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Fluid Pressure Modules

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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 : 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 : Bernoulli's Equation   ±

Calculate gas and liquid pressure using the Bernoulli equation.

The Bernoulli equation describes the conservation of energy in a static or moving fluid. For a frictionless fluid flow where no work is done by or to the system and the temperature is constant, energy is conserved. The Bernoulli equation can be expressed as conservation of energy, conservation of pressure or conservation of fluid head. The total pressure is referred to as the Bernoulli pressure (Pb) or the Energy Grade Line (EGL).

`Pb = Ps + Pd + Pz `
`Pg = Ps + Pd `
`Ph = Ps + Pz `

where :

Pb = Bernoulli pressure or total pressure or energy grade line (EGL) (= constant for frictionless flow)
Ps = static pressure
Pz = potential or pressure
Pd = dynamic pressure
Pg = stagnation pressure
Ph = hydraulic or piezometric pressure or hydraulic grade line (HGL)

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CALCULATOR MODULE : Bernoulli's Equation Hydraulic Grade Line   ±

Calculate gas and liquid pipeline hydraulic pressure or hydraulic grade line (HGL) from data points using the Bernoulli equation.

The hydraulic or piezometric pressure is calculated by

`Ph = Ps + Pz `

where :

Ps = static pressure
Pz = potential or pressure
Ph = hydraulic or piezometric pressure (HGL)

For constant diameter pipelines, the friction pressure loss can be calculated from the difference in hydraulic pressure (changes in dynamic pressure are ignored). For gas pipelines, the changes in dynamic pressure are usually small compared to the other terms.

Note : The pressure terms are calculated at the selected data point. The data point option is set to pipe inlet when the page loads. Click calculate to update the data point options to include all of the data points before you select the data point. Click calculate each time you change the position data (X) values, and before you select the data point. Data points can be entered as comma separated values (Xi, Zi, Pi) with each set on a new line, or copy and paste from a spreadsheet.

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CALCULATOR MODULE : Bernoulli's Equation Energy Grade Line   ±

Calculate gas pipeline Bernoulli pressure or energy grade line (EGL) from data points using the Bernoulli equation.

The Bernoulli or total pressure (EGL) is calculated by

`Pb = Ps + Pd + Pz `
`Ph = Ps + Pz `

where :

Pb = Bernoulli pressure or total pressure (EGL)
Ps = static pressure
Pz = potential pressure
Pd = dynamic pressure
Ph = hydraulic or piezometric pressure (HGL)

For constant diameter pipelines, the friction pressure loss can be calculated from the difference in Bernoulli pressure. For gas pipelines, the changes in dynamic pressure are usually small compared to the other terms so that the hydraulic pressure (HGL) can also be used to calculate pressure loss.

Note : The pressure terms are calculated at the selected data point. The data point option is set to pipe inlet when the page loads. Click calculate to update the data point options to include all of the data points before you select the data point. Click calculate each time you change the position data (X) values, and before you select the data point. Data points can be entered as comma separated values (Xi, Zi, Pi) with each set on a new line, or copy and paste from a spreadsheet.

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CALCULATOR MODULE : Bernoulli's Equation Stationary Pressure From Elevation   ±

Calculate static pressure from elevation for gases and liquids using the Bernoulli equation.

For stationary fluid, the hydraulic or piezometric pressure is constant. The static pressure at any point can be calculated from a known pressure and relative elevation. For liquids, the fluid density is assumed to be constant. For gases, the fluid density varies with pressure.

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CALCULATOR MODULE : Bernoulli's Equation Prandtl Tube   ±

Calculate fluid velocity from the pressure difference across a Pitot-Static or Prandtl tube using the Bernoulli equation.

Prandtl tubes or Pitot-Static tubes are used to measure the fluid static pressure, and the fluid stagnation pressure (the sum of the static pressure and the dynamic pressure). The fluid velocity can be calculated from the dynamic pressure. The dynamic pressure is equal to the stagnation pressure minus the static pressure.

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CALCULATOR MODULE : Bernoulli's Equation Pitot Tube   ±

Calculate fluid velocity from the Pitot tube pressure measurement using the Bernoulli equation.

Pitot tubes are used to measure the fluid stagnation pressure (the sum of the static pressure and the dynamic pressure). The fluid velocity can be calculated from the Pitot tube pressure for cases where the static pressure is negligible. For example in shallow water where the stagnation pressure is measured by gauge pressure.

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CALCULATOR MODULE : Bernoulli's Equation Flow Meter   ±

Calculate fluid flowrate from flowmeter pressure measurements using the Bernoulli equation.

The flowrate through a flow meter can be calculated from the difference in static pressure using the Bernoulli equation. The discharge coefficient accounts for friction losses through the flow meter. Bernoulli flow meters are normally installed horizontal so that changes in elevation can be ignored.

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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 Pipeline Pressure Loss From The Moody Diagram   ±

Calculate pressure loss for single phase liquid pipelines and ducts 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..

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CALCULATOR MODULE : Liquid Pipeline Pressure Loss From The AGA Equation   ±

Calculate pressure loss for single phase liquid pipelines using the AGA equation.

`Tr = 4 log(3.7 / (rr)) `
`Ts = 4 log((Re) / (Ts)) - 0.6 `
`Tt = 4 Df log((Re) / (1.4125 Ts)) `
`Tf = min(Tr, Tt) `
`fd = (2 / (Tf))^2 `

where :

Tr = rough pipe transmission factor
Ts = smooth pipe transmission factor
Tt = turbulent pipe transmission factor
Tf= Fanning transmission factor
fd = Darcy friction factor
rr = pipe relative roughness
Re = Reynolds number
Df = AGA drag factor

The AGA equation is used to calculate the Fanning transmission factor using an iteration method. Check that the convergence is close to or equal to one. The pressure loss is calculated from the Darcy friction factor using the Darcy-Weisbach 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 the AGA equation. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated.

Pipe bends can be specified as either a bend angle, AGA bend index (degrees of bend per mile), or AGA drag factor. The drag factor is interpolated from the AGA table. The drag factor includes pipe roughness. Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : Water Pipeline Pressure Loss From The Hazen Williams Equation   ±

Calculate pressure loss for single phase liquid pipelines using the Hazen Williams equation. For SI units

`Q = 0.85 c.A.rh^0.63 s^0.54 `
`rh = ID/4 `

where :

Q = flow rate
A = cross section area
ID = inside diameter
rh = hydraulic radius
s = channel slope
c = Hazen Williams friction factor

The Hazen Williams equation was developed for water pipes. Pipe roughness is accounted for using the Hazen Williams friction factor. The hydraulic radius is the ratio of pipe cross section area over pipe circumference (r/2 = ID/4). Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : Water Open Channel Or Culvert Flow Rate From The Manning Equation   ±

Calculate flowrate in circular or rectangular water channels using the Manning equation.

`Q = A (rh^2)/3 s^(1/2) / n `
`rh = A/P `

where :

Q = flow rate
A = cross section area
P = wetted perimeter
rh = hydraulic radius
s = channel slope
n = Manning friction factor

The channel is assumed to be either open, or partly full and at ambient pressure. The head loss equals the change in elevation. Channel roughness is accounted for using the Manning friction factor. The hydraulic radius is the ratio of channel cross section area over the wetted perimeter. Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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

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

`Po = √(P^2 - m^2(fd.L / D + K) ls (16mma.SG.ZRoT)/(pi^2D^4) ) / (es) `
`ss = (z2 - z2) SG.mma.g / (Ro T Z) `
`es = e^(ss) `
`ls = (es^2 - 1) / (ss) `

where :

Po = outlet pressure
P = inlet pressure
fd = Darcy friction factor
L = piping length
D = piping inside diameter
K = total friction loss factor for fittings
m = gas mole flowrategas
mma = air molar mass
SG = gas specific gravity
Z = gas compressibility factor
Ro = universal gas constant
T = gas temperature
g = gravity constant
zi = inlet elevation
zo = outlet elevation
ss = elevation exponent
es = elevation pressure factor
ls = elevation length factor

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 with the Darcy friction factor. 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.

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 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 Pipeline Pressure Loss From The AGA Equation   ±

Calculate pressure loss for single phase gas pipelines using the AGA equation.

`Tr = 4 log(3.7 / (rr)) `
`Ts = 4 log((Re) / (Ts)) - 0.6 `
`Tt = 4 Df log((Re) / (1.4125 Ts)) `
`Tf = min(Tr, Tt) `
`fd = (2 / (Tf))^2 `

where :

Tr = rough pipe transmission factor
Ts = smooth pipe transmission factor
Tt = turbulent pipe transmission factor
Tf= Fanning transmission factor
fd = Darcy friction factor
rr = pipe relative roughness
Re = Reynolds number
Df = AGA drag factor

The AGA equation is used to calculate the Fanning transmission factor using an iteration method. Check that the convergence is close to or equal to one. The pressure loss is calculated from the Darcy friction factor using the Darcy-Weisbach 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 the AGA equation. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated.

Pipe bends can be specified as either a bend angle, AGA bend index (degrees of bend per mile), or AGA drag factor. The drag factor is interpolated from the AGA table. The drag factor includes pipe roughness. Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : Gas Pipeline Pressure Loss From The Weymouth And Panhandle Equation   ±

Calculate pressure loss for single phase gas pipelines using either the Weymouth equation, the Panhandle A equation, the Panhandle B equation, or the general equation (user defined Darcy friction factor).

`Q = 77.57 ((Tb) / (Pb)) ((P^2 - ess. Po^2) / (SG .T. L. ls Z. fd))^0.5 D^2.5 `General ` `
`Q = 433.5 ((Tb) / (Pb)) E ((P^2 - ess. Po^2) / (SG .T. L. ls. Z))^0.5 D^2.667 `Weymouth` `
`Q = 437.87 ((Tb) / (Pb))^1.0788 E ((P^2 - ess. Po^2) / (SG^0.8539. T .L. ls. Z))^0.5394 D^2.6182 `Panhandle A` `
`Q = 738.73 ((Tb) / (Pb))^1.02 E ((P^2 - ess. Po^2) / (SG^0.961. T. L. ls. Z))^0.51 D^2.53 `Panhandle B` `
`ss = (z2 - z2) SG. mma. g / (Ro T Z) `
`es = exp(ss) `
`ls = (es^2 - 1) / (ss) `

where :

Q = mole flowrate (SCFD)
Po = outlet pressure (psia)
P = inlet pressure (psia)
Tb = base temperature (60 F)
Pb = base pressure (1 atm)
fd = Darcy friction factor
E = efficiency factor
L = piping length (mi)
D = piping inside diameter (in)
K = total friction loss factor for fittings
g = gravity constant
zi = inlet elevation
zo = outlet elevation
ss = elevation exponent
es = elevation pressure factor
ls = elevation length factor

Pipe roughness can be accounted for using the efficiency factor. Minor losses such as bends, valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length. The calculations are not suitable for laminar flow.

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CALCULATOR MODULE : Gas Pipeline Line Pack   ±
CALCULATOR MODULE : Low Pressure Air Pressure Loss From The Moody Diagram   ±

Calculate pressure loss for low pressure air circular and rectangular ducts using the Moody diagram.

The calculators use the Darcy-Weisbach pressure loss 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.

Minor losses can be entered as either a K friction factor, a length, or length over diameter ratio. The minor losses are used to account for pipeline fittings such as bends, tees, valves etc.. :sg:For air the gas specific gravity SG = 1.0. For low pressure air the compressibility factor is assumed equal to one.

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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 : Gas Pipeline Local Pressure   ±
CALCULATOR MODULE : API RP 14E General Gas Piping Pressure Loss Equation   ±

Calculate API RP 14E gas piping pressure loss from the general equation.

The pressure loss is calculated using the Darcy-Weisbach form of the Moody diagram. For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Hagen-Poiseuille laminar flow option should be used. In the transition region 2000 < Re < 4000, the flow is unstable and cannot be reliably calculated. For turbulent flow (Re > 4000), either the original Colebrook White equation or the modified Colebrook White equation can be used. Minor losses are used to account for pipeline fittings such as bends, tees, valves etc.

Reference : API 14E Recommended Practice For Design and Installation of Offshore Production Platform Piping Systems

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CALCULATOR MODULE : API RP 14E Weymouth Gas Piping Pressure Loss Equation   ±

Calculate API RP 14E gas piping pressure loss from the Weymouth equation.

The Weymouth equation was developed for fully developed turbulent flow in long pipelines. It is not suitable for low Reynolds number, or short piping sections. Minor losses are used to account for pipeline fittings such as bends, tees, valves etc. Compare the results for the Weymouth equation, the general equation (Moody diagram), and the Panhandle A and B equations.

Reference : API 14E Recommended Practice For Design and Installation of Offshore Production Platform Piping Systems

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CALCULATOR MODULE : API RP 14E Panhandle Gas Piping Pressure Loss Equation   ±

Calculate API RP 14E gas piping pressure loss from the Panhandle equation.

The Panhandle equations were developed for fully developed turbulent flow in long pipelines. They are not suitable for low Reynolds number, or short piping sections. Minor losses are used to account for pipeline fittings such as bends, tees, valves etc. Compare the results for the Weymouth equation, the general equation (Moody diagram), and the Panhandle A and B equations.

Reference : API 14E Recommended Practice For Design and Installation of Offshore Production Platform Piping Systems

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CALCULATOR MODULE : API RP 14E Liquid Piping Pressure Loss Equation   ±

Calculate API RP 14E liquid piping pressure loss from the Moody diagram.

The pressure loss is calculated using the Darcy-Weisbach form of the Moody diagram. For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Hagen-Poiseuille laminar flow option should be used. In the transition region 2000 < Re < 4000, the flow is unstable and cannot be reliably calculated. For turbulent flow (Re > 4000), either the original Colebrook White equation or the modified Colebrook White equation can be used. Minor losses are used to account for pipeline fittings such as bends, tees, valves etc.

Reference : API 14E Recommended Practice For Design and Installation of Offshore Production Platform Piping Systems

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CALCULATOR MODULE : Pipeline Flow Rate   ±
CALCULATOR MODULE : Compressible Flow Area And Internal Diameter   ±

Calculate compressible flow cross section area and diameter.

Pipe inside diameter and internal cross section area are calculated from the pipe diameter and wall thickness. Use the Result Table option to display a table of the inside diameter and cross section area versus either outside diameter or wall thickness.

Effective nozzle orifice diameter and cross section area for pressure relief valves is calculated from API letter designation (API 526 type D to T). The combination of valve and nozzle must be tested with the operating fluid, and certified as having a flow rate greater than or equal to the calculated flow rate for the effective size. Use the Result Table option to display the effective diameter and cross section area versus API letter designation.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Pressure Relief Valve   ±

Calculate compressible flow pressure relief valve capacity for isentropic, isothermal, and adiabatic conditions.

For pressure relief valves with no header, the mass flow rate can be calculated for isentropic or isothermal flow. The pressure relief valve is assumed to exit directly to ambient pressure. If the ambient pressure is less than the critical pressure the flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If the ambient pressure is greater than the critical nozzle pressure, the flow is sub critical (M < Mc). For isothermal flow the stagnation temperature should be close to or equal to the ambient temperature (for example a gas transmission pipeline). Phase changes are ignored.

For a combined pressure relief valve and pressure relief header, the mass flow rate can be calculated for

  • Isentropic nozzle and adiabatic header
  • Isentropic nozzle and isothermal header
  • Isothermal nozzle and isothermal header

The pressure relief valve is assumed to exit directly into the header. If the header inlet pressure is less than or equal to the nozzle critical pressure the nozzle flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow), and the mass flow rate is restricted by the nozzle. The header inlet pressure is calculated so that the header mass flow rate equals the nozzle mass flow rate. If the header inlet pressure is greater than the critical nozzle pressure, the nozzle flow is sub critical (M < Mc), and the mass flow rate is restricted by the header. The mass flow rate is calculated so that the header inlet pressure is equal to the nozzle pressure. The mass flow rate through the nozzle is always equal to the mass flow rate through the header.

For a pressure relief header, the mass flow rate can be calculated for adiabatic or isothermal flow. If the header is attached directly to the outlet of a pressure relief valve (PRV), the header inlet pressure should be set equal to the PRV nozzle outlet pressure. The header should be sized so that the calculated header mass flowrate is greater than or equal to the PRV mass flowrate. For headers with more than one PRV, the header mass flowrate is divided by the number of PRV's. If the header is oversized, the header inlet pressure will reduce so that the actual header mass flowrate is equal to the nozzle mass flowrate (there is a pressure drop between the PRV outlet and the header inlet).

Note : If the PRV is attached to a small diameter header which feeds into a larger diameter header (possibly with multiple PRVs), the large diameter header should be sized first. The inlet pressure for the large diameter header is used as the ambient pressure for the smaller diameter header (and PRV).

Header pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The Darcy friction factor f is calculated for fully turbulent flow using the rough pipe equation. The header is assumed to be constant diameter. Minor losses can be included by the minor loss K factor, and should include valves and bends etc. The header entry and exit losses should not be included (the fluid dynamic pressure loss is included in the calculation). The discharge coefficient can also be used for minor losses, and as a safety factor. If the ambient pressure is less than the critical header pressure the header exit flow is critical (Mc = 1 for isentropic flow and Mc = √(1/γ) for isothermal flow). If the ambient pressure is greater than the critical header pressure, the header exit flow is sub critical (M < Mc). The header entry flow is assumed to be sub critical for all flow conditions.

The effective PRV valve nozzle orifice diameter and cross section area can be calculated from API letter designation (API 526 type D to T). API effective orifice sizing is used to compensate for the friction pressure losses in the relief valve. The combination of valve and nozzle orifice must be tested with the operating fluid at the design conditions, and certified as having a flow rate greater than or equal to the calculated flow rate for the equivalent size. The API 526 orifice sizing assumes isentropic flow. For certified API 526 valves, the isentropic nozzle calculation option should be used.

Note : The pressure relief header calculation is not suitable for pressure relief vents. Headers are assumed to be part of a PRV system. Vents are constant diameter piping attached to a pipeline or pressure vessel.

Use the Result Plot option to plot pressure, mach number and mass flow rate.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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Related Modules :

CALCULATOR MODULE : Compressible Flow Pitot Tube   ±
CALCULATOR MODULE : Compressible Flow Blowdown Time   ±

Calculate compressible flow pipeline or vessel blow down time through a constant diameter vent for adiabatic and isothermal flow using either the integration method, or the simplified method.

The integration method uses numerical integration to calculate the elapsed time between the initial pressure, and the final blow down pressure. At high pressure the vent exit flow is critical (Mc = 1 for adiabatic flow and 1/√γ for isothermal flow). At lower pressures the vent exit flow is sub critical (M < Mc). The vent entry is subsonic at all conditions. Increase the number of steps to improve the accuracy. Use the minimum number of steps required (the method is reasonably accurate with 16 steps). Using a large number of steps may slow down the calculation, especially on older computers. The accuracy of the integration method decreases at pressure less than 1.1 x ambient pressure (ie 110 kPa or 16.2 psi for atmospheric pressure discharge). The blow down time tends to infinity as the final pressure approaches ambient pressure.

The simplified method calculates the blow down time from the initial pipeline gas moles, and the initial vent mole flow rate. The flow is assumed to be always critical, and the pipeline pressure is assumed to decrease exponentially. The simplified method is reasonably accurate for final pressure ≥ 2 x ambient pressure. At low pressures flow is sub critical and the simplified method underestimates the elapsed time relative to the integration method (both methods are less accurate at very low pressure). The simplified method is not recommended for final pressure less than 1.2 x ambient pressure. The blow down time tends to infinity as the final pressure approaches absolute zero.

Minor losses should include the vent entry valves and bends etc. The vent exit should not be included as the fluid dynamic pressure is included in the calculation. Minor losses can be accounted for by using the minor loss factor K, or the discharge coefficient Cd. The discharge coefficient is used to factor the mole flow rate. The gas in the pipeline is assumed to be stationary (stagnation conditions), ie the pipeline diameter >> the vent diameter. Phase changes are ignored. The Darcy friction factor is calculated from pipe roughness assuming fully turbulent flow.

Note : The final blow down pressure should be above ambient pressure (final blow down pressure ≤ ambient pressure causes a divide by zero error).

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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Related Modules :

CALCULATOR MODULE : Compressible Flow Pressure Relief Vent   ±

Calculate compressible flow pressure relief vent flow rate and pressure drop for either adiabatic or isothermal flow.

The vent is modelled as a frictionless entry, combined with a frictional constant diameter duct. For adiabatic flow the vent entry is assumed to be isentropic. For isothermal flow, the vent entry is assumed to be isothermal. The vent entry is assumed to be subsonic at all conditions. The pipeline is assumed to be at stagnation conditions (M = 0). At high pressure the vent exit flow is critical flow (Mc = 1 for adiabatic low and `Mc = 1 / (√γ)` for isothermal flow : γ = the gas specific heat ratio). At lower pressures the vent exit flow is sub critical (M < Mc).

Vent flow rate is calculated from the vent pressure loss factor (fld).

`fld = fd L/D + K `

where :

fld = vent pressure loss factor
fd = Darcy friction factor
L = vent length
D = vent inside diameter
K = minor loss K factor

The Darcy friction factor is calculated assuming fully turbulent flow. Minor losses should include the vent entry, and valves, bends etc.. The vent exit should not be included (the fluid dynamic pressure is included in the calculation). The discharge coefficient can be used as a safety factor.

Note : The vent calculation is not suitable for pressure relief headers which are part of a pressure relief valve (PRV) system.

Use the Result Plot option to plot inlet and exit pressure versus stagnation pressure, inlet and exit mach number versus stagnation pressure, or mass flow rate versus stagnation pressure and flow type.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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Related Modules :

CALCULATOR MODULE : Compressible Flow Pressure Loss Factor   ±
CALCULATOR MODULE : Compressible Flow Nozzle Flow Rate   ±

Calculate compressible flow mass flow rate and mole flow rate through a nozzle for isentropic and isothermal flow.

At high pressure the nozzle flow is critical (the critical exit pressure is ≥ the ambient pressure). The critical Mach number Mc = 1 for adiabatic low and Mc = 1 / √γ for isothermal flow (γ = the gas specific heat ratio). At lower pressures the nozzle flow is sub critical (M < Mc) (the critical exit pressure is < the ambient pressure). For isothermal flow the stagnation temperature should be close to or equal to the ambient temperature (eg gas transmission pipeline). The discharge coefficient can be used to account for friction losses, and as a design factor.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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Related Modules :

CALCULATOR MODULE : DNVGL RP F115 Pipeline Pre Commissioning   ±
CALCULATOR MODULE : DNVGL RP F115 Pipeline Test Pressure   ±

Calculate DNVGL RP-F115 pipeline test pressure from design pressure and elevation.

The system test pressure is calculated from the local incidental pressure. The required system test pressure and mill test pressure should be calculated for all points on the pipeline or pipeline section. Use the Result Plot option to plot the test pressure and hoop stress from minimum to maximum elevation.

Reference : DNVGL-RP-F115 Pre-commissioning of Submarine Pipelines (Download from the DNVGL website)

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Related Modules :

CALCULATOR MODULE : DNVGL RP F115 Pipeline Pressure Response   ±
CALCULATOR MODULE : DNVGL RP F115 Pipeline Temperature Correction   ±
CALCULATOR MODULE : DNVGL RP F115 Pipeline Tidal Correction   ±
CALCULATOR MODULE : DNVGL RP F115 Pipeline Local Pressure   ±

Calculate DNVGL RP-F115 pipeline local stationary internal and external pressure from elevation.

The external pressure is calculated from the water depth. The internal fluid density is assumed constant. Elevation is measured relative to any arbitrary datum (+ve above the datum -ve below the datum). Use the Result Plot option to plot pressure versus elevation.

Reference : DNVGL-RP-F115 Pre-commissioning of Submarine Pipelines (Download from the DNVGL website)

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Related Modules :

CALCULATOR MODULE : API 520 Pressure Relief Device   ±
CALCULATOR MODULE : API 520 Gas Pressure Relief Valve   ±

Calculate API 520 gas pressure relief valve (PRV) and rupture disk size.

The flow through the relief valve nozzle is assumed to be sonic (M = 1), adiabatic, and isentropic. If the back pressure is greater than the critical (sonic) pressure the flow is subsonic (M < 1).

Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.975. The actual nozzle diameter and the rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

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

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CALCULATOR MODULE : API 520 Steam Pressure Relief Valve   ±

Calculate API 520 steam pressure relief valve (PRV) and rupture disk size.

The flow through the relief valve nozzle is analysed using the Napier equation. For temperatures above 1200 F (922 K), the gas PRV calculation should be used. If the back pressure is greater than the critical (sonic) pressure the flow is sub sonic (M < 1).

Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.975. The actual nozzle diameter and rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

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

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CALCULATOR MODULE : API 520 Liquid Pressure Relief Valve   ±

Calculate API 520 liquid pressure relief valve (PRV) and rupture disk size (certified and non certifed devices).

The flow through the relief valve nozzle is analysed using the Bernoulli equation. Friction losses are accounted for using the discharge coefficient Kd. For initial sizing of PRV's the effective nozzle diameter should be used with the discharge coefficient Kd = 0.65 for certified PRV's and Kd = 0.62 for non certified PRV's. The actual nozzle diameter and rated coefficient of discharge should be used to verify that the selected PRV is suitable for the required flow rate. The PRV effective diameter is taken from API 526 (letter designation D to T). Changes in phase are not accounted for.

The PRV calculation can also be used for rupture disks. The rupture disk diameter should be substituted for the nozzle diameter, with a discharge coefficient Kd = 0.62. Rupture disks can also be analysed as part of a relief vent system using the flow resistance method.

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

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Related Modules :

CALCULATOR MODULE : API 520 Correction Factor   ±
CALCULATOR MODULE : API 520 Critical Flow Ratio   ±
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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Related Modules :

CALCULATOR MODULE : API 520 Pressure Relief Vent   ±

Calculate API 520 flow rate through a constant diameter pressure relief vent.

The vent entry is assumed to be a pressure vessel or piping at stagnation pressure (valid when the pipe or vessel diameter is much greater than the vent diameter). The calculated vent exit pressure is flowing pressure (stagnation pressure minus dynamic pressure).

Vent pressure losses are calculated from the vent pressure loss factor (fld = fL/D + K). Minor losses should include the vent entry, valves and bends etc. The vent exit should not be included. The discharge coefficient can be used to factor the flow rate, depending on the design requirements.

For rupture disks, the flow resistance factor of the rupture Kr should be included in the minor losses (the resistance factor should be factored for the vent diameter). A discharge coefficient of 0.9 or less should be used for rupture disks. Alternatively, the PRV calculators can be used for rupture disk calculations.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

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

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Related Modules :

CALCULATOR MODULE : API 520 Back Pressure   ±

Calculate API 520 back pressure from mass flow rate through a constant diameter vent.

The calculated vent entry and exit pressures are flowing pressure (stagnation pressure minus dynamic pressure). Minor losses should include bends and valves etc. The vent entry and exit should not be included in the minor losses. The discharge coefficient can be used to factor the mass flow rate, depending on design requirements.

Where multiple pressure relieving devices share a common vent, the back pressure should be calculated for the total mass flow rate.

For relief vents with sections of increasing diameter, the back pressure should be calculated for each constant diameter section, going backwards from exit. The (flowing) exit pressure for each section equals the (flowing) inlet pressure for the previous section.

For pressure relief valves or rupture disks, the (flowing) inlet pressure for the vent is used as the (flowing) back pressure for the pressure relief device. This is valid provided that the vent diameter is greater than the diamter of the PRV nozzle or rupture disk.

Note : The ideal gas calculators use the ideal gas compressible flow equations. The API 520 gas and steam calculations use an approximation of the ideal gas compressible flow equations. Use the ideal gas calculators for a comparison with the API 520 calculators.

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

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CALCULATOR MODULE : Water Hammer Transient Pressure   ±

Calculate water hammer transient pressure and pressure wave velocity.

Water hammer is caused by a sudden reduction of flow rate in liquid pipelines. Water hammer commonly occurs in water pipes, but it can occur in any liquid piping system. The transient pressure is reduced if gas is present in the liquid, or if the effective shut off time is greater than the maximum shut off time. The maximum shut off time is the time taken for the pressure transient to travel to the pipe inlet, and back again.

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CALCULATOR MODULE : Transient Pressure Wave Velocity   ±

Calculate water hammer transient pressure wave velocity.

A sudden reduction of velocity in a liquid pipeline initiates a pressure wave which travels to the pipe inlet, and then back. The wave velocity increases with pipe stiffness. Any gas present in the liquid reduces the pressure wave velocity. The maximum shut off time is the time taken for the pressure transient to travel to the pipe inlet, and back again.

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CALCULATOR MODULE : Pump Delta Pressure Versus Flowrate Curve   ±

Calculate pump curve (pressure versus flowrate) for viscous and non viscous flow. Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt.

The pump curve is calculated using a three term quadratic curve (ΔP = ΔPo - A Q - B Q^2) calculated from the shut-in delta pressure (zero flow), the maximum flowrate, and the best efficiency point (BEP).

Note : The delta stagnation pressure is required for the calculation. Some pump curves show delta static pressure (the pressure equals zero at maximum flow) instead of delta stagnation pressure (the pressure equals the dynamic pressure at maximum flow). Use the pump pressure and head conversion calculator to convert delta static pressure to delta stagnation pressure.

The pump flowrate, delta pressure, inside diameter and efficiency can be scaled for a geometrically similar pump using the affinity or similarity laws. For geometric similarity the pump inside diameter should be proportional to the impeller diameter. In practice the pump inside diameter is usually limited to pipe sizes (eg 10 inch, 12 inch etc). The impeller diameter is also normally limited to fixed sizes. It is often more practical to select an available pump inside diameter and impeller diameter, and vary the pump speed. Pump efficiency scaling is based on an empirical formula. Pump efficiency scaling should be combined with flowrate scaling. Pump efficiency varies with flowrate. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3).

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

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CALCULATOR MODULE : Pump Cavitation And NPSH   ±

Calculate pump cavitation number (Ca), nett positive suction pressure (NPSP), and suction specific speed (Nss).

`Nss = n* Q*^1/2 (ρ/NPSP*)^3/4 `
`NPSP* = Ps + 1/2 ρ V^2 - Pv = Ps + Pd - Pv = Pg - Pv `
`Ca = (Ps - Pv) / Pd `

where :

Nss = pump suction specific speed at BEP `
`NPSP* = nett positive suction pressure at BEP `
`Ca = cavitation number `
`n* = pump rotational speed at BEP `
`Q* = flowrate at BEP `
`Ps = static pressure at inlet `
`Pg = stagnation pressure at inlet `
`Pd = dynamic pressure at inlet `
`Pv = vapour pressure `
`V = fluid velocity at inlet `
`ρ = fluid density

The pump suction specific speed and nett positive suction pressure are calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency. The pump suction specific speed, nett positive suction pressure and cavitation number can be used to determine the onset of cavitation. The minimum recommended values are dependent on the pump geometry and operating conditions, and should be obtained from the manufacturer.

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

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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 : Pump Liquid Vapour Pressure Viscosity And Density   ±
CALCULATOR MODULE : Single Phase Gas Density   ±
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 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.

    Related Modules :

    CALCULATOR MODULE : Fluid Vapour Pressure   ±
    CALCULATOR MODULE : IAPWS R7-97 Steam Table   ±

    Calculate IAPWS R7-97 steam tables from temperature and pressure.

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

    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 Vapour Pressure   ±

    Calculate IAPWS R7-97 saturated vapour pressure and temperature.

    The saturation point can be calculated from either the saturation temperature, or the saturation pressure.

    Steam properties can be calculated for saturated liquid, saturated vapour, and mixed saturated liquid and vapour from quality factor. The enthalpy and internal energy are calculated from the mass. Use the Result Plot option to plot the steam pressure and steam properties versus temperature.

    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 Fresh Water Density At Atmospheric Pressure   ±

    Calculate IAPWS R7-97 fresh water density from temperature at atmospheric pressure.

    The calculation is valid between the melting point (273.15 K), and the boiling point (373.15 K).

    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 : TEOS-10 Seawater Density   ±

    Calculate TEOS-10 seawater density from temperature, pressure and practical salinity.

    The hydrostatic pressure used in TEOS-10 can be calculated from water depth or relative elevation. The water density is assumed constant. Changes in water density with water depth, salinity and temperature are ignored. Elevation is measured relative to an arbitrary datum (+ve up -ve down). Mean sea level (MSL) is often used as a datum.

    Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

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    CALCULATOR MODULE : TEOS-10 Seawater Conductivity   ±

    Calculate TEOS-10 seawater conductivity from pressure, temperature and practical salinity.

    Practical salinity is measured by comparing the sea water conductivity with a reference conductivity.

    To convert pressure: 1 MPa = 100 dbar (deci bars) or 1 dbar = 1e4 Pa. To convert conductivity 1 S/m = 10 mS/cm.

    Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

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    CALCULATOR MODULE : TEOS-10 Seawater Salinity   ±

    Calculate TEOS-10 seawater practical salinity from pressure, temperature and conductivity.

    Practical salinity is measured by comparing the sea water conductivity with a reference conductivity.

    To convert pressure: 1 MPa = 100 dbar (deci bars) or 1 dbar = 1e4 Pa. To convert conductivity 1 S/m = 10 mS/cm.

    Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

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    CALCULATOR MODULE : TEOS-10 Seawater Dynamic And Kinematic Viscosity   ±

    Calculate TEOS-10 seawater dynamic and kinematic viscosity from temperature, pressure, and practical salinity.

    Seawater viscosity is calculated from fresh water viscosity using the equation from Sharqawy (2010). The fresh water viscosity is calculated from temperature and density using the IAPWS R12-08 industrial equations. Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity (absolute salinity equals reference salinity). The absolute salinity anomaly δSA is ignored.

    Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

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    CALCULATOR MODULE : TEOS-10 Seawater Vapour Pressure   ±

    Calculate TEOS-10 seawater vapour pressure from temperature, and practical salinity.

    Seawater vapour pressure is calculated from fresh water vapour pressure using the equation from Sharqawy (2010). The fresh water vapour pressure is calculated from temperature using the IAPWS R7-97 steam equations. Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity (absolute salinity equals reference salinity). The absolute salinity anomaly δSA is ignored.

    Reference : TEOS-10 Thermodynamic Equation Of Seawater (2010)

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    CALCULATOR MODULE : IAPWS R12-08 Fresh Water Dynamic And Kinematic Viscosity   ±

    Calculate the dynamic viscosity and kinematic viscosity of water and steam using the IAPWS R12-08 industrial equation (u2 = 1).

    The viscosity can be either calculated directly from temperature and density, or from temperature and pressure using IAPWS R7-97 to calculate the density.

    Note : There is an anomaly in the calculated density and viscosity close to the critical point. Refer to the help pages for more details (click the utility button on the data bar).

    References :

    IAPWS R12-08 Industrial Formulation 2008 for the Viscosity of Ordinary Water Substance
    IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

      Related Modules :

      CALCULATOR MODULE : Spherical Tank Or Pressure Vessel Volume   ±

      Calculate the fluid volume and mass for a full or part full spherical tanks and pressure vessels.

      Fluid volume and mass can be calculated for liquid tanks (the gas volume is ignored), gas tanks (full tank only), and mixed gas and liquid tanks. For part full tanks the fluid level is measured from the inside base of the tank.

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      CALCULATOR MODULE : Cylindrical Tank Or Pressure Vessel Volume   ±

      Calculate the fluid volume and mass for a full or part full cylindrical tanks and pressure vessels.

      Fluid volume and mass can be calculated for liquid tanks (the gas volume is ignored), gas tanks (full tank only), and mixed gas and liquid tanks. For part full tanks the fluid level is measured from the inside base of the tank. Cylindrical tanks can be either horizontla or certical. Tank ends can be either flat, or spherical. Pressure vessels normally have spherical ends.

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      CALCULATOR MODULE : Rectangular Tank Or Pressure Vessel Volume   ±

      Calculate the fluid volume and mass for a full or part full rectangular tanks and vessels.

      Fluid volume and mass can be calculated for liquid tanks only (the gas volume is ignored). For part full tanks the fluid level is measured from the inside base of the tank. Rectangular tanks are assumed to be unpressurised.

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      CALCULATOR MODULE : Tank Or Pressure Vessel Piping Volume   ±

      Calculate the fluid volume and mass for tank and vessel piping.

      Fluid volume and mass can be calculated for liquid piping, gas piping, two phase gas and liquid piping, or three phase gas, water and oil (black oil). The piping is assumed to be full and mixed (ie flowing).

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      CALCULATOR MODULE : Tank Or Pressure Vessel Diameter And Circumference   ±

      Calculate the circumference and inside diameter for circular tanks and vessels.

      Measuring the external circumference of a tank or vessel is a common method to calculate the tank outside diameter. The tank inside diameter can be calculated by subtracting 2 x the tank wall thickness from the tank outside diameter.

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      Related Modules :

      DATA MODULE : Fluid Density And Specific Gravity ( Open In Popup Workbook )   ±
      DATA MODULE : Fluid Dynamic And Kinematic Viscosity ( Open In Popup Workbook )   ±
      DATA MODULE : Fluid Vapour Pressure ( Open In Popup Workbook )   ±
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