The K factor can be used with any consistent set of units.
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| CALC : Flow : Flowrate 001 : Flow Rate For Converging or Contracting Circular Nozzles : Calculator
Description : Calculate the volume flow rate Q from friction pressure loss values ΔPf for converging or contracting circular nozzles.
Discussion : If D1 is smaller than D2 the tool will return invalid values.
Figures :
References :
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- θ = Converging Nozzle Cone Angle
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
- Q = Fluid Volume Flowrate
Calculation :
Β = D2 / D1
Α = Β 2
If Θ <= 45
K2 = 0.8 ( 1 - Α )sin( Θ π / 360 )
Otherwise If Θ <= 180
K2 = 0.5 ( 1 - Α ) √( sin( Θ π / 360 ) )
Otherwise
K2 = 0.5 ( 1 - Α )
End of If Block
K1 = K2 / Α 2
Q = π D2 2 √( ΔPf / ( 8 K2 ρ ) )
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| CALC : Flow : Flowrate 002 : Fluid Flow Rate For Diverging or Expanding Circular Nozzle : Calculator
Description : Calculate the volume flow rate Q from friction pressure loss values ΔPf for diverging or expanding circular nozzles.
Discussion : If D1 is smaller than D2 the tool will return invalid values.
Figures :
References :
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- θ = Diverging Nozzle Cone Angle
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
- Q = Fluid Volume Flowrate
Calculation :
Β = D1 / D2
Α = Β 2
If Θ <= 45
K1 = 2.6 ( 1 - Α ) 2 sin( Θ π / 360 )
Otherwise
K1 = ( 1 - Α ) 2
End of If Block
K2 = K1 / Α 2
Q = π D1 2 √( ΔPf / ( 8 K1 ρ ) )
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| CALC : Flow : Flowrate 003 : Flow Rate From K Friction Factor and Pressure Loss : Calculator
Description : Calculate the volume flow rate Q from the friction pressure loss ΔPf and the friction factor K.
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- ρ = Fluid Density
- D = Section Internal Diameter
- K = Dimensionless Friction Pressure Loss Factor K
Output Variables :
- Q = Fluid Volume Flowrate
Calculation :
Q = π D 2 √( ΔPf / ( 8 K ρ ) )
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| CALC : Flow : Flowrate 004 : Flow Rate Total For Sections of Same Diameter : Calculator
Description : Calculate the volume flow rate Q from the friction pressure loss ΔPf and a list of K values.
Discussion : The list of K values should all relate to the same section ID or the results will be invalid.
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- ρ = Fluid Density
- D = Section Internal Diameter
- K = K Friction Factor List
Output Variables :
- Kt = Dimensionless Friction Pressure Loss Factor K
- Q = Fluid Volume Flowrate
Calculation :
Kt = ArraySum( K )
Q = π D 2 √( ΔPf / ( 8 Kt ρ ) )
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| CALC : Flow : Flowrate 005 : Flow Rate Total For Sections of Different Diameter : Calculator
Description : Calculate the volume flow rate Q from the friction pressure loss ΔPf and a list of K values with different internal diameter.
Discussion : The K factors are converted to equivalent K factors relative to section diameter Do. Changing the section diameter Do does not affect the friction pressure loss ΔPf.
Figures :
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- ρ = Fluid Density
- D = Section Internal Diameter List
- Do = Section Internal Diameter
- K = K Friction Factor List
Output Variables :
- Ke = K Equivalent Friction Factor List
- Kt = Dimensionless Friction Pressure Loss Factor K
- Q = Fluid Volume Flowrate
Calculation :
Loop i
Ke[i] = K[i] ( Do / D[i] ) 4
End of i Loop
Kt = ArraySum( Ke )
Q = π Do 2 √( ΔPf / ( 8 Kt ρ ) )
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| CALC : Flow : Friction 00 : K Friction Factor From Discharge Coefficient Cd : Calculator
Description : Calculate K factor values from the discharge coefficient Cd.
Discussion : The discharge coefficient Cd accounts for the friction losses through an entrant nozzle or orifice. A frictionless nozzle would have a discharge coefficient of 1.
Figures :
Input Variables :
- Cd = Dimensionless Discharge Coefficient Cd
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
Output Variables :
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Calculation :
K2 = ( 1 / Cd 2 - 1 )( 1 - ( D2 / D1 ) 4 )
K1 = K2 ( D1 / D2 ) 4
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| CALC : Flow : Friction 001 : K Friction Factor For Converging or Contracting Circular Nozzle : Calculator
Description : Calculate K factor values for converging or contracting circular nozzles.
Discussion : Calculated values are approximate only. Always use manufacturers data if available. If D1 is smaller than D2 the tool will return invalid values.
Generally it is convenient to use K values relative to the ID of the piping system. The K values of the various pipeline components can then be simply added together to determine the total system K value.
Figures :
References :
Input Variables :
- θ = Converging Nozzle Cone Angle
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Calculation :
Β = D2 / D1
Α = Β 2
If Θ <= 45
K2 = 0.8 ( 1 - Α )sin( Θ π / 360 )
Otherwise If Θ <= 180
K2 = 0.5 ( 1 - Α ) √( sin( Θ π / 360 ) )
Otherwise
K2 = 0.5 ( 1 - Α )
End of If Block
K1 = K2 / Α 2
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| CALC : Flow : Friction 002 : K Friction Factor For Diverging or Expanding Circular Nozzle : Calculator
Description : Calculate K factor values for diverging or expanding circular nozzles. If D1 is larger than D2 the tool will return invalid values. Calculated values are approximate only. Always use manufacturers data if available.
Figures :
References :
Input Variables :
- θ = Diverging Nozzle Cone Angle
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Calculation :
Β = D1 / D2
Α = Β 2
If Θ <= 45
K1 = 2.6 ( 1 - Α ) 2 sin( Θ π / 360 )
Otherwise
K1 = ( 1 - Α ) 2
End of If Block
K2 = K1 / Α 2
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| CALC : Flow : Friction 003 : K Friction Factor From Pressure Loss and Flow Rate : Calculator
Description : Calculate K factor values from the volume flow rate Q and the friction pressure loss ΔPf.
Discussion : For pipe fittings valves flanges etc it is usual to calculate K in terms of the pipeline section internal diameter. K can also be calculated for the internal diameter of the fitting.
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- ρ = Fluid Density
- D = Section Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- K = Dimensionless Friction Pressure Loss Factor K
Calculation :
K = ΔPf π 2 D 4 / ( 8 ρ Q 2 )
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| CALC : Flow : Friction 004 : K Friction Factor Equivalent For An Arbitrary Section ID : Calculator
Description : Calculate equivalent K factor values for different circular sections.
Discussion : To calculate the equivalent friction factor k for section 2 relative to the ID of section 1: For pipe systems with different diameter sections it is convenient to calculate the equivalent friction loss factors relative to a nominal diameter. The friction loss factor for the pipe system can then be calculated simply by summing all of the individual loss factors. In the figure D1 is larger than D2. This tool is also valid where D1 is smaller than D2.
Figures :
Input Variables :
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- K2e = Equivalent Dimensionless Friction Pressure Loss Factor K
Calculation :
Β = D2 / D1
Α = Β 2
K2e = K2 / Α 2
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| CALC : Flow : Friction 005 : K Friction Factor Total For Sections of Same Diameter : Calculator
Description : Calculate the total K factor value and pressure loss from a list of K values with the same internal diameter.
Discussion : The total pressure loss is calculated from the sum of the K factors.
Input Variables :
- K = K Friction Factor List
Output Variables :
- Kt = Dimensionless Friction Pressure Loss Factor K
Calculation :
Kt = ArraySum( K )
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| CALC : Flow : Friction 006 : K Friction Factor Equivalent Total - Different Diameters : Calculator
Description : Calculate the total equivalent K factor values from a list of K values with different internal diameter.
Discussion : The tool converts the K values to equivalent K values, then sums the equivalent K values. The equivalent K factors are relative to section diameter Do. Enter an ID for every K factor value in the same order, otherwise the result will be invalid.
Input Variables :
- D = Section Internal Diameter List
- Do = Section Internal Diameter
- Kt = K Friction Factor List
Output Variables :
- K = Dimensionless Friction Pressure Loss Factor K
- Ke = K Equivalent Friction Factor List
Calculation :
Loop i
Ke[i] = Kt[i] ( Do / D[i] ) 4
End of i Loop
K = ArraySum( Ke )
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| CALC : Flow : Friction 007 : K Friction Factor From Volume Flow Coefficient Factor Av or Cv : Calculator
Description : Calculate equivalent K factor values from the volume flow coefficient Av or Cv, Kv etc..
Discussion : Manufacturers often quote flow coefficient values for valves and other pipeline fittings. The flow coefficient Av is the volume flow rate in m³ / s of a fluid of density 1 kg / m³ which results in a pressure drop of 1 Pa through the fitting. The volume flow coefficient can also be expressed as Cv (US, UK and Metric) or Kv.
Input Variables :
- Av = Volume Flow Coefficient Av or Cv
- ID = Section Internal Diameter
Output Variables :
- K = Dimensionless Friction Pressure Loss Factor K
Calculation :
K = π 2 ID 4 / ( 8 Av 2 )
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| CALC : Flow : Friction 009 : K Friction Factor Total From Flow Coefficient Factor Av or Cv : Calculator
Description : Calculate the total K factor from a list of Av or Cv coefficient values.
Discussion : The tool converts the Av values to equivalent K values, then sums the equivalent K values. The equivalent K factors are relative to section diameter Do.
Input Variables :
- Av = K Friction Factor List
- Do = Section Internal Diameter
Output Variables :
- K = Dimensionless Friction Pressure Loss Factor K
- Ke = K Equivalent Friction Factor List
Calculation :
Loop i
Ke[i] = ( π 2 Do 4 ) / ( 8 Av[i] 2 )
End of i Loop
K = ArraySum( Ke )
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| CALC : Flow : Friction 011 : Friction Pressure Loss For Converging or Contracting Circular Nozzle : Calculator
Description : Calculate friction pressure loss values ΔPf for converging or contracting circular nozzles.
Discussion : If D1 is smaller than D2 the tool will return invalid values. The friction pressure loss ΔPf is generally different from the measured static pressure difference ΔP because of the velocity effect. The fluid is flowing faster in the smaller ID section and hence the velocity head is higher.
Figures :
References :
Input Variables :
- θ = Converging Nozzle Cone Angle
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- ΔP = Fluid Static Pressure Difference
- ΔPf = Fluid Friction Pressure Loss
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Calculation :
Β = D2 / D1
Α = Β 2
If Θ <= 45
K2 = 0.8 ( 1 - Α )sin( Θ π / 360 )
Otherwise If Θ <= 180
K2 = 0.5 ( 1 - Α ) √( sin( Θ π / 360 ) )
Otherwise
K2 = 0.5 ( 1 - Α )
End of If Block
K1 = K2 / Α 2
ΔPf = 8 K2 ρ Q 2 / ( π 2 D2 4 )
ΔP = ΔPf - 8 ρ Q 2 / π 2 ( D2 4 - D1 4 ) / ( D2 4 D1 4 )
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| CALC : Flow : Friction 012 : Friction Pressure Loss For Diverging or Expanding Circular Nozzle : Calculator
Description : Calculate friction pressure loss values ΔPf for diverging or expanding circular nozzles.
Discussion : If D1 is larger than D2 the tool will return invalid values. The friction pressure loss ΔPf is generally different from the measured static pressure difference ΔP because of the velocity effect. The fluid is flowing faster in the smaller ID section and hence the velocity head is higher.
Figures :
References :
Input Variables :
- θ = Diverging Nozzle Cone Angle
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- Α = Internal Cross Section Area Ratio
- Β = Internal Diameter Ratio
- ΔP = Fluid Static Pressure Difference
- ΔPf = Fluid Friction Pressure Loss
- K1 = Section 1 Dimensionless Friction Pressure Loss Factor K
- K2 = Section 2 Dimensionless Friction Pressure Loss Factor K
Calculation :
Β = D1 / D2
Α = Β 2
If Θ <= 45
K1 = 2.6 ( 1 - Α ) 2 sin( Θ π / 360 )
Otherwise
K1 = ( 1 - Α ) 2
End of If Block
K2 = K1 / Α 2
ΔPf = 8 K1 ρ Q 2 / ( π 2 D1 4 )
ΔP = ΔPf - 8 ρ Q 2 / π 2 ( D2 4 - D1 4 ) / ( D2 4 D1 4 )
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| CALC : Flow : Friction 013 : Friction Pressure Loss From K Friction Factor and Flow Rate : Calculator
Description : Calculate the friction pressure loss ΔPf from the friction factor K and the volume flow rate Q.
Input Variables :
- ρ = Fluid Density
- D = Section Internal Diameter
- K = Dimensionless Friction Pressure Loss Factor K
- Q = Fluid Volume Flowrate
Output Variables :
- ΔPf = Fluid Friction Pressure Loss
Calculation :
ΔPf = 8 K ρ Q 2 / ( π 2 D 4 )
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| CALC : Flow : Friction 014 : Friction Pressure Loss Total For Sections of Same Diameter : Calculator
Description : Calculate the friction pressure loss ΔPf from the flow rate and a list of K values.
Discussion : The K list values should all correspond to the same internal diameter or an error will result.
Input Variables :
- ρ = Fluid Density
- D = Section Internal Diameter
- K = K Friction Factor List
- Q = Fluid Volume Flowrate
Output Variables :
- ΔPf = Fluid Friction Pressure Loss
- Kt = Dimensionless Friction Pressure Loss Factor K
Calculation :
Kt = ArraySum( K )
ΔPf = 8 Kt ρ Q 2 / ( π 2 D 4 )
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| CALC : Flow : Friction 015 : Friction Pressure Loss Total For Sections of Different Diameter : Calculator
Description : Calculate the friction pressure loss ΔPf from a list of K values with different internal diameter.
Discussion : The K factors are converted to equivalent K factors relative to section diameter Do. Changing the section diameter Do does not affect the friction pressure loss ΔPf.
Figures :
Input Variables :
- ρ = Fluid Density
- D = Section Internal Diameter List
- Do = Section Internal Diameter
- K = K Friction Factor List
- Q = Fluid Volume Flowrate
Output Variables :
- ΔPf = Fluid Friction Pressure Loss
- Ke = K Equivalent Friction Factor List
- Kt = Dimensionless Friction Pressure Loss Factor K
Calculation :
Loop i
Ke[i] = K[i] ( Do / D[i] ) 4
End of i Loop
Kt = ArraySum( Ke )
ΔPf = 8 Kt ρ Q 2 / ( π 2 Do 4 )
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| CALC : Flow : Friction 018 : Pressure Loss From Total Flow Coefficient Factor Av or Cv and Flow Rate : Calculator
Description : Calculate the friction pressure loss ΔPf from a list of Av coefficient values. :new:The tool converts the Av coefficients to equivalent K factor values relative to section diameter Do, then sums the equivalent K values. Changing the section diameter Do does not affect the friction pressure loss ΔPf.
Input Variables :
- ρ = Fluid Density
- Av = K Friction Factor List
- Do = Section Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- ΔPf = Fluid Friction Pressure Loss
- K = Dimensionless Friction Pressure Loss Factor K
- Ke = K Equivalent Friction Factor List
Calculation :
Loop i
Ke[i] = ( π 2 Do 4 ) / ( 8 Av[i] 2 )
End of i Loop
K = ArraySum( Ke )
ΔPf = 8 K ρ Q 2 / ( π 2 Do 4 )
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| CALC : Flow : Friction 041 : Friction Pressure Loss From Static Pressure Difference : Calculator
Description : Calculate the friction pressure loss ΔPf from the static pressure difference ΔP between sections with varying diameter.
Discussion : The static pressure difference ΔP is the measured pressure difference. It is different from the friction pressure loss ΔPf because of the different velocity pressure in the sections. Changes in diameter between the two measurement points (D1 and D2) do not affect the result.
Figures :
Input Variables :
- ΔP = Fluid Static Pressure Difference
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- ΔPf = Fluid Friction Pressure Loss
Calculation :
ΔPf = ΔP + 8 ρ Q 2 / π 2 ( D2 4 - D1 4 ) / ( D2 4 D1 4 )
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| CALC : Flow : Friction 042 : Static Pressure Difference From Friction Pressure Loss : Calculator
Description : Calculate the static pressure difference ΔP from the friction pressure loss ΔPf between sections with varying diameter.
Discussion : The friction pressure loss is the pressure lost by fluid friction. It is different to the static pressure difference ΔP, the measured pressure difference, because of the different velocity pressure in the sections. Changes in diameter between the two measurement points (D1 and D2) do not affect the result.
Figures :
Input Variables :
- ΔPf = Fluid Friction Pressure Loss
- ρ = Fluid Density
- D1 = Section 1 Internal Diameter
- D2 = Section 2 Internal Diameter
- Q = Fluid Volume Flowrate
Output Variables :
- ΔP = Fluid Static Pressure Difference
Calculation :
ΔP = ΔPf - 8 ρ Q 2 / π 2 ( D2 4 - D1 4 ) / ( D2 4 D1 4 )
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