Important Note: 


We would always recommend using the Compressible Flow Calculation Engine to solve compressible gas systems (rather than using the non-compressible calculation engine with the Darcy-Weisbach equation). 


The following notes in this section are included for completeness only.


The Darcy-Weisbach equation is normally applicable to incompressible Newtonian fluids, since the density of these fluids can be considered to be constant even with changes in pressure, however this equation is also sometimes used for compressible systems provided that they operate within certain criteria. 


When the Non-Compressible Calculation Engine is selected on the Calculations tab in Configuration Options then Pipe Flow Expert uses the Colebrook-White equation to calculate friction factors and the Darcy-Weisbach equation to calculate the friction loss in a pipe.


These equations assume a constant fluid density & viscosity and they provide a very accurate solution when working with non-compressible fluids (liquids) and they are sometime used for low velocity gas systems where there is a relatively small amount of pressure loss.


If the user select the Non-Compressible Calculation Engine when using the software to model gas systems then there are certain criteria that the model must operate within to ensure the solution is of acceptable accuracy.


Changes in pressure and temperature will affect the gas density and viscosity. These property changes affect the actual pressure drop and are not automatically accounted for in the Darcy-Weisbach equation, therefore some limitations must be applied to ensure that the calculated results are within an acceptable accuracy.


Generally systems which involve gases fall into two categories: 


Low pressure loss gas systems:


Where the pressure loss is less than 10% of the highest absolute pressure in the system, if the pressure drop is calculated using the entering fluid density then good reliability of the results can be expected.


High pressure loss gas systems:


Where the pressure loss is more than 10% but less than 40% of the highest absolute pressure in the system, if the pressure drop is calculated using the average fluid density then good reliability of the results can be expected.  


Where a system has a total pressure loss which exceeds 40% of the highest absolute pressure in the system, then if you are using the Non-Compressible Flow Calculation Engine (which is not recommended for gas systems) it will be necessary to model the system using a number of different fluid zones with the fluid density data defined for different pressure conditions). Up to 20 fluid zones can be used in a Pipe Flow Expert model.


Note: We include the above information for completeness, however we would recommend using the Compressible Flow Calculation Engine to solve gas system, which will automatically account for density changes with pressure losses (even for losses higher than 40% of the highest absolute pressure) and these systems can then be modeled with a single fluid zone (provided that there are no significant temperature changes).


Using Fluid Zones with gas systems:


Where a gas system has been split into a number of separate fluid zones, the fluid density and the fluid viscosity for each fluid zone should be set independently.


The density of each fluid zone in the gas system must reflect the average density of the compressed fluid condition in that fluid zone, in order for the Darcy-Weisbach equation to give a reasonably accurate result.


When a gas system is solved with the Non-Compressible Calculation Engine (and the Darcy-Weisbach equation), if the fluid density is not within 5% of the average fluid density for a particular zone, a warning will be issued in the results log. Suggestions to Update Fluid Zone Data to have a particular density based on the average pressure within the fluid zone will be issued in the results log.


General Suggestions:


For systems that contain compressible fluids the following should be noted.


The mass flow rates entering the system and the mass flow rates leaving the system must be balanced. Normally In-Flow or Out-Flow values are entered using units of mass flow or units of gas flow at standard volume (volume at standard temperature and pressure). Users should avoid specifying gas flow rates in regular volumetric units such as m³/hour since these refer to actual volume of gas at whatever density has been defined in the fluid data (i.e. the density at some pressure condition). Volume in standard units such as SCMH (Standard Cubic Meters per Hour) should be used instead. 


Where volumetric In-Flow rates entering the system are to be used, these values should generally be specified in gas flow standard volume units, such as SCFM, or in mass flow units, such as lb/min. If the flow rates are entered in regular volume, such as ft³/min, then this defines the actual flow rate of the fluid at the density specified in the fluid data for the current fluid zone (and not the uncompressed volumetric flow rate of the gas at standard conditions). 


Where volumetric Out-Flow rates leaving the system are to be used then these values should generally be specified in gas flow standard volume units, such as SCFM, or in mass flow units, such as lb/min (the same as for In-Flow values as described above). 


With the Non-Compressible Flow Calculation Engine, Pipe Flow Expert uses a constant value for the fluid density throughout each individual fluid zone in the pipeline system. Where regular volumetric flow rates are used to specify the In-Flows and Out-Flows to the system, the individual density for each fluid zone is used to convert from volumetric flow rate units to the mass flow rate units used internally by Pipe Flow Expert. 


As described above, we would recommend not specifying flow rates in volume units related to the density of the fluid zone, but rather use mass flow unit or gas flow standard volume units (volume at standard conditions).


The calculations are performed using mass flow rates to achieve mass flow rate continuity at each node and an overall pressure balance within the pipeline system. 


When using the Non-Compressible Flow Calculation Engine, the effects of pressure changes on the fluid density are not modeled.


Note 1:


The Fluid density at the compressed fluid condition can be calculated using the normal density of the compressible fluid and the fluid pressure.


Compressed fluid density = 

Normal fluid density x (Fluid pressure + Atmospheric pressure) /Atmospheric pressure


Example: If a volume of 10 m³ of air at normal temperature and pressure is compressed to 6 bar g 


The Fluid density would be:         1.2047 x (6.000 + 1.01325) / 1.01325 = 8.3384 kg/m³



Note 2:


The Actual volumetric flow rate of the fluid at the compressed fluid condition can be calculated using the uncompressed volume of the fluid at standard condition and the compressed fluid pressure.


Actual flow rate = 

Uncompressed fluid volume x (Atmospheric pressure / (Fluid pressure + Atmospheric pressure))



Example: If a flow of 10 m³/s of air at normal temperature and pressure is compressed to 6 bar g 


The Actual flow rate would be:         10 x (1.01325 / (6.000 +1.01325)) = 1.445 m³/s