Compressible Flow Fanno Line

Calculate gas pipe flow Darcy friction factor and pressure loss factor from either the Moody diagram or the Von Karman rough pipe equation.

At high Reynolds numbers the Moody diagram friction factor is fully turbulent friction factor and is dependent on the pipe roughness only. The pressure loss factor (fL/D) 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.

Tool Input

• schdtype : Pipe Schedule Type
• diamtype : Pipe Diameter Type
  • ODu : User Defined Outside Diameter
  • IDu : User Defined Inside Diameter
• wtntype : Wall Thickness Type
  • tnu : User Defined Wall Thickness
• rfactype : Pipe Internal Roughness Type
  • ru : User Defined Surface Roughness
  • rru : User Defined Relative Roughness
• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
  • SGu : User Defined Gas Specific Gravity
• zfactype : Factor Type
  • Zu : User Defined Compressibility Factor
• vctype : Speed Of Sound Type
  • Cu : User Defined Sound Velocity
• machtype : Flow Rate Type
  • Vu : User Defined Velocity
  • Mu : User Defined Mach Number
  • mfu : User Defined Mass Flow Rate
  • ngu : User Defined Mole Flow Rate
  • Reu : User Defined Reynolds Number
• visctype : Viscosity Type
  • μu : User Defined Dynamic Viscosity
  • νu : User Defined Kinematic Viscosity
• fdtype : Darcy Friction Factor Type
  • fdu : User Defined Darcy Friction Factor
• leqtype : Minor Pressure Loss Type
  • Ku : User Defined Minor Loss K Factor
  • lu : User Defined Minor Loss Length
  • lodu : User Defined Minor Loss Diameters (L/ID)
  • Leu : User Defined Equivalent Length
  • fL/Du : User Defined Pressure Loss Factor
• P : Fluid Pressure
• T : Fluid Temperature
• L : Pipe Length

Tool Output

• γ : Specific Heat Ratio
• μ : Dynamic Viscosity
• ρ : Fluid Density
• Ax : Nominal Cross Section Area
• C : Speed Of Sound
• ID : Inside Diameter
• Le : Pipe Eqivalent Length
• M : Flow Mach Number
• Qf : Volume Flowrate
• Re : Reynolds Number
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity Relative To Air
• V : Fluid Velocity
• Z : Compressibility Factor
• cvg : Convergence Factor (≅ 1)
• fL/D : Pressure Loss Factor Including Minor Losses
• fd : Darcy Friction Factor
• mf : Mass Flowrate
• mmg : Gas Molar Mass
• ng : Mole Flow Rate
• rr : Surface Roughness Ratio
• vg : Mole Specific Volume

Calculate steam table properties from temperature and pressure (IAPWS R7-97 Steam Table).

Steam table values can be calculated for water and steam, saturated water, saturated steam, saturated water and steam, metastable water, and metastable steam. The calculations for water and steam are valid between 273.15 K and 1073.15 K (0 to 100 MPa), and between 1073.15 K and 2273.15 K (0 to 50 MPa).

The saturated water and steam calculations are valid between 273.15 K and 647.096 K.

The metastable calculation is valid between 273.15 K and 647.096 K, and for pressure from the saturated vapour line to the 5% equilibium moisture line (user defined). Use the Result Plot option to plot the steam properties versus temperature and pressure.

Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the regions 2/3 boundary, and the critical pressure. Select either region 2 or region 3 for calculations in the anomaly zone.

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

Tool Input

• anomtype : Region 2/3 Anomaly Type
• proptype : Steam Phase
  • Pu : User Defined Pressure
  • Tu : User Defined Temperature
  • Xu : User Defined Saturated Steam Quality

Tool Output

• ρ : Density
• Cp : Specific Heat Constant Pressure
• Cp-Cv : Delta Specific Heat (Cp - Cv)
• Cp/Cv : Specific Heat Ratio
• Cv : Specific Heat Constant Volume
• P : Pressure
• T : Temperature
• Vc : Speed Of Sound
• Z : Compressibility Factor
• cvg : Convergence Check
• h : Enthalpy
• s : Entropy
• u : Internal Energy
• vg : Mole Specific Volume
• vm : Specific Volume
• wv : Specific Weight

Calculate steam duct Fanno lines or flow ratios for adiabatic (constant enthalpy) and isothermal (constant temperature) flow.

Fanno lines or flow ratios are calculated for critical flow with friction loss. The inlet Mach number can be calculated from the friction loss factor (fLD), or the friction loss factor can be calculated from the inlet Mach number. Critical flow conditions occur when the exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). For isothermal flow the critical exit Mach number = √γ.

Note : Fanno flow is normally calculated for adiabatic duct flow with friction. The calculator also calculates Fanno lines for isothermal (constant temperature) flow.

Use the Result Plot option to plot critical pressure loss factor versus inlet Mach number and either flow type or specific heat ratio; or Fanno lines for pressure ratio, temperature ratio, density ratio, speed of sound ratio, and velocity ratio, versus either Mach number or pressure loss factor, and versus either flow type or specific heat ratio. The plot range is set from the calculated value of either the inlet Mach number, or the pressure loss factor in the main calculation. Change the main calculation values to change the plot range.

Use the steam table to calculate a suitable value for the specific heat ratio γ. For super heated steam γ = 1.334 can be used as an estimate.

Tool Input

• fluidtype : Specific Heat Ratio Type
  • γu : User Defined Specific Heat Ratio
• fldtype : Pressure Loss Factor Type
  • Mciu : User Defined Inlet Mach Number
  • fL/Du : User Defined Pressure Loss Factor
• flowtype : Fluid Flow Type

Tool Output

• γ : Specific Heat Ratio
• ρi/ρ* : Inlet Density Over Critical Exit Density Ratio
• Ci/C* : Inlet Speed Of Sound Over Critical Exit Speed Of Sound Ratio
• M* : Critical Exit Mach Number
• Mi : Inlet Mach Number
• Pi/P* : Inlet Pressure Over Critical Exit Pressure Ratio
• Ti/T* : Inlet Temperature Over Critical Exit Temperature Ratio
• Vi/V* : Inlet Velocity Over Critical Velocity Ratio
• cvg : Convergence Factor (≅ 1)
• fL/D* : Critical Duct Pressure Loss factor