**Standards Used**

There are very few standards available for use when making fluid flow calculations.

Piping Systems FluidFlow makes use of the latest standards and guides where possible.

For calculating pressure losses across control valves for liquid and gas flow the

software uses the following guide: ANSI/ISA-75,01.01-2002 - Flow Equations for Sizing

Control Valves.

For predicting all physical properties of water we use the IFC-97 formulations

developed by the International Association for the Properties of Water and Steam.

For calculation of liquid or gas flow pressure losses across orifice plates we use the

publication from the International Organisation for Standardisation - ISO 5167-1:2003

Part 1. Measurement of fluid flow by means of pressure differential devices inserted in

circular cross-section conduits running full.

For calculation of liquid or gas pressure losses through nozzles we use ISO 5167-

1:2003 Part 3.

Liquid Pressure Loss Calculations

For calculating liquid friction losses in a physical pipe of any material, we use the Darcy

Weisbach equation and the Haaland formula for calculating friction factor. (Haaland, SE

(1983). "Simple and Explicit Formulas for the Friction Factor in Turbulent Flow". Trans.

ASIVIE, J. of Fluids Engineering 103: 89–90.)

It is possible to configure the software to use the Hazen-Williams method for

predicting friction loss, this may be useful for designing fire protection and irrigation

systems. It is not recommended that users use this method for substances other than

water. Overall fire sprinkler system design guidelines, are provided by the National Fire

Protection Association (NFPA) 13, (NFPA) 13D, and (NFPA) 13R.

Pressure losses through sprinklers can use the K method or the user can enter data

directly from a specific manufacturer.

For the calculation of pressure losses through bends, tee and cross junction the user

can select from one of 4 available relationships:

Using relationships and data found in the Handbook of Hydraulic Resistance - 3rd Ed

- I.E. Idelchik.

Using relationships and data found in Internal Flow Systems - 2nd Ed - D.S. Miller

Using relationships and data found in Flow of Fluids through Valves Fittings and Pipe

- Crane Technical Paper 410

Using relationships and data found in AIR1168/1 - Thermodynamics of Incompressible

and Compressible Fluid Flow

Performance data for centrifugal pumps, positive displacement pumps are usually taken

from manufacturers data. We have developed utility software that can read and

convert data directly from manufacturers catalogues.

Pressure Losses through valves can be calculated from generic relationships found in

the Miller and Idelchik references above. Additionally, the software can use

relationships based on Cv or Kv values which the user can enter.

Pressure losses through check valves use the K method.

**Gas Pressure Loss Calculations**

For accurately calculating pressure losses in gas pipes there is no simple formula, as is

the case for liquids. This is because the specific fluid physical properties of density,

temperature and enthalpy do not remain constant over the pipe length.

The FluidFlow gas calculation routines are rigorous calculations which allow for the

increase in kinetic energy and changing physical properties that occur as gas

accelerates with pressure loss. The calculations allow for the changing non-ideal

behaviour of the gas as it flows by using an equation of state to describe the changes

in gas physical properties.

There are three equations of state (EOS) available within the software (Benedict Webb

Rubin with Hans Starling modifications; Lee Kesler and Peng Robinson), it is possible to

select the most appropriate EOS for each physical property. Using the EOS the gas

thermophysical properties such as enthalpy and density are calculated as the gas

accelerates. An analytical solution to the EOS, energy and momentum equations is not

possible and FluidFlow solves these equations numerically. FluidFlow make no

assumptions of gas ideality or adiabatic flowing conditions.

Our algorithm dynamically splits the pipe into segments based on an incremental

density change. For each segment, upstream conditions of flow, static pressure, static

density and static enthalpy are known and these are used to calculate downstream

static temperature and density. From these values it is possible to backsolve the EOS

to obtain downstream static pressure. The energy equation and momentum equations

can now be solved for each segment. The method is a development of a paper

originally published in The Chemical Engineer - Relief Line Sizing for Gases Part1 and 2.

Dec 1979 - HA Duxbury.

For pressure loss calculations across other fluid equipment items refer to the liquids

section.

**Non-newtonian Fluid Pressure Loss Calculations**

Piping Systems FluidFlow provides the user with the option of selecting one of 4

possible calculation methods for determining pressure loss for Non-Newtonian fluids

flowing within a pipe system.

The available calculation methods are based on the relationships used to describe the

fluid rheology data. It is recommended that the user obtains fluid rheology data prior

to making a Non-Newtonian calculation.

**The available rheology models are:**

- Power Law with the friction factors calculated according to the relationships

provided by Ron Darby - Chemical Engineering Fluid Mechanics

- Bingham Plastic with friction factors calculated according to the relationships

provided in Darby together with the solution of Buckingham Reiner equation

- Hershel-Bulkley with friction factors calculated according to the method of Dodge

and Metzner

- Casson with friction factors calculated according to the method of Wilson Thomas

- For calculation of pressure losses across other fluid equipment items the K factor

method is used. K factors are adjusted at low Reynolds numbers as recommended by Steffe - Non-Newtonian Flows in the Food Industry

**Settling Slurry Pressure Loss Calculations**

Piping Systems FluidFlow provides the user with the option of selecting one of 3

possible calculation methods for determining pressure loss for the flow of settling

slurries through a piping system.

For settling slurries, i.e., a “carrier fluid” conveying

solid particles, the calculation is considerably more complicated than a liquid

calculation, due to the wide range of variables involved, viz particle size and size

distribution, solids density and shape, percent solids, mixture velocity etc.

The accepted approach is to determine the ‘solids effect’, the extra friction loss

caused by the solids content over that for an equivalent flow of the carrier fluid alone.

The carrier fluid may be clean water if the solids are relatively coarse with no fraction

below about 0.4mm but solids smaller than 0.4mm can be held in suspension and

create a ‘homogeneous’ carrier fluid, the friction characteristics of which needs to be

determined.

A number of inter-related factors influence the excess pressure drop in a pipeline over

the pressure loss for water alone (or the carrier fluid if a fine particle fraction exists).

The two main factors are the solids characteristics and the velocity of flow of the

mixture but pipe inclination is also important.

The design method is highly empirical. “Slurry Transport Using Centrifugal Pumps”, by

KC Wilson, GR Addie, A Sellgren and R Clift provides the best reference with a

synthesis of the authors’ many papers together with “Introduction to Practical Fluid

Flow” by R.P. King providing some useful additions.

These two references, and a considerable amount of literature research, provided the

basis for the development of the FluidFlow3 Slurry simulator.

FluidFlow simulates heterogeneous settling slurries according to five correlations:

- Durand-Condolios-Worster

- Wilson-Addie-Sellgren-Clift

- WASP

- 4-Component Model

- Liu Dezhong method

**Two Phase Pressure Loss Calculations**

When two-phase liquid gas flow occurs in pipes, many different flow patterns are

created, depending on fluid properties, the relative rates of each fluid and the pipe

inclination. There are large differences in flow behavior between horizontal, inclined

and vertical pipe flow. The pressure gradient (pressure loss per unit length) is flow

pattern dependant. For a rigorous estimation of two-phase pressure drop we also need

to split the pipe into segmental lengths, similar to the approach used in gas pipe

calculations.

Our pressure loss algorithm dynamically splits the pipe into segments based on an

incremental pressure change.

The user can select from any one of 7 available models:

Whalley Criteria (uses Friedel, Chisholm or Lockhart Martinelli, selection of method is

made by FluidFlow according to the criteria of Whalley)

- Drift Flux Model (2007 correlations)

- Beggs and Brill (Extended Regions)

- Friedel

- Muller Steinhagen Heck

- Chisolm Baroczy

- Lockhart Martinelli

**Physical Property Estimation Methods**

Piping Systems FluidFlow can use any of the following thermophysical properties during

flow calculations. Density, Specific Heat, Thermal Conductivity, Viscosity, Heat of

Vaporisation, Enthalpy, Melting Point, Vapour Pressure and Surface Tension.

The physical properties are often complex functions of pressure, temperature and

phase state. Data needed to evaluate these properties at phase states, pressures and

temperatures in the physical world are stored in a physical property database that

contains over 900 fluids.

The user can select any one of the following estimation methods:

For Liquid Density Prediction:

- A single fixed Value

- Yamada Gunn method with a reference density

- Spencer Danner method

- Yamada Gunn method without a reference density

- Interpolation from a table of values

- Peng Robinson Equation of State

- Benedict Webb Rubin Equation of State

- Lee Kesler law of Corresponding States

For Liquid Specific Heat Capacity Prediction:

- A single fixed Value

- A polynomial approximation

- Bondi estimation method

- Lee Kesler

- Interpolation from a table of values

For Liquid Specific Heat Capacity Prediction:

- A single fixed Value

- A polynomial approximation

- Latini estimation method

- Sato Riedel estimation method

- A log power law approximation method

- Interpolation from a table of values

For Liquid Viscosity Prediction:

- A single fixed Value

- A log polynomial approximation

- A natural log series

- Interpolation from a table of values

- Andrade method

- Przezdziecki estimation method

For Vapour Pressure Prediction:

- A log polynomial approximation

- Interpolation from a table of values

- Wagner estimation

- Antoine estimation

For Gas Density Prediction:

- Peng Robinson Equation of State

- Benedict Webb Rubin Equation of State

- Lee Kesler law of Corresponding States

For Gas Specific Heat Capacity Prediction:

- A polynomial based on ideal gas constants

- Lee Kesler law of Corresponding States

For Gas Thermal Conductivity Prediction:

- A polynomial approximation

- Chung estimation method

- Interpolation from a table of values

For Gas Viscosity Prediction:

- A polynomial approximation

- Chung estimation method

- Interpolation from a table of values

- Lucas corresponding states estimation

For Heat of Vaporisation Prediction:

- A single fixed Value which is adjusted by the software as a function of temperature

- An estimation method based on critical properties

For Liquid Surface Tension Prediction:

- A linear approximation

- An estimation method based on critical properties

Relief Valves and Bursting Disks:

- Relief Valves and Bursting Disks can automatically size according to the International

- Standards of API 520 Part 1 or ISO 4126.

- Sizing for liquid, critical gas and non-critical gas flow are available for both standards.

- Sizing of 2-Phase flow systems only uses API 520 guidelines.

There are two calculation methods available in FluidFlow for predicting the pressure loss through relief valves, API RP 520 & ISO 4126. API RP 520 caters for Newtonian liquids, steam, gas/vapors and two-phase flow. ISO 4126 caters for liquid and gas flow only.