Calculate API 520 mass flow rate through a combined steam pressure relief valve and pressure relief header for isentropic and isothermal valve flow, and adiabatic and isothermal header flow using ideal gas compressible flow equations.
Flow conditions can be calculated for
- Isentropic valve and adiabatic header
- Isentropic valve and isothermal header
- Isothermal valve 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), the header is over sized 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. An over sized header is recommended.
If the header inlet pressure is greater than the critical nozzle pressure, the nozzle flow is sub critical (M < Mc), the header is under sized and the mass flow rate is restricted by the header (or low stagnation pressure relative to ambient). 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.
Header pressure losses are calculated from the pressure loss factor (fld = fL/D + K). The Darcy friction factor fd 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 or an equivalent length, 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). If the ambient pressure is less than the critical header pressure the header exit flow is critical. 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 nozzle orifice diameter and cross section area can be calculated from API letter designation (API 526 type D to T). For API certified valves, the orifice size is an effective size (the actual area is greater than the effective area). 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 area. For API certified nozzles use the Isentropic nozzle options with the compressibility factor Z = 1. For other cases use the API size as an actual size with an appropriate discharge coefficient.
For isothermal flow the inlet temperature should be set equal to the estimated isothermal temperature (eg ambient temperature). The stagnation temperature is constant for isentropic/adiabatic flow, and varies with Mach number for isothermal flow. Phase changes are ignored. Use the multiple valve options if the header is shared by two or more pressure relief valves. Use the valve and header discharge coefficients to compensate for valve friction losses and as a safety factor. The discharge coefficients can be set independently, or set equal (the header coefficient equals the valve coefficient). Use the steam table to calculate a suitable value for the specific heat ratio γ, and the compressibility factor Z. For super heated steam γ = 1.334 can be used as an estimate.
Use the Result Plot option to plot nozzle, header inlet and header exit pressure versus stagnation pressure, nozzle, header inlet and header exit mach number versus stagnation pressure, mass flow rate versus stagnation pressure and flow type, or mass flow rate versus stagnation pressure and discharge coefficient.
Tool Input
- schdtype : Header Schedule Type
- diamtype : Header Diameter Type
- ODu : User Defined Header Outside Diameter
- IDu : User Defined Header Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Header Wall Thickness
- rfactype : Header Internal Roughness Type
- ru : User Defined Surface Roughness
- rru : User Defined Relative Roughness
- 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)
- fL/Du : User Defined Pressure Loss Factor
- numtype : Number Of PRV's Type
- Nu : User Defined Number Of PRVs
- fluidtype : Specific Heat Ratio Type
- γu : User Defined Specific Heat Ratio
- antype : Nozzle Effective Area Type
- Dnu : User Defined Nozzle Diameter
- Anu : User Defined Nozzle Area
- cdtypen : Valve Discharge Coefficient Type
- Cdvu : User Defined Valve Discharge Coefficient
- cdtypeh : Header Discharge Coefficient Type
- Cdhu : User Defined Header Discharge Coefficient
- zfactype : Factor Type
- Zu : User Defined Compressibility Factor
- flowtype : Fluid Flow Type
- Tou : User Defined Isentropic Stagnation Temperature
- Tiu : User Defined Isothermal Temperature
- Po : Stagnation Pressure
- Pa : Ambient Pressure At Exit
- L : Header Length
Tool Output
- γ : Specific Heat Ratio
- ρe : Header Exit Density
- ρi : Header Inlet Density
- ρn : Nozzle Density
- An : Nozzle Effective Area
- Cdh : Header Discharge Coefficient
- Cdv : Valve Discharge Coefficient
- Ce : Header Exit Speed Of Sound
- Ci : Header Inlet Speed Of Sound
- Cn : Nozzle Speed Of Sound
- Dn : Nozzle Effective Diameter
- Fe : Combined Exit Reaction Force (All PRVs)
- Fn : Nozzle Reaction Force
- Ge : Header Exit Mass Flux
- Gi : Header Inlet Mass Flux
- Gn : Nozzle Mass Flux
- ID : Header Inside Diameter
- Le : Header Eqivalent Length
- Mce : Header Critical Exit Mach Number
- Mci : Header Critical Inlet Mach Number
- Mcn : Nozzle Critical Mach Number
- Me : Header Exit Mach Number
- Mi : Header Inlet Mach Number
- Mn : Nozzle Mach Number
- N : Number Of PRV's Sharing The Header
- Pe : Header Exit Pressure
- Pi : Header Inlet Pressure
- Pn : Nozzle Pressure
- Rg : Specific Gas Constant
- SG : Gas Specific Gravity
- Te : Header Exit Temperature
- Ti : Header Inlet Temperature
- Tn : Nozzle Temperature
- Toe : Header Exit Stagnation Temperature
- Ve : Header Exit Velocity
- Vi : Header Inlet Velocity
- Vn : Nozzle Fluid Velocity
- Z : Fluid Compressibility Factor
- cvg : Convergence Factor (≅ 1)
- fL/D : Pressure Loss Factor Including Minor Losses
- fd : Darcy Friction Factor
- mh : Header Mass Flowrate Per PRV
- mmg : Gas Molar Mass
- mn : Nozzle Mass Flowrate
- mt : Total Mass Flowrate N PRV's
- nn : Nozzle Mole Flowrate
- nt : Total Mole Flow Rate N PRV's
- rr : Surface Roughness Ratio