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Design Factor Modules

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CALCULATOR MODULE : Beam Lateral Vibration Frequency   ±

Calculate the damped and undamped beam natural vibration frequency for lateral vibration (simply supported, fixed, and cantilever beams).

Added mass should be included for submerged or wet beams. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one.

The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration. For multi layer pipes the bending stiffness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which affect the pipe stiffness.

Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Beam Lateral Vibration Frequency With Axial Load   ±

Calculate the damped and undamped beam natural vibration frequency for lateral vibration with axial load (simply supported, fixed, and cantilever beams).

For beams with axial load the axis with minimum stiffness (I1 or I2) should be used unless the beam is constrained to deflect on an alternative axis (buckling normally occurs on the minimum stiffness axis). Use the general beam calculators for cases where vibration and buckling are not parallel. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). The buckling load is dependent on the end type, and is used for mode 1 vibration only.

Added mass should be included for submerged or wet beams. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one. For pipes the axial load is calculated from temperature and pressure. For general beams the axial load is user defined.

The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration. For multi layer pipes the bending stiffness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which affect the pipe stiffness.

Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Beam Vibration Added Mass   ±

Calculate submerged beam added mass coefficient and added mass from gap height.

Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The equation is suitable for undamped vibration of circular beams in a still fluid. For other beam profiles use the beam width. The method may not be valid for other profiles (engineering judgment is required). The gap height is measured along the axis of vibration and is assumed to be perpendicular to the adjacent surface.

Use the Result Table and Result Plot options to display tables and plots. Refer to the help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Beam Vibration Concrete Stiffness Factor CSF   ±

Calculate beam concrete stiffness factor and effective EI from the concrete beam EI ratio.

`CSF = kc ((EIc) / (EIp))^0.75 `
`EIe = EIc (1 + CSF) `

where :

CSF = concrete stiffness factor
kc = coating factor (kc = 0.33 for asphalt and 0.25 for PP/PE coating)
EIc = concrete bending stiffness
EIb = pipe bending stiffness
EIe = eqivalent bending stiffness

The concrete stiffness factor is used to account for the effect of the concrete layer on the natural frequency, deflection and bending stress. The concrete stiffness factor is calculated from the ratio of concrete EI over pipe EI. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. The method is suitable for circular pipes. The method may not be valid for other profiles (engineering judgment is required).

Use the Result Table and Result Plot options to display tables and plots. Refer to the help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Beam Cross Section   ±

Calculate beam cross section properties for circular pipes: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, section modulus, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity.

Unit mass can be calculated with or without added mass. Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient can be calculated in accordance with DNVGL RP F105. For multi layer pipes the bending stifness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. Use the Result Table option to display the cross section properties versus wall thickness. Refer to the help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Beam Cross Section Concrete Stiffness Factor   ±

Calculate beam cross section concrete stiffness factor (CSF) and effective EI from the concrete to beam EI ratio.

Concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The bending stress should also be multiplied by the factor (1 + CSF) to account for stress localisation at the field joints.

The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. The method is suitable for circular beams and pipes. For other profile shapes engineering judgement is required.

Use the Result Plot option to plot the concrete stiffness factor (CSF) versus EI ratio and CSF type, or effective EI versus EI ratio and CSF type. Refer to the help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Pipe Beam Bending   ±

Calculate beam bending shear force, bending moment, slope and deflection for pipe beams using the Euler Bernoulli beam equation.

The Euler Bernoulli beam equation is suitable for slender beams (it does not include the effect of shear), and for small angles (θ < 0.5 rad). The calculations are not valid past the beam end points. For combined loads, the shear force, bending moment, slope and deflection are assumed to be additive. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends.

Combined loads include axial loads, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature gradient.

For beams with compressive axial loads the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

For multi layer beams the concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The bending stress at the field joint should also be multiplied by the factor (1 + CSF) to account for stress localisation (select the pipe joint option for bending stiffness) . The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI in accordance with DNVGL RP F105. The method is suitable for circular beams and pipes. For other profile shapes engineering judgement is required.

The stress check includes longitudinal stress, Tresca combined stress, and von Mises equivalent stress. The bending stress is calculated at the pipe mid wall. The hoop stress is calculated using the Barlow mid wall equation with the nominal wall thickness.

:

`Sh = (P - Pe) (OD - tn) / (2 tn) `

where :

Sh = hoop stress
P = internal pressure
Pe = external pressure
OD = pipe outside diameter
tn = pipe nominal thickness

Use the Result Plot option to plot the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Pipe Beam Buckling Load   ±

Calculate beam buckling load for pipe beams.

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed).

The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The buckling load is positive. The axial load is negative in compression. Buckling will generally occur about the axis with the lowest EI, depending on constraints.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

Concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI in accordance with DNVGL RP F105. The method is suitable for circular beams and pipes. For other profile shapes engineering judgement is required.

Use the Result Plot option to plot the buckling load versus nominal length. Use the Result Table option to plot the buckling load versus end type. Refer to the figures and help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Line Pipe Thermal Conductivity And Heat Transfer   ±
CALCULATOR MODULE : Line Pipe Concrete Stiffness Factor   ±

Calculate pipe concrete stiffness factor and effective EI from the concrete beam EI ratio.

The concrete stiffness factor is used to account for the effect of the concrete layer on the pipe EI. The concrete stiffness factor is calculated from the ratio of concrete EI over pipe EI in accordance with DNVGL RP F105. The effective EI can be calculated for asphalt coating, PE/PP coating, user defined coating factor Kc, user defined concrete stiffness factor CSF, or from the sum of the internal and external EI.

Use the Result Table and Result Plot options to display preset tables and plots. Refer to the help pages for more details about the tools.

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CALCULATOR MODULE : ASME B31.3 Process Piping Design Factor   ±

Calculate ASME B31.3 process piping design factors (Y factor and W factor).

The Y factor is calculated from diameter for thick wall pipe (D/t < 6), or from temperature for thin wall pipe. The weld factor (W) is only relevant for design temperatures in the creep range. For design temperatures below the creep onset temperature W = 1. The weld factor does not apply for seamless pipe (W = 1).

Reference : ANSI/ASME B31.3 : Process Piping (2018)

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CALCULATOR MODULE : ASME B31.8 Gas Pipeline Temperature Derating   ±
CALCULATOR MODULE : ASME B31.1 Power Piping Design Factor   ±

Calculate ASME B31.1 power piping design factors (Weld factor W, Y factor and thinning allowance B).

The Y factor is calculated from diameter for thick wall pipe (D/t < 6), or from temperature for thin wall pipe. The weld factor (W) is only relevant for design temperatures in the creep range. For design temperatures below the creep onset temperature W = 1. The weld factor does not apply for seamless pipe (W = 1). The thinning allowance (B) is an approximate estimate of the thinning on the outside radius due to bending (ASME B31.3 table 102.4.5). A power law curve has been fitted to the data values in the table. Use the workbook ASME B31.1 data tables to look up allowable stress data.

Reference : ANSI/ASME B31.1 : Power Piping (2014)

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CALCULATOR MODULE : ASME B31.5 Refrigeration Piping Design Factor   ±
CALCULATOR MODULE : Hot Pipeline Temperature Decay Curve   ±
CALCULATOR MODULE : Hot Pipeline End Expansion   ±
CALCULATOR MODULE : Hot Pipeline Walking   ±
CALCULATOR MODULE : Hot Pipeline Soil Friction   ±
CALCULATOR MODULE : Hot Pipeline Heat Transfer Coefficient   ±
CALCULATOR MODULE : API RP 1111 Pipeline Temperature Derating   ±
CALCULATOR MODULE : API RP 1102 Pipeline Crossing Design Factor   ±

Calculate API RP 1102 highway and railroad pipeline crossing design factors.

The design factors are calculated from the figures using the US values. Use the constant slope option to extrapolate values outside the range in the figures. Extrapolated values should be used carefully. Use the Result Plot option to display the selected figure with preset values (click the Result Plot button on the plot bar, then click the Make Plot button).

Reference : API RP 1102 : Steel Pipelines Crossing Railroads and Highways (2012)

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CALCULATOR MODULE : ASME B31 Stress Intensity Factor   ±
CALCULATOR MODULE : ASME B31.1 Power Piping Flexibility And Stress Factor   ±
CALCULATOR MODULE : ASME B31.3 Process Piping Flexibility And Stress Factor   ±
CALCULATOR MODULE : ASME B31.4 Liquid Pipeline Flexibility And Stress Factor   ±
CALCULATOR MODULE : ASME B31.5 Refrigeration Piping Flexibility And Stress Factor   ±
CALCULATOR MODULE : ASME B31.8 Gas Pipeline Flexibility And Stress Factor   ±
CALCULATOR MODULE : DNVGL RP F101 Maximum Defect Depth   ±
CALCULATOR MODULE : Piping Fitting Minor Loss Factor   ±

Calculate pipe fitting minor loss factors.

Minor loss factors can be defined as:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The K factor and discharge coefficient are dimensionless and can be used with any consistent set of units. The dimensionless flow coefficient has inconsistent units, and is unit specific. The flow coefficient Av, Cv-us, Cv-uk, Cv-met and Kv have dimensions length squared, and can not be used interchangeably between different systems of units.

Note : The friction factor K, discharge coefficient Cd, dimensionless flow coefficient Cv*, and flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv are used in different situations. The discharge coefficient is usually used for discharge through an orifice, but can also be used in other situations (for example pressure relief valves). The flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv, and the dimensionless flow coefficient Cv* are usually used for valves, but can also be used for other fittings. Engineering judgement is required to determine the correct minor loss factor to use.

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CALCULATOR MODULE : Parallel And Series Piping Fitting   ±

Calculate minor loss factors for parallel and series pipe fittings.

The effective K factor for fittings in series equals the sum of the K factors.

`Ke = ΣKi `

For fittings in parallel the inverse effective K factor equals the sum of the inverse K factors.

`1/(Ke) = Σ1/(Ki) `

The calculators can be used for parallel and series K factor, discharge coefficient Cd, dimensionless flow coefficient Cv*, and flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

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CALCULATOR MODULE : Piping Fitting Pressure Loss   ±

Calculate outlet pressure and pressure loss through piping and fittings.

The pressure loss is calculated from the Moody diagram using the Darcy-Weisbach friction factor. The Darcy friction factor can be calculated using either the Hagen-Poiseuille laminar flow equation, the original Colebrook White turbulent flow equation, or the modified Colebrook White equation. Changes in elevation are ignored.

For liquid piping with fittings the outlet pressure is calculated by:

`Po = P - 8 (fL/D+ΣK) ρ (Q^2) / (pi^2D^4) `
`ΔP = P - Po `

where :

ΔP = pressure loss
P =inlet pressure
Po = outlet pressure
Po = outlet pressure
ρ = fluid density
Q= fluid volume flowrate
f = Darcy friction factor
L = pipe length
D = pipe inside diameter
Σ K = total fitting K factor

For gas piping with fittings the outlet pressure is calculated by:

`Po = √(P^2 - 16m^2(fd.L / D + ΣK) (mma.SG.ZRoT)/(pi^2D^4) ) `

where :

m = gas mole flowrate
mma = air molar mass
SG = gas specific gravity
Z = gas compressibility factor
Ro = universal gas constant
T = gas temperature

For liquid fittings the outlet pressure is calculated by:

`Po = P - 8 K ρ (Q^2) / (pi^2D^4) `

where :

K = fitting K factor

For gas fittings the outlet pressure is calculated by:

`Po = √(P^2 - m^2K (16mma.SG.ZRoT)/(pi^2D^4) ) `

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CALCULATOR MODULE : Piping Fitting Fluid Property   ±

Calculate pipe fitting gas and liquid density and viscosity.

Calculate liquid density, specific gravity, degrees Baume, degrees Twaddell, or degrees API. For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell.

Calculate gas density, viscosity and compressibility factor for: methane CH4, ethane C2H6, propane C3H8, iso-butane C4H10, n-butane C4H10, iso-pentane C5H12, n-pentane C5H12, n-hEAne C6H14, n-heptane C7H16, n-octane C8H18, n-nonane C9H20, n-decane C10H22, air N2 + O2, ammonia NH3, argon Ar, carbon dioxide CO2, carbon monoxide CO, chlorine Cl2, helium He, hydrogen H2, hydrogen chloride HCl, hydrogen sulphide H2S, nitrogen N2, oxygen O2, and steam H2O. The gas compressibility factor is calculated from the critical point temperature, critical point temperature, and the accentric factor using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals equations of state (EOS).

Steam table properties can be calculated for water, saturated water, saturated steam, saturated water and steam, metastable water, and metastable steam.

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CALCULATOR MODULE : Piping Reducer And Enlarger Minor Loss Factor   ±

Calculate typical pipe reducer and enlarger minor loss factors.

The minor loss factors can be calculated for either the small diameter, and the large diameter. The nozzle can be either tapered with a transition, or abrupt with no transition. The taper angle is equal to half the cone angle.

Note : The calculated values are typical. Manufacturers data should be used if it is available.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Wye And Tee Minor Loss Factor   ±

Calculate typical pipe wye and tee minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

The minor loss factors can be calculated for converging and diverging wyes and tees, and for the run and the branch. The run is assumed to be constant diameter. The branch diameter should be smaller than or equal to the run diameter. The flow ratio should be 0 ≤ Qb/Qc ≤ 1. The flow ratio can be either the mass flowrate ratio, the volume flowrate ratio (for liquids), or the mole flowrate ratio (for gases).

Note : In some cases the friction factor K can be negative due to the acceleration of slow moving fluid to the velocity of the combined flow. The discharge coefficient and flow coefficients are invalid for negative friction factor K.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Entry And Exit Minor Loss Factor   ±

Calculate typical pipe entry and exit minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

Minor loss factors canbe calculated for pipe exits, inward protruding entries, sharp edged flush entries, and radiused flush entries.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Bend And Elbow Minor Loss Factor   ±

Calculate typical pipe bend and elbow minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

Minor loss factors can be calculated for miter bends (single miter and multiple miter), formed bends, close return bends, and standard elbows.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Valve Minor Loss Factor   ±

Calculate typical pipe valve minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

The valves are assumed to be fully open. For full port valves the valve port cross section area equals the nominal internal cross section area. For reduced port valves the valve port cross section area is less than the nominal internal cross section area. For circular valve ports the diameter ratio is equal to the valve port diameter over the nominal inside diameter. For non circular valve ports, use the square root of the internal area ratio (the square root of the valve port area over the nominal internal area).

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Check Valve Minor Loss Factor   ±

Calculate typical gas and liquid pipe check valve minimum velocity and minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

The minimum flowrate is the flowrate required to keep the check valve fully open. For full port valves the valve port cross section area equals the nominal internal cross section area. For reduced port valves the valve port cross section area is less than the nominal internal cross section area. For circular valve ports the diameter ratio is equal to the valve port diameter over the nominal inside diameter. For non circular valve ports, use the square root of the internal area ratio (the square root of the valve port area over the nominal internal area).

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The calculated values are typical. Manufacturers data should be used if it is available.

Reference : Crane Technical Paper 410M Metric Version : Flow Of Fluids Through Valves, Fittings And Pipe

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CALCULATOR MODULE : Piping Control Valve Sizing   ±

Calculate typical gas and liquid pipe control valve sizing and minor loss factors (K, Cd, Cv*, Av, Cv-uk, Cv-us, Cv-met and Kv).

The control valve sizing is calculated in two steps using the ISA-75.01.01 iteration method for Kv flow coefficient. The other flow factors (Av, Cv-uk, Cv-us, Cv-met, Cv*, K, and Cd) are calculated from Kv.

Step 1 : Calculate the required valve flow coefficient (Av, Cv-uk, Cv-us, Cv-met and Kv) assuming that the valve ID is equal to the pipe ID. Use the required flow coefficient to select a suitable valve.

Step 2 : Select a suitable valve size, type and flow coefficient based on manufacturers data. If a full bore valve is too large, a smaller valve should be selected, with assumed concentric reducers. Calculate the required flow coefficient for the selected valve. The required flow coefficient should be less than or equal to the valve flow coefficient. A trial and error process may be required to determine the appropriate valve. It is recommended that the valve diameter is not less than half the pipe diameter. The calculation is not valid if the valve diameter is greater than the pipe diameter. The calculation might not converge if the valve size is too small.

For viscous fluids or very low flow velocity flow, with low Reynolds number (Rev < 10,000) use the Reynolds number factor option. For most flow cases the Reynolds number can be ignored (Fr = 1).

Check for choked conditions. If the outlet pressure for step 1 or step 2 is greater than the minimum (choked) outlet pressure, set the outlet pressure equal to the choked outlet pressure. The maximum (choked) flowrate, maximum (choked) delta pressure and minimum (choked) outlet pressure are calculated from the fluid vapour pressure, and the fluid critical point pressure. Specially designed valves are required to operate at choked conditions.

The K factors should include fittings located with 2D upstream and 6D downstream. The fluid velocity is calculated from the valve ID. The piping is assumed to be constant diameter upstream and downstream of the valve. The liquid pressure recovery factor Fl, and the valve design factor Fd depend on the valve type and geometry. Typical values are included in the data tables. Manufacturers data should be used if it is available. Check that the convergence is close to or equal to one. Convergence problems can indicate that the selected valve size is too small.

The dimensionless flow coefficient Cv* equals Cv-us / IDin^2, where IDin is the valve inside diameter in inches. For control valves, a maximum Cv* value of 30 is recommended, equivalent to a minimum K factor of 1.

Minor loss factors are calculated for:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

Reference : ISA-75.01.01 Industrial Process Control Valves Part 2-1 Flow Capacity Sizing Equations For Fluid Flow Under Installed Conditions

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CALCULATOR MODULE : Gas Piping Minor Loss Factor   ±

Calculate gas pipe fitting minor loss factors.

Minor loss factors can be defined as:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The K factor and discharge coefficient are dimensionless and can be used with any consistent set of units. The dimensionless flow coefficient has inconsistent units, and is unit specific. The flow coefficient Av, Cv-us, Cv-uk, Cv-met and Kv have dimensions length squared, and can not be used interchangeably between different systems of units.

Note : The friction factor K, discharge coefficient Cd, dimensionless flow coefficient Cv*, and flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv are used in different situations. The discharge coefficient is usually used for discharge through an orifice, but can also be used in other situations (for example pressure relief valves). The flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv, and the dimensionless flow coefficient Cv* are usually used for valves, but can also be used for other fittings. Engineering judgement is required to determine the correct minor loss factor to use.

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CALCULATOR MODULE : Liquid Piping Minor Loss Factor   ±

Calculate liquid pipe fitting minor loss factors.

Minor loss factors can be defined as:

  • Av (SI) flow coefficient - the flow in cubic meters per second fluid density 1 kilogram per cubic meter which gives a pressure drop of 1 Pa
  • Cv-uk (UK) flow coefficient - the flow in UK gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-us (US) flow coefficient - the flow in US gallons per minute of water at 60 degrees F which gives a pressure drop of 1 psi
  • Cv-met (Metric) flow coefficient - the flow in liters per minute of water at 16 degrees C which gives a pressure drop of 1 bar
  • Kv (EU) flow coefficient - the flow in cubic meters per hour of water at 16 degrees C which gives a pressure drop of 1 bar
  • Cv* the dimensionless US flow factor = Cv-us / din^2 (din is the inside diameter in inches)
  • K factor - the ratio of pressure loss over the dynamic pressure
  • Cd or discharge coefficient - the ratio of the actual flow rate of the fluid through the fitting over the frictionless flow rate.

The K factor and discharge coefficient are dimensionless and can be used with any consistent set of units. The dimensionless flow coefficient has inconsistent units, and is unit specific. The flow coefficient Av, Cv-us, Cv-uk, Cv-met and Kv have dimensions length squared, and can not be used interchangeably between different systems of units.

Note : The friction factor K, discharge coefficient Cd, dimensionless flow coefficient Cv*, and flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv are used in different situations. The discharge coefficient is usually used for discharge through an orifice, but can also be used in other situations (for example pressure relief valves). The flow coefficients Av, Cv-uk, Cv-us, Cv-met and Kv, and the dimensionless flow coefficient Cv* are usually used for valves, but can also be used for other fittings. Engineering judgement is required to determine the correct minor loss factor to use.

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CALCULATOR MODULE : Liquid Pipeline Pressure Loss From The Darcy Weisbach Equation   ±

Calculate single phase liquid pipeline pressure loss using the Darcy Weisbach equation.

`Po = P - (fd L / (ID) + K) 1/2 ρ V^2 + ρ g (zi - zo) `

where :

Po = outlet pressure
P = inlet pressure
fd = Darcy friction factor
L = piping length
ID = piping inside diameter
K = total friction loss factor for fittings
ρ = fluid density
V = fluid velocity
g = gravity constant
zi = inlet elevation
zo = outlet elevation

The Darcy friction factor can be calculated for

  • Hagen-Poiseuille laminar flow equation
  • original Colebrook White equation
  • modified Colebrook White equation
  • Prandtl Nikuradse smooth pipe equation
  • Blasius smooth pipe equation
  • Colebrook smooth pipe equation
  • Miller smooth pipe equation
  • Konakov smooth pipe equation
  • Von Karman rough pipe equation

For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc..

The calculators use the Darcy-Weisbach pressure loss equation. The Fanning friction factor is used with the Fanning pressure loss equation. The transmission factors are commonly used for gas flow. The results for the Darcy and Fanning equations are identical provided that the correct friction factor is used.

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CALCULATOR MODULE : Liquid Rectangular Duct Pressure Loss   ±

Calculate single phase liquid flow in a rectangular duct.

The Moody diagram is valid for rectangular ducts provided that the Reynolds number is calculated from the hydraulic diameter (equal to four times the cross section area divided by the perimeter). The Darcy friction factor can be calculated from the Moody diagram using either the Hagen-Poiseuille laminar flow equation, the original Colebrook White equation or the modified Colebrook White equation. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc.. Change flow coefficient units on the setup page (Av, Kv, or Cv).

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CALCULATOR MODULE : Gas Pipeline Pressure Loss From The Moody Diagram   ±

Calculate pressure loss for single phase gas pipelines using the Darcy Weisbach version of the Moody Diagram.

`fdl = 64/(Re) `
`1/(√fdo) = -2 log10(r/3.7 + 2.51 / (Re √(fdo))) `
`1/(√fdm) = -2 log10(r/3.7 + 2.825 / (Re √(fdm))) `

where :

fdl = Hagen-Poiseuille laminar flow equation Darcy friction factor
fdo = original Colebrook White equation Darcy friction factor
fdm = modified Colebrook White equation Darcy friction factor
Re = Reynolds number
r = relative roughness

For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated. The minor loss K factor is used to account for pipeline fittings such as bends, tees, valves etc..

The calculators use the Darcy-Weisbach version of the Moody diagram. The Fanning transmission factor combined with the Fanning equation is commonly used for gas flow. The results for the Darcy and Fanning equations are identical provided that the correct friction factor is used.

`ff = (fd) / 4 `
`tf = 1 / (√ff)= 2 / (√fd) `

where :

fd = Darcy friction factor
ff = Fanning friction factor
tf = Fanning transmission factor

The gas specific gravity is the ratio of gas density over the density of dry air at base temperature and pressure. The compressibility factor is assumed to equal 1 at the base conditions. The gas specific gravity is proportional to the gas molar mass.

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CALCULATOR MODULE : Gas Rectangular Duct Pressure Loss   ±

Calculate single phase gas flow in a rectangular duct.

The Darcy friction factor can be calculated from the Moody diagram using either the Hagen-Poiseuille laminar flow equation, the original Colebrook White equation or the modified Colebrook White equation. The Moody diagram can be used for rectangular ducts if the Reynolds number is calculated from the hydraulic diameter (equals four times the cross section area divided by the perimeter). Minor losses can be calculated using either the K factor, an equivalent length, equivalent diameters, or the flow coefficient. Change flow coefficient units on the setup page (Av, Kv, or Cv).

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CALCULATOR MODULE : Pipeline Flow Rate   ±
CALCULATOR MODULE : Compressible Flow Gas Property   ±

Calculate compressible flow gas properties.

Calculate gas specific heat constant pressure, specific heat constant volume, specific heat ratio, molar mass, gas constant, gas specific gravity, gas compressibility factor and density from gas temperature and pressure. The gas compressibility factor is calculated from the critical point temperature, critical point temperature, and the accentric factor using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals equation of state (EOS).

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Pressure Loss Factor   ±
CALCULATOR MODULE : API 520 Correction Factor   ±
CALCULATOR MODULE : API 520 Darcy Friction Factor   ±

Calculate API 520 Darcy friction factor and pressure loss factor for single phase liquid and single phase gas.

The Darcy friction factor can be caclulated from either the Moody diagram or the Von Karman rough pipe equation (API 520 Annex E).

At high Reynolds numbers the Moody diagram friction factor is fully turbulent and is dependent on the pipe roughness only. The pressure loss factor (fLe/ID) includes minor losses. Minor losses can be entered as either a K factor, an equivalent added length, or an equivalent added length over diameter ratio.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : API 520 Fluid Property   ±

Calculate API 520 gas and steam properties.

Properties include density, specific heat constant pressure, specific heat constant volume, specific heat ratio, molar mass, gas constant, gas specific gravity, and gas compressibility factor. The gas compressibility factor is calculated from the critical point temperature, critical point temperature, and the accentric factor using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals equations of state (EOS).Steam properties are calculated from IAPWS R7-97, industrial properties of steam.

Gas specific gravity at standard conditions is approximately equal to the gas molar mass divided by the molar mass of dry air. The molar mass of dry air is taken as 28.964 kg/kg-mole.

Reference : API 520 Sizing, Selection And Installation Of Pressure Relieving Devices (2014)

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CALCULATOR MODULE : Pump Flowrate Pressure And Power Coefficient   ±

Calculate pump flow coefficient (Cq), pressure coefficient (Cp), power coefficient (Cw) and pump specific speed from flowrate, delta pressure, pump speed and impeller diameter. The pump coefficients are calculated at the best efficiency point (BEP).

`Cq = Q / (n d^3) `
`Cp = (ΔP) / (ρ n^2 d^2) = (gΔH) / (n^2 d^2) `
`Cw = Cq. Cp = (Q ΔP) / (ρ n^3 d^5) `
`Ns = (Cq^(1/2)) / (Cp^(3/4)) = nQ^(1/2) (ΔP^(3/4)) / ρ `

where :

Cq = flowrate coefficient at BEP
Cp = pressure coefficient at BEP
Cw = power coefficient at BEP
Ns = pump specific speed at BEP
n = pump rotational speed at BEP
d = impeller diameter at BEP
Q = flow rate at BEP
ΔP = delta pressure at BEP
ΔH = delta head at BEP
ρ = fluid density
g = gravity constant

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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CALCULATOR MODULE : Gas Compressibility Factor   ±

Calculate gas compressibility factor or Z factor.

The compressibility factor is used to account for the non ideal behaviour of real gases. The non ideal gas law is expressed as

` P V = Z Ro T `

where :

P = gas pressure `
`T = gas temperature `
`V = gas mole volume `
`Z = gas compressibility factor `
`Ro = universal gas constant

The compressibility factor canbe calculated using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals cubic equations of state (EOS), or using the virial equation.

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CALCULATOR MODULE : Gas Compressibility Factor From The Virial Equation   ±

Calculate gas compressibility factor or Z factor from the virial equation.

The compressibility factor is calculated using the second order virial equation

`Z = (P.vm) / (Ro .T) = 1 + B / (vm) `
`B = a - b.e^(c / T) `

where :

Z = the compressibility factor
P = gas pressure
T = gas temperature
vm = gas mole volume
Ro = the universal gas constant
B = the second order virial coefficient
a, b, c are Virial constants

The gas mole volume is calculated by solving the quadratic equation, and the compressibility factor is calculated from the mole volume.

Reference : Kaye And Laby : Tables Of Physical And Chemical Constants

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CALCULATOR MODULE : Gas Compressibility Factor From The Cubic Equation   ±

Calculate gas compressibility factor or Z factor from the cubic equation (Poling).

The compressibility factor is used to account for the non ideal behaviour of real gases. The non ideal gas law is expressed as

`P V = Z Ro T `

where :

P = gas pressure
T = gas temperature
V = gas mole volume
Z = gas compressibility factor
Ro = universal gas constant

The compressibility factor can be calculated using either the Peng Robinson, Soave, Redlich Kwong or Van Der Waals cubic equations of state (EOS). The gas data is taken from Poling.

Reference : Poling, Prausnitz And O'Connell : The Properties of Gases And Liquids : McGraw Hill

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CALCULATOR MODULE : Fluid Mixture From Kay's Rule   ±

Calculate pseudo-critical properties (temperature, pressure, accentric factor, molar mass) of a fluid mixture using the simple form of Kay's rule with no interaction parameters.

The mole fraction of component one is automatically adjusted so that the sum of the mole fractions equals one. The mixture properties are approximate.

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    CALCULATOR MODULE : IAPWS R7-97 Steam Adiabatic Constant Enthalpy   ±

    Calculate IAPWS R7-97 constant enthalpy adiabatic steam temperature from initial enthalpy and final pressure.

    For an adiabatic process the enthalpy is constant. Initial enthalpy can be calculated from the steam table or user defined. The anomaly zone is set to region 2 (region 3 does not converge properly).

    Note : The steam is assumed to be stationary at the initial and final conditions. For moving steam use the constant entropy calculator for constant stagnation enthalpy (ho = h + 1/2 V^2).

    Use the Result Plot option to plot final (adiabatic) properties versus initial enthalpy.

    Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the region 2/3 boundary, and the critical pressure. Refer to the region 3 anomaly help page for more details (click the utility button on the data bar). IAPWS R7-97 is intended for industrial use, and is a simplified version of IAPWS R6-95 for scientific use. IAPWS R7-97 was developed as an improvement of the IFC-67 model.

    Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

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    CALCULATOR MODULE : IAPWS R7-97 Steam Isentropic Constant Entropy   ±

    Calculate IAPWS R7-97 constant entropy isentropic steam temperature from initial entropy and final pressure.

    For an isentropic process the entropy is constant. Initial entropy can be calculated from the steam table or user defined. The anomaly zone is set to region 2 (region 3 does not converge properly).

    Note : For an isentropic process the stagnation enthalpy is constant (ho = h + 1/2 V^2). The stagnation enthalpy can be used to calculate the steam velocity.

    Use the Result Plot option to plot final (isentropic) steam properties versus initial entropy.

    Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the region 2/3 boundary, and the critical pressure. Refer to the region 3 anomaly help page for more details (click the utility button on the data bar). IAPWS R7-97 is intended for industrial use, and is a simplified version of IAPWS R6-95 for scientific use. IAPWS R7-97 was developed as an improvement of the IFC-67 model.

    Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

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    CALCULATOR MODULE : IAPWS R7-97 Steam Isoenergetic Constant Internal Energy   ±

    Calculate IAPWS R7-97 constant internal energy isoenergetic steam temperature from initial internal energu and final pressure.

    For an isoenergetic process the internal energy is constant. Initial internal energy can be calculated from the steam table or user defined. The anomaly zone is set to region 2 (region 3 does not converge properly). Use the Result Plot option to plot final (isoenergetic) properties and temperature versus initial internal energy.

    Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the region 2/3 boundary, and the critical pressure. Refer to the region 3 anomaly help page for more details (click the utility button on the data bar). IAPWS R7-97 is intended for industrial use, and is a simplified version of IAPWS R6-95 for scientific use. IAPWS R7-97 was developed as an improvement of the IFC-67 model.

    Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

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    CALCULATOR MODULE : Yaws Gas Density From Critical Point   ±

    Calculate gas density from critical pressure, critical temperature and acentric factor data for organic and inorganic fluids (Yaws).

    The compressibility factor can be calculated from either the Peng Robinson, Soave, Redlich Kwong, or van der Waals cubic equation. The compressibility factor calculation is valid for gas phase only. The gas specific gravity is approximately equal to the ratio of the gas molar mass over the molar mass of air (28.964 g/mol).

    Reference : Yaws Chemical Properties Handbook, McGraw Hill
    CALCULATOR MODULE : Maths Nett Present Value NPV   ±

    Calculate net present value from annual cash flow and compound interest rate.

    Net present value is often used to evaluate the relative profitability of various business options. The option with the highest net present value is generally considered to be the best option from a financial perspective. The net present value is calculated by discounting future cash flows by the compounded interest rate, or value of money.

    `NPV =Σ (Ci) / (1 + R)^i, i = 0 to n `

    where :

    Ci = yearly cash flow
    R = interest rate or cost of money
    NPV = net present value
    i = the year

    The interest rate is assumed to be constant.

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    CALCULATOR MODULE : Maths Polynomial   ±

    Calculate polynomial coefficients, roots or zeros, maximum and minimum, points of inflection, and interpolate polynomial value, slope and curvature.

    Polynomials can be calculated for linear (first order), quadratic (second order), cubic (third order), quartic (fourth order), quintic (fifth order), sextic (sixth order), septic (seventh order), octic (eighth order) or nth degree. For polynomials with all real roots, all roots can sometimes be solved simultaneously using the Durand Kerner method. In other cases solve for individual roots. The maximum or minimum points (slope equals zero) and the inflection points (curvature equals zero) can also be calculated. Use a plot page to plot the polynomial and identify the approximate root values if any.

    Lagrange's method is used to interpolate between data points. This method is useful for interpolating between data points, but can give poor results when extrapolating outside the data range. Evenly spaced data points can result in cyclic behaviour.

    Polynomial coefficients can be calculated from the real roots, and the nth coefficient. There are an infinite number of polynomials with the same roots. The nth coefficient is required in order to calculate unique coefficients. This method only applies if all of the roots are real. Polynomial coefficients can also be calculated from XZ data points.

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    CALCULATOR MODULE : Maths Polynomial Coefficient   ±

    Calculate polynomial coefficients from real roots or zeros, or from XZ data points.

    To calculate the coeficients from real roots, the value of An (the nth order coefficient) must be included in order to calculate a unique set of polynomial coefficients. The coefficients are listed in the order A0, A1, A2....An where An is the coefficient for the nth power of x (x^n) etc... The calculation is only valid for polynomials with no imaginary roots, ie the number of real roots equals the polynomial order.

    The polynomial value, slope and curvature are calculated at X. The maximum and minimum points (zero slope), and the points of inflection (zero curvature), can not be calculated unless all points are real numbers.

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    CALCULATOR MODULE : Material Elastic Modulus   ±

    Calculate material elastic modulus.

    The elastic stiffness of a material is defined by the elastic modulus, Poisson's ratio, Lame's first parameter, bulk modulus, shear modulus and p-wave modulus. Calculate material Poisson ratio, bulk modulus, Lames first parameter, shear modulus and p-wave modulus. These six properties are interdependent so that if any two properties are known the other four properties can be calculated.

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    CALCULATOR MODULE : DNVGL RP C203 Pipeline Fatigue Stress   ±
    CALCULATOR MODULE : DNVGL RP C203 Fatigue Stress Concentration Factor   ±
    CALCULATOR MODULE : DNVGL RP C203 Fatigue System Effect   ±
    CALCULATOR MODULE : DNVGL RP C203 Mean Stress Factor   ±
    CALCULATOR MODULE : Ocean Current   ±

    Calculate current velocity versus water depth using either the logarithmic profile or the 1/7th power law profile.

    The current velocity is calculated relative to a measured reference velocity at a reference elevation. For best results the reference velocity should be measured at an elevation close to the target elevation. Current flow can be stratified with different layers moving at different speeds and directions. The current velocity can be calculated at a single point or averaged over a range. The logarithmic and power law profiles are only valid in the current boundary layer near the seabed.

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      CALCULATOR MODULE : Morison's Equation Drag Lift And Inertia Coefficient   ±

      Calculate drag coefficient, lift coefficient and inertia coefficient for Morison's equation.

      Drag, lift, and inertia coefficients are affected by proximity to the seabed or another structure. In open water the lateral coefficient tends to zero. The Keulegan Carpenter number is a measure of the ratio of inertial forces and drag forces.

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      CALCULATOR MODULE : Ocean Wave And Current Seabed Stability   ±

      Calculate subsea critical seabed velocity for seabed stability and sediment movement from the critical shields number.

      The Shields parameter is used to calculate the onset of seabed instability due to sediment movement. For subsea waves and currents the critical Shields parameter is approximately 0.04. For laminar flow the critical Shields parameter is approximately 0.03.

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      CALCULATOR MODULE : JONSWAP Wave Directionality And Spreading   ±

      Calculate JONSWAP wave spreading and velocity reduction factor from relative heading and spreading factor.

      Wave spreading accounts for the effect of short crested "choppy" waves with non uniform velocity and heading. By comparison, long ocean swells tend to have uniform velocity and direction, expecially in mid ocean. Use small spreading factors for "choppy" waves, and large spreading factors for ocena swells.

      Reference : Hasselmann K et al : Measurements of Wind-Wave Growth And Swell Decay During The Joint North Sea Wave Project (JONSWAP)

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      CALCULATOR MODULE : DNVGL RP F109 Check Value   ±
      DATA MODULE : Pipeline Surface Roughness ( Open In Popup Workbook )   ±

      Pipeline surface roughness and efficiency data.

      Typical pipe surface roughness values, API 14E Panhandle equation efficiency factors for pipeline pressure drop, and Hazen Williams and Manning coefficients for pipeline pressure loss.

        Related Modules :

        DATA MODULE : Pipe Fitting And Valve ( Open In Popup Workbook )   ±
        DATA MODULE : Fluid Critical Point And Molar Mass ( Open In Popup Workbook )   ±
        DATA MODULE : Fluid Compressibility Factor ( Open In Popup Workbook )   ±

        Fluid ideal gas law Z factor or compressibility factor data.

        The Z factor is commonly used to adjust the ideal gas law to account for the behaviour of real gases. The Z factor can be obtained from tables, or calculated using cubic equations of state (Van Der Waals, Peng Robinson, Soave, Redlich Kwong equations), or from other relationships such as the Virial equation.

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          DATA MODULE : Fluid Thermal Expansion Coefficient ( Open In Popup Workbook )   ±

          Fluid thermal expansion coefficient data.

          Thermal expansion is commonly measured as either volumetric expansion (relative change of volume dV/(V.dT)), or as linear expansion (relative change of length (dL/(L.dT)). The volumetric expansion is approximately three times the linear expansion.

            Related Modules :

            DATA MODULE : Yaws Critical Point And Accentric Factor ( Open In Popup Workbook )   ±
            DATA MODULE : Maths Table And Constant ( Open In Popup Workbook )   ±
            DATA MODULE : Material Density And Specific Gravity ( Open In Popup Workbook )   ±
            DATA MODULE : Material Tensile Strength ( Open In Popup Workbook )   ±
            DATA MODULE : Material Thermal Expansion Coefficient ( Open In Popup Workbook )   ±
            DATA MODULE : Material Heat Transfer And Thermal Capacity ( Open In Popup Workbook )   ±
            DATA MODULE : ASME ANSI API Design Factor ( Open In Popup Workbook )   ±
            DATA MODULE : DNVGL Design Factor ( Open In Popup Workbook )   ±
            DATA MODULE : ASME B31.1 Power Piping Thermal Expansion ( Open In Popup Workbook )   ±

            Thermal expansion coefficient data for ASME B31.1 power piping (Table B SI values).

            Thermal expansion (mm/m) is measured from a base temperature of 68 F or 20 C. Use the ASME B31.1 thermal expansion calculators (see link below) to interpolate thermal expansion data values, calculate thermal expansion coefficient, or calculate thermal expansion from a different base temperature.

            Reference : ANSI/ASME B31.1 : Power Piping

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            Related Modules :

            DATA MODULE : ASME B31.1 Power Piping Design Factor ( Open In Popup Workbook )   ±
            DATA MODULE : ASME B31.3 Process Piping Thermal Expansion ( Open In Popup Workbook )   ±

            Thermal expansion coefficient data for ASME B31.3 process piping (Table C SI values).

            Thermal expansion (mm/m) is measured from a base temperature of 68 F or 20 C. Use the ASME B31.3 thermal expansion calculators (see link below) to interpolate thermal expansion data values, calculate thermal expansion coefficient, or calculate thermal expansion from a different base temperature.

            Reference : ANSI/ASME B31.3 : Process Piping (2018)

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            DATA MODULE : ASME B31.3 Process Piping Weld Quality Factor ( Open In Popup Workbook )   ±
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            DATA MODULE : Soil Properties : Density Uplift Coefficient Shear Strength And Friction Factor ( Open In Popup Workbook )   ±

            Soil properties, soil density, uplift coefficient, shear strength and friction factors.

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