Equations and Variables

Introduction

In the topic Process Design an overview is given about how an equation for a Unit Operation can be modeled and how data can be linked to variables in that equation.

In this topic this overview is completely detailed.

Equation

We saw that the head of a pump in metric units can be expressed in metric units as:

h = 1000*(p2 - p1)/(? g) + v22/(2*g) where: h = total head developed (m) p2 = pressure at outlet (1000*N/m2 = kPa) p1 = pressure at inlet (1000*N/m2 = kPa) ? = density (kg/m3) g = acceleration due to gravity (9.81) m/s2 v2 = velocity at the outlet (m/s)

Modeling an equation

First of all it should be mentioned that the transfer functions and their equations are hidden in the software and are, for the sake of lifecycle information integration, not important.

Variables, like the inlet pressure, are represented by means of ISO 15926 templates that have the value in their "signature".

If an equation is modeled, it can be represented in MathML, which makes it suitable for handling in an XML environment.

The relationship between the equation and its variables and constants is shown in the template below:

Functional mapping of the equation for centrifugal pump head

Example

Assume:

UO137 - an instance of ClassOfActivity called UO_Centrifugal_Pump;
P137 - an instance of ClassOfInanimatePhysicalObject performing UO137;
STRM137in - an instance of ClassOfStream being the inlet to P137;
STRM137out - an instance of ClassOfStream being the outlet from P137.

and the following process data, as shown in above template:

p1 = 211.8 kPa - inlet pressure = pressure of STRM137in;
p2 = 584.3 kPa - outlet pressure = pressure of STRM137out;
ρ = 1237 kg/m^>3> - density of STRM137in;
v2 = 5.3 m/s - fluid velocity of STRM137out.
g = 9.81 m/s^>2> - accelleration due to gravity.

Code for the ClassOfFunctionalMapping

New reference data must be defined:

@prefix : <http://www.rdl.xyz-corp.com/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix dc: <http://purl.org/dc/elements/1.1/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dm: <http://data.15926.org/dm/> .
@prefix lci: <http://data.15926.org/lci/> .
@prefix meta: <http://data.15926.org/meta/> .
@prefix tpl: <http://data.15926.org/tpl/> .
@prefix rdl: <http://data.15926.org/rdl/> .

#    //////////////////////////////////////////////////////////////////////////////////////////////////
#    //
#    // THIS ONTOLOGY REPRESENTS ADDITIONAL CONCEPTS FOR THE LOCAL RDL EXTENSION OF THE XYZ CORPORATION
#    //
#    //////////////////////////////////////////////////////////////////////////////////////////////////

# Definition of Unit Operation
:666c950e-296e-424d-a5b9-459d8e3d874c rdf:type dm:ClassOfActivity ;
     rdfs:subclassOf rdl:RDS2223591 ; # UO_CENTRIFUGAL_PUMP
     rdfs:label "our_UO_CENTRIFUGAL_PUMP"@en ;
     skos:definition "PUMPING with a CENTRIFUGAL PUMP as defined for the XYZ Corp." ; # because not yet defined in the RDL
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:3d32caaa-39a7-444c-bda1-0636a969e2d6 rdf:type tpl:ClassifiedDefinitionOfClassOfIndividualWithInformationRepresentation ;
     tpl:hasDefined :666c950e-296e-424d-a5b9-459d8e3d874c ; # our_UO_CENTRIFUGAL_PUMP
     tpl:hasDefinition :0f264d91-f5af-456d-b867-9a8361ec59a6 ; # UO_CENTRIFUGAL_PUMP TRANSFER FUNCTION
     tpl:hasDefinitionType rdl:RDS2225201 ; # DEFINITION WITH A MATHEMATICAL EQUATION
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Equation is a part of Transfer Function (TFs for other equipment may have upto 50 equations)
:88bd9e3a-5aae-4825-a0fd-91c12ca49120 rdf:type tpl:ClassOfCompositionDefinition ;
     tpl:hasClassOfWhole :0f264d91-f5af-456d-b867-9a8361ec59a6 ;
     tpl:hasClassOfPart :d21f81ed-b0d8-4b78-9666-3d1832d9e76f ;
     tpl:hasCardinalityOfWhole rdl:RDS222625 ;
     tpl:hasCardinalityOfPart rdl:RDS222625 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:0f264d91-f5af-456d-b867-9a8361ec59a6 rdf:type dm:ClassOfInformationRepresentation ;
     rdfs:subclassOf lci:InformationObject ;
     rdfs:label "UO_CENTRIFUGAL_PUMP TRANSFER FUNCTION"@en ;
     skos:definition "A <UO_CENTRIFUGAL_PUMP TRANSFER FUNCTION> is an <InformationObject> that represents the transfer function of <UO_CENTRIFUGAL_PUMP>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:d21f81ed-b0d8-4b78-9666-3d1832d9e76f rdf:type dm:ClassOfInformationRepresentation ;
     rdfs:label "UO_CENTRIFUGAL_PUMP EQUATION FOR HEAD CALCULATION"@en ;
     skos:definition "<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac><mrow><mn>1000</mn><mo>⁢</mo><mrow><mo>(</mo><mrow><mi>p2</mi><mo>-</mo><mi>p1</mi></mrow><mo></mo></mrow></mrow>           <mrow><mi>g</mi><mo>⁢</mo><mi>p</mi></mrow></mfrac><mo>+</mo><mfrac><msup><mi>v2</mi><mn>2</mn></msup><mrow><mn>2</mn><mo>⁢</mo><mi>g</mi></mrow></mfrac></mrow></math>" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration of ClassOfFunctionalMapping
:3e9eaf76-a5ad-41f4-9110-df328322f8d5 rdf:type dm:ClassOfFunctionalMapping;
     dm:codomain :c972f70f-5ade-4a42-afa7-2298e6fc8819 ; # the RoleAndDomain defining "h AND head in m"
     dm:domain :899b0d9a-14ff-4727-a732-ac3fbeab1818 ; # the ClassOfMultidimensionalObject defining the variables and constants
     dc:description "pump head equation h = 1000*(p2 - p1)/(?*g) + v2^2/(2*g)"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of transfer function represented by ClassOfFunctionalMapping
:39ee18c1-3ff1-443d-818a-263a43997c6b rdf:type tpl:ClassifiedDefinitionOfClassOfIndividualWithInformationRepresentation ;
     tpl:hasDefined :3e9eaf76-a5ad-41f4-9110-df328322f8d5 ;
     tpl:hasDefinition :d21f81ed-b0d8-4b78-9666-3d1832d9e76f ;
     tpl:hasDefinitionType rdl:RDS2225201 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of ClassOfMultidimensionalobject that is input for ClassOfFunctionalMapping
:899b0d9a-14ff-4727-a732-ac3fbeab1818 rdf:type dm:ClassOfMultidimensionalObject;
     :role1 :35fa0afd-29f1-4ad2-9af1-ff7de44931e0 ; # p1 AND NORMAL INLET PRESSURE IN KILOPASCAL
     :role2 :3ba114fb-19f4-4c68-9dae-33c561da2ea9 ; # p2 AND NORMAL OUTLET PRESSURE IN KILOPASCAL
     :role3 :e28b9a51-81c8-43e7-b223-49161b5a956e ; # ? AND DENSITY IN KILOGRAM PER METRE CUBED
     :role4 :10be33a2-04dd-4ae6-b44a-2201ddce1824 ; # v2 AND AVERAGE VELOCITY IN METRE PER SECOND
     :role5 :dcac8f2d-4d8c-4e92-b7a3-fdfe030a6f9c ; # g AND ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED
     rdfs:label "VARIABLES FOR PUMP EQUATION"@en ;
     skos:definition "<VARIABLES FOR PUMP HEAD EQUATION> is a <MultidimensionalObject> that defines the variables for h = (p2 - p1)/(?*g) + v2^2/(2*g)"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of 5 instances of RoleAndDomain combined in ClassOfMultidimensionalobject
# DEFINITION OF VARIABLE p1(kPa) AS PROXY FOR NORMAL INLET PRESSURE IN KILOPASCAL
:35fa0afd-29f1-4ad2-9af1-ff7de44931e0 rdf:type dm:RoleAndDomain;
     rdfs:label "p1 AND NORMAL INLET PRESSURE IN KILOPASCAL" ;
     skos:definition "A <p1 AND NORMAL INLET PRESSURE IN KILOPASCAL> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <p1(kPa)> as the <Role> and <ClassOfIndirectProperty> <NORMAL INLET PRESSURE IN KILOPASCAL> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:06837fa8-0ade-4538-9669-c767e6c29731 rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :0c90f6a7-c797-4994-97bc-0022c555a5e5 ; # NORMAL INLET PRESSURE IN KILOPASCAL
     tpl:hasRole :4b42ba7c-a57c-4aa9-9014-b84b83706fa7 ; # p1(kPa)
     tpl:hasDefined :35fa0afd-29f1-4ad2-9af1-ff7de44931e0 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:0c90f6a7-c797-4994-97bc-0022c555a5e5 rdf:type dm:ClassOfIndirectProperty;
     rdfs:subclassOf rdl:RDS7343782, rdl:RDS1330559 ; # NORMAL INLET PRESSURE, KILOPASCAL
     rdfs:label "NORMAL INLET PRESSURE IN KILOPASCAL"@en ;
     skos:definition "A <NORMAL INLET PRESSURE IN KILOPASCAL> is a <NORMAL INLET PRESSURE> of which the value of the related <PRESSURE> is mapped to the <Scale> <KILOPASCAL>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:4b42ba7c-a57c-4aa9-9014-b84b83706fa7 rdf:type dm:Role ;
     rdfs:subclassOf :a56bf0cd-9228-42ba-a229-1568289cca6e ; # p1
     rdfs:label "p1(kPa)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:a56bf0cd-9228-42ba-a229-1568289cca6e rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "p1" ;
     dc:description "<p1> is a <VARIABLE IN EQUATION> and a proxy for a <PRESSURE>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# DEFINITION OF VARIABLE p2(kPa) AS PROXY FOR NORMAL OUTLET PRESSURE IN KILOPASCAL
:3ba114fb-19f4-4c68-9dae-33c561da2ea9 rdf:type dm:RoleAndDomain;
     rdfs:subclassOf dm:Class ;
     rdfs:label "p2 AND NORMAL OUTLET PRESSURE IN KILOPASCAL" ;
     skos:definition "A <p2 AND NORMAL OUTLET PRESSURE IN KILOPASCAL> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <p2(kPa)> as the <Role> and <ClassOfIndirectProperty> <NORMAL OUTLET PRESSURE IN KILOPASCAL> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:8aae8b12-9f2e-42ab-9fe5-b8579490db0a rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :32fa1489-a70a-4171-a330-74767d88764b ; # NORMAL OUTLET PRESSURE IN KILOPASCAL
     tpl:hasRole :737f3ffb-535f-4713-be07-9eb354935846 ; # p2(kPa)
     tpl:hasDefined :3ba114fb-19f4-4c68-9dae-33c561da2ea9 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:32fa1489-a70a-4171-a330-74767d88764b rdf:type dm:ClassOfIndirectProperty;
     rdfs:subclassOf rdl:RDS14261705, rdl:RDS1330559 ; # NORMAL OUTLET PRESSURE, KILOPASCAL
     rdfs:label "NORMAL OUTLET PRESSURE IN KILOPASCAL"@en ;
     skos:definition "A <NORMAL OUTLET PRESSURE IN KILOPASCAL> is a <NORMAL OUTLET PRESSURE> of which the value of the related <PRESSURE> is mapped to the <Scale> <KILOPASCAL>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:737f3ffb-535f-4713-be07-9eb354935846 rdf:type dm:Role ;
     rdfs:subclassOf :9c7eb502-3ec5-4393-8483-3d56b58517c4 ; # p2
     rdfs:label "p2(kPa)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:9c7eb502-3ec5-4393-8483-3d56b58517c4 rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "p2" ;
     dc:description "<p2> is a <VARIABLE IN EQUATION> and a proxy for a <PRESSURE>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# DEFINITION OF VARIABLE ?(kg/m3) AS PROXY FOR DENSITY IN KILOGRAM PER METRE CUBED
:e28b9a51-81c8-43e7-b223-49161b5a956e rdf:type dm:RoleAndDomain;
     rdfs:subclassOf dm:Class ;
     rdfs:label "? AND DENSITY IN KILOGRAM PER METRE CUBED"@en ;
     skos:definition "A <? AND DENSITY IN KILOGRAM PER METRE CUBED> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <?(kg/m3)> as the <Role> and <SinglePropertyDimension> <DENSITY IN KILOGRAM PER METRE CUBED> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:bcce02c5-719b-484f-b253-d9ab0cc940f8 rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :273922e3-f48d-447a-86fa-e87ef4b4c7bf ; # DENSITY IN KILOGRAM PER METRE CUBED
     tpl:hasRole :37d8ecab-7d82-4bc7-95f3-b2669bb94ec2 ; # ?(kg/m3)
     tpl:hasDefined :e28b9a51-81c8-43e7-b223-49161b5a956e ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:273922e3-f48d-447a-86fa-e87ef4b4c7bf rdf:type dm:SinglePropertyDimension ;
     rdfs:subclassOf rdl:RDS358874, rdl:RDS1354454 ; # DENSITY, KILOGRAM PER METRE CUBED
     rdfs:label "DENSITY IN KILOGRAM PER METRE CUBED"@en ;
     skos:definition "A <DENSITY IN KILOGRAM PER METRE CUBED> is a <DENSITY> of which the value is mapped to the <Scale> <KILOGRAM PER METRE CUBED>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:37d8ecab-7d82-4bc7-95f3-b2669bb94ec2 rdf:type dm:Role ;
     rdfs:subclassOf :13b34a15-f546-470f-9ccb-9967ad3d56cb ; # ?
     rdfs:label "?(kg/m3)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:13b34a15-f546-470f-9ccb-9967ad3d56cb rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "?" ;
     dc:description "<?> is a <VARIABLE IN EQUATION> and a proxy for a <DENSITY>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# DEFINITION OF VARIABLE v2(m/s) AS A PROXY FOR AVERAGE VELOCITY IN METRE PER SECOND
:10be33a2-04dd-4ae6-b44a-2201ddce1824 rdf:type dm:RoleAndDomain;
     rdfs:subclassOf dm:Class ;
     rdfs:label "v2 AND AVERAGE VELOCITY IN METRE PER SECOND"@en ;
     skos:definition "A <v2 AND AVERAGE VELOCITY IN METRE PER SECOND> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <v2(m/s)> as the <Role> and <ClassOfIndirectProperty> <AVERAGE VELOCITY IN METRE PER SECOND> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:868bb316-6a76-42b9-8a24-5ea2d31141c5 rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :b11d99c6-eac2-4e34-9af6-a54a1c9ea41e ; # AVERAGE VELOCITY IN METRE PER SECOND
     tpl:hasRole :ae7fde8e-846a-419c-b176-f0c360401684 ; # v2(m/s)
     tpl:hasDefined :10be33a2-04dd-4ae6-b44a-2201ddce1824 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:b11d99c6-eac2-4e34-9af6-a54a1c9ea41e rdf:type dm:ClassOfIndirectProperty;
     rdfs:subclassOf rdl:RDS13107740, rdl:RDS1354499 ; # AVERAGE VELOCITY, METRE PER SECOND
     rdfs:label "AVERAGE VELOCITY IN METRE PER SECOND"@en ;
     skos:definition "An <AVERAGE VELOCITY IN METRE PER SECOND> is an <AVERAGE VELOCITY> of which the value of the related <VELOCITY> is mapped to the <Scale> <METRE PER SECOND>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:ae7fde8e-846a-419c-b176-f0c360401684 rdf:type dm:Role ;
     rdfs:subclassOf :e63f0f18-b766-4eb9-bc84-54ffd1e2c799 ; # v2
     rdfs:label "v2(m/s)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:e63f0f18-b766-4eb9-bc84-54ffd1e2c799 rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "v2" ;
     dc:description "<v2> is a <VARIABLE IN EQUATION> and a proxy for a <VELOCITY>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# DEFINITION OF VARIABLE g(m/s2) AS A PROXY FOR ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED
:dcac8f2d-4d8c-4e92-b7a3-fdfe030a6f9c rdf:type dm:RoleAndDomain;
     rdfs:subclassOf dm:Class ;
     rdfs:label "g AND ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED" ;
     skos:definition "A <g AND ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <g(m/s2)> as the <Role> and <SinglePropertyDimension> <ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:a1779a16-9317-454b-a5c6-7c22b7fa1e26 rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :2117a4a9-d8af-4d81-bcbe-3c86f1c6064e ; # ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED
     tpl:hasRole :42629425-35a1-44fc-a89d-1d6d71eee8ce ; # g(m/s2)
     tpl:hasDefined :dcac8f2d-4d8c-4e92-b7a3-fdfe030a6f9c ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:2117a4a9-d8af-4d81-bcbe-3c86f1c6064e rdf:type dm:SinglePropertyDimension ;
     rdfs:subclassOf rdl:RDS548083371, rdl:RDS1333169 ; # ACCELLERATION OF GRAVITY, METRE PER SECOND SQUARED
     rdfs:label "ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED"@en ;
     skos:definition "An <AVERAGE VELOCITY IN METRE PER SECOND> is an <AVERAGE VELOCITY> of which the value of the related <VELOCITY> is mapped to the <Scale> <METRE PER SECOND>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:42629425-35a1-44fc-a89d-1d6d71eee8ce rdf:type dm:Role ;
     rdfs:subclassOf :6ec723de-6d9f-4ab5-a24b-cdda450ee7f6; # g
     rdfs:label "g(m/s2)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:6ec723de-6d9f-4ab5-a24b-cdda450ee7f6 rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "g" ;
     dc:description "<g> is a <VARIABLE IN EQUATION> and a proxy for an <ACCELLERATION OF GRAVITY>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of the result of FunctionalMapping
# DEFINITION OF VARIABLE h(m) AS A PROXY FOR HEAD IN METRE
:106a0a24-f412-4a7a-bca5-3a1c74b91572 rdf:type dm:RoleAndDomain;
     rdfs:subclassOf dm:Class ;
     rdfs:label "h AND HEAD IN METRE"@en ;
     skos:definition "A <h AND HEAD IN METRE> is an instance of <RoleAndDomain> with <VARIABLE IN EQUATION> <h(m)> as the <Role> and <SinglePropertyDimension> <HEAD IN METRE> as the domain."@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:ac1e1ff6-c137-49b6-a431-5243151bed53 rdf:type tpl:DefinitionOfRoleAndDomain;
     tpl:hasDomain :bd118228-e9ca-46f1-ba96-faa25efb732f ; # HEAD IN METRE
     tpl:hasRole :42cd20cd-c1b9-46a5-bf05-cc3e252fadbf ; # h(m)
     tpl:hasDefined :106a0a24-f412-4a7a-bca5-3a1c74b91572 ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:bd118228-e9ca-46f1-ba96-faa25efb732f rdf:type dm:SinglePropertyDimension;
     rdfs:subclassOf rdl:RDS362609, rdl:RDS1332674 ; # HEAD, METRE
     rdfs:label "HEAD IN METRE"@en ;
     skos:definition "A <HEAD IN METRE> is a <HEAD> of which the value is mapped to the <Scale> <METRE>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:42cd20cd-c1b9-46a5-bf05-cc3e252fadbf rdf:type dm:Role ;
     rdfs:subclassOf :15f66d41-cc74-4e61-94f5-f15fa17958cf ; # h
     rdfs:label "h(m)" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:15f66d41-cc74-4e61-94f5-f15fa17958cf rdf:type dm:Role;
     rdfs:subclassOf rdl:RDS2229037 ; # VARIABLE IN EQUATION
     rdfs:label "h" ;
     skos:definition "<h> is a <VARIABLE IN EQUATION> that indicates a proxy for a <HEAD>"@en ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

CODE FOR THE EXAMPLE

@prefix : <http://www.p1234.xyz-corp.com/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dm: <http://data.15926.org/dm/> .
@prefix lci: <http://data.15926.org/edm/> .
@prefix meta: <http://data.15926.org/meta/> .
@prefix tpl: <http://data.15926.org/tpl/> .
@prefix rdl: <http://data.15926.org/rdl/> .
@prefix xyzrdl: <http://www.rdl.xyz-corp.com/> . # local RDL extension

#    ////////////////////////////////////////////////////////////////
#    //
#    // THIS ONTOLOGY REPRESENTS AN EQUATION WITH DETAILED VARIABLES
#    //
#    ////////////////////////////////////////////////////////////////
#    ///////////////////
#    //
#    // DECLARED OBJECTS
#    //
#    ///////////////////

# Declaration of Unit Operation UO137
:UO137 rdf:type dm:ClassOfActivity ;
     rdfs:subclassOf rdl:RDS2223591 ; # UO_CENTRIFUGAL_PUMP
     rdfs:label "UO137" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration of Pump P137
:P137 rdf:type dm:ClassOfInanimatePhysicalObject ;
     rdfs:subclassOf rdl:RDS416834 ; # CENTRIFUGAL PUMP
     rdfs:label "P137" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration of Stream STRM137in
:STRM137in rdf:type lci:ClassOfStream ;
     rdfs:subclassOf dm:Stream ;
     rdfs:label "STRM137in" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration of Stream STRM137out
:STRM137out rdf:type lci:ClassOfStream ;
     rdfs:subclassOf dm:Stream ;
     rdfs:label "STRM137out" ;
     meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

#    //////////////////////////////////////////////////////////////
#    //
#    // INSTANTIATING THE TEMPLATE FunctionalMappingOf5ExpressReals
#    //
#    //////////////////////////////////////////////////////////////

:87D68D3F4F6448B3ABC99D4424206362 rdf:type tpl:FunctionalMappingOf5ExpressReals ;
    tpl:valInput1 "211.8"^^xsd:decimal ;
    tpl:valInput2 "584.3"^^xsd:decimal ;
    tpl:valInput3 "1237"^^xsd:decimal ;
    tpl:valInput4 "5.3"^^xsd:decimal ;
    tpl:valInput5 "9.81"^^xsd:decimal ;
    tpl:valResult "32.12"^^xsd:decimal ;
    tpl:hasFunction :3e9eaf76-a5ad-41f4-9110-df328322f8d5 ;
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# NOTE - The above template instance can only be populated with a SPARQL query result, where the values of the role tpl:valPropertyValue of the templates for variables (below) are being used. There cannot be a permanent link because, other than ExpressReal with its 'content' property, RDF Literals do not have a URI.

#    /////////////////////////////////////////////////////////////////////////////////////////////////
#    //
#    // TEMPLATES FOR QUANTIFICATION OF VARIABLES AS FETCHED WITH A SPARQL QUERY (normally in JSON-LD)
#    //
#    /////////////////////////////////////////////////////////////////////////////////////////////////

# Template for value of inlet pressure p1
:D0798298B72941EBB2340D4E30C12A7C rdf:type tpl:ClassOfIndividualHasIndirectPropertyWithValue ;
    tpl:hasPossessorType :STRM137in ;
    tpl:hasIndirectPropertyType rdl:RDS7343782 ; # NORMAL INLET PRESSURE
    tpl:valPropertyValue "211.8"^^xsd:decimal ;
    tpl:hasScale rdl:RDS1330559 ; # KILOPASCAL
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for value of outlet pressure p2
:6742BC68C09B4D42A463531B194300C0 rdf:type tpl:ClassOfIndividualHasIndirectPropertyWithValue ;
    tpl:hasPossessorType :STRM137out ;
    tpl:hasIndirectPropertyType rdl:RDS14261705 ; # NORMAL OUTLET PRESSURE
    tpl:valPropertyValue "584.3"^^xsd:decimal ;
    tpl:hasScale rdl:RDS1330559 ; # KILOPASCAL
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for value of density ?
:735EC4CCB35146CA97815C4048B5BB02 rdf:type tpl:ClassOfIndividualHasPropertyWithValue ;
    tpl:hasPossessorType :STRM137in ;
    tpl:hasPropertyType rdl:RDS358874 ; # DENSITY
    tpl:valPropertyValue "1237"^^xsd:decimal ;
    tpl:hasScale rdl:RDS1354454 ; # KILOGRAM PER METRE CUBED
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for value of outlet fluid velocity v2
:835A33699AD042A4A63EE46A41E8ED33 rdf:type tpl:ClassOfIndividualHasIndirectPropertyWithValue ;
    tpl:hasPossessorType :STRM137out ;
    tpl:hasIndirectPropertyType rdl:RDS13107740 ; # AVERAGE VELOCITY
    tpl:valPropertyValue "5.3"^^xsd:decimal ;
    tpl:hasScale rdl:RDS1354499 ; # METRE PER SECOND
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for value of head h
:3CD1FB18A2D84C7680E64D60D1E6864B rdf:type tpl:ClassOfIndividualHasIndirectPropertyWithValue ;
    tpl:hasPossessorType :P137 ;
    tpl:hasIndirectPropertyType rdl:RDS362609 ; # HEAD
    tpl:valPropertyValue "32.12"^^xsd:decimal ;
    tpl:hasScale rdl:RDS1332674 ; # METRE
    meta:hasLifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN
    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .