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Compressible Flow Modules

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CALCULATOR MODULE : Compressible Flow   ±

Calculate compressible flow ratios and gas properties for isentropic and isothermal flow (critical over stagnation ratios, flowing over stagnation ratios, and flowing over critical flow ratios).

For isentropic flow, critical flow occurs at M = 1. For isothermal flow, critical flow occurs at M = 1 / √k, where k is the specific heat ratio (Cp/Cv). For isothermal flow the isothermal temperature is assumed equal to the stagnation temperature. Phase changes are ignored.

For flow through a throat, the flow upstream from the throat is sub critical (M ≤ Mc). The flow downstream is super critical (M > Mc). The area ratio is inversely proportional to the mass flux ratio. At stagnation conditions, the area ratio is infinite.

Use the Result Plot option to plot flow ratios versus Mach number, or nozzle area ratio and diameter ratio versus Mach number.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Speed Of Sound   ±

Calculate gas and liquid speed of sound and Mach number.

The Mach number is the ratio of the flow velocity to the speed of sound. It applies to either a moving fluid or to a moving object passing through stationary fluid. For a Mach number greater than one, the flow is supersonic. For a Mach number less than one, the flow is subsonic.

For an ideal gas, the speed of sound or sonic velocity can be calculated from the gas temperature, gas specific heat ratio and the gas specific gravity. For liquids the speed of sound can be calculated from the liquid bulk modulus and the liquid density.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow Critical Flow   ±
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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CALCULATOR MODULE : Compressible Flow Normal Shock Wave   ±
CALCULATOR MODULE : Compressible Flow Gas Property   ±

Calculate compressible flow gas properties.

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

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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CALCULATOR MODULE : Compressible Flow 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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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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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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CALCULATOR MODULE : Compressible Flow Fanno Line   ±

Calculate Fanno flow ratios from pressure loss factor for critical adiabatic and isothermal flow.

Fanno ratios are calculated for critical exit flow. For example the Fanno pressure ratio (P/P*) equals the ratio of inlet pressure (P) over the critical exit pressure (P*). Critical flow occurs when the exit Mach number = 1 for adiabatic flow, or the exit Mach number = √γ for isothermal flow where γ is the specific heat ratio. The inlet Mach number at critical flow is dependent on the duct pressure loss factor (fL/D). Fanno ratios are normally calculated for adiabatic flow. This calculator includes the option to calculate Fanno ratios for isothermal flow. For isothermal flow the temperature ratio = 1.

The pressure loss factor is calculated from the Darcy friction factor and the minor loss factors

`fld = (f L) / D + K `

where :

fld = pressure loss factor
f = Darcy friction factor
L = pipe length
D = pipe internal diameter
K = sum of minor loss factors

Minor losses can also be accounted for using an equivalent length. For critical flow (high velocity and high Reynolds numbers) the flow is assumed to be fully turbulent. The Von Karmen rough pipe equation is used to calculate the Darcy friction factor (fd). The Von Karmen Equation is independent of Reynolds number and fluid viscosity.

Use the Result Plot option to plot the Fanno flow ratio 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 (adiabatic or isothermal) or specific heat ratio.

Reference : Fluid Mechanics, Frank M White, McGraw Hill

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