELL
square inches The tube pressure must be greater than 150% of the shell pressure. The ruptured tube is assumed to provide a flow area of one tube and a flow coefficient of 0.62. The is no allowance in the formula for flashing or thermal expansion. K d is 1 for 25% overpressure, 0.82 for 16% and 0.62 for 10%.
Fluid Properties These are calculated using common chemical formulae with each item corrected for pressure and temperature. Some fluids show deviations from the formulae, the user should check typical calculated values against known values. In all cases if accurate laboratory information is available it should be used. Density uses the Redlich-Kwong Equation. Nomenclature
A Relief area A TUBE Tube cross section area
square inches square inches
B C Gf
Liquid cubical expansion at flow temp
per degF
Liquid specific heat
BTU/lb/degF
Specific gravity at flowing temperature
dimensionless
H Kd
Total heat transfer
BTU/hour
Coefficient of discharge
dimensionless
Kp
Overpressure correction factor
dimensionless
Kw
Liquid back pressure correction factor
dimensionless
Kv
Viscosity correction factor
dimensionless
% overpressure
dimensionless
Molecular weight
dimensionless
Maximum back pressure
psig
OV M Pbmax
PSHELL Shell maximum allowable working pressure PTUBE Tube maximum allowable working pressure
