Equations and Variables

latest update: 30 April 2015     

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)/(ρ  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)

    ρ =   density (kg/m3)

    g = acceleration of 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. If modeled, they can be represented in MathML, which makes it suitable for handling in an XML environment.

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

The relationship between these variables-in-template-signature and the transfer function can be represented by an instance of the following template:

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/m3 - density of STRM137in;
  • v2 = 5.3 m/s - fluid velocity of STRM137out.

and one constant:

  • g = 9.81 m/s2 - accelleration of gravity.

Code for the ClassOfFunctionalMapping

New reference data must be defined:

These are temporarily stored in a local RDL extension. The final RDS-numbers of the core RDL will be entered later.

@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://rds.posccaesar.org/2008/02/OWL/ISO-15926-2_2003#> .

@prefix meta: <http://data.posccaesar.org/meta/> .

@prefix tpl: <http://data.posccaesar.org/tpl/> .

@prefix rdl: <http://data.posccaesar.org/rdl/> .

 

#    //////////////////////////////////////////////////////////////////////////////////////////////////

#    //

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

#    //

#    //////////////////////////////////////////////////////////////////////////////////////////////////

 

# Definition of Unit Operation

:C4cb5ade5-ecdd-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfActivity, owl:Class ;

     rdfs:subclassOf rdl:RDS3149 ; # ISO 15926-4 ACTIVITY

     rdfs:label "UNIT OPERATION"@en ;

     skos:definition "an ISO 15926-4 ACTIVITY that is a basic step in a process involving a physical change or chemical transformation; a process may require many unit operations to obtain the desired product from the starting materials, or feedstocks."@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cb21a5d30-ecdc-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfActivity, owl:Class ;

     rdfs:subclassOf :C4cb5ade5-ecdd-11e4-b80c-0800200c9a66 ;

     rdfs:label "UO_CENTRIFUGAL_PUMP"@en ;

     skos:definition "a UNIT OPERATION that entails the PUMPING with a CENTRIFUGAL PUMP" ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Ta5be2c62-ee6c-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedDefinitionOfClassOfIndividual, owl:Thing ;

     tpl:hasDefined :Cb21a5d30-ecdc-11e4-b80c-0800200c9a66 ;

     tpl:hasDefinition :Ca5be2c63-ee6c-11e4-b80c-0800200c9a66 ; # UO_CENTRIFUGAL_PUMP TRANSFER FUNCTION

     tpl:hasDefinitionType :Ca5be2c60-ee6c-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Equation is a part of Transfer Function

:Ta5be2c64-ee6c-11e4-b80c-0800200c9a66 rdf:type tpl:ClassOfCompositionDefinition, owl:Thing ;

     tpl:hasClassOfWhole :Ca5be2c63-ee6c-11e4-b80c-0800200c9a66 ;

     tpl:hasClassOfPart :Ca5be2c64-ee6c-11e4-b80c-0800200c9a66 ;

     tpl:hasCardinalityOfWhole :Cc8878ae3-dbc2-11e1-9b23-0800200c9a66 ;

     tpl:hasCardinalityOfPart :Ce269fc71-678a-11e1-b86c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Ca5be2c63-ee6c-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfInformationRepresentation, owl:Class ;

     rdfs:subclassOf rdl:RDS1685084301 ; # ISO 15926-4 INFORMATION REPRESENTATION

     rdfs:label "UO_CENTRIFUGAL_PUMP TRANSFER FUNCTION"@en ;

     skos:definition "an ISO 15926-4 INFORMATION REPRESENTATION that represents the transfer function of UO_CENTRIFUGAL_PUMP"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Ca5be2c64-ee6c-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfInformationRepresentation, owl:Class ;

     rdfs:subclassOf rdl:RDS1685084301 ; # ISO 15926-4 INFORMATION REPRESENTATION

     rdfs:label "UO_CENTRIFUGAL_PUMP EQUATION FOR HEAD CALCULATION"@en ;

     skos:definition "an ISO 15926-4 INFORMATION REPRESENTATION that represents the equation for the head calculation of UO_CENTRIFUGAL_PUMP"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration of ClassOfFunctionalMapping

:Cf228c940-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfFunctionalMapping, owl:Class ;

     dm:codomain :Cf228c941-ecc1-11e4-b80c-0800200c9a66 ; # the RoleAndDomain defining "h AND head in m"

     dm:domain :Cf228c942-ecc1-11e4-b80c-0800200c9a66 ; # the ClassOfMultidimensionalObject defining the variables and constants

     dc:description "pump head equation h = (p2 - p1)/(ρ*g) + v2^2/(2*g)"@en ;

     skos:definition "<math><mrow><mi>h</mi><mo>=</mo><mo>(</mo><mi>p</mi><mn>2</mn><mo>-</mo><mi>p</mi><mn>1</mn><mo>)</mo><mo>/</mo><mi>rho</mi><mo>*</mo><mi>g</mi><mo>+</mo><mi>v</mi><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>*</mo><mi>g</mi></mrow></math>" ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of the ClassOfFunctionalMapping with an equation

:Ta5be2c61-ee6c-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedDefinitionOfClassOfRelationship, owl:Thing ;

     tpl:hasDefined :Cf228c940-ecc1-11e4-b80c-0800200c9a66 ;

     tpl:hasDefinition :Ca5be2c64-ee6c-11e4-b80c-0800200c9a66 ; # UO_CENTRIFUGAL_PUMP EQUATION FOR HEAD CALCULATION

     tpl:hasDefinitionType :Ca5be2c60-ee6c-11e4-b80c-0800200c9a66 ; # DEFINITION OF A CLASS WITH A MATHEMATICAL EQUATION

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Ca5be2c60-ee6c-11e4-b80c-0800200c9a66 rdf:type  dm:ClassOfClassOfDefinition, owl:Class ;

    rdfs:subclassOf rdl: ; # ISO 15926-4 DEFINITION CLASS

    rdfs:label "DEFINITION OF A CLASS WITH A MATHEMATICAL EQUATION"@en ;

    skos:definition "An ISO 15926-4 DEFINITION CLASS that indicates a definition of a Class via a mathematical equation."@en ;

    dm:hasClassOfPattern rdl:RDSNEW310 ; # MATHEMATICAL EQUATION IN ASCII

    dm:hasClassOfRepresented rdl:RDS16735730 ; # ISO 15926-4 CLASS

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of ClassOfMultidimensionalobject

:Cf228c942-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfMultidimensionalObject, owl:Class ;

     :role1 :Cf228c943-ecc1-11e4-b80c-0800200c9a66 ; # p1 AND NORMAL INLET PRESSURE IN KILOPASCAL

     :role2 :Cf228c944-ecc1-11e4-b80c-0800200c9a66 ; # p2 AND NORMAL OUTLET PRESSURE IN KILOPASCAL

     :role3 :Cf228c945-ecc1-11e4-b80c-0800200c9a66 ; # ρ AND DENSITY IN KILOGRAM PER METRE CUBED

     :role4 :Cf228c946-ecc1-11e4-b80c-0800200c9a66 ; # v2 AND AVERAGE VELOCITY IN METRE PER SECOND

     :role5 :Cf228c947-ecc1-11e4-b80c-0800200c9a66 ; # 9.81 AND ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED

     skos:definition "an ISO 15926-4 CLASS OF MULTIDIMENSIONAL OBJECT that defines four variables and one constant for h = (p2 - p1)/(ρ*g) + v2^2/(2*g)"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of 6 instances of RoleAndDomain

:Cf228c943-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a variable p1 AND NORMAL INLET PRESSURE IN KILOPASCAL"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597860-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :Cbafbfe61-ecda-11e4-b80c-0800200c9a66 ; # NORMAL INLET PRESSURE IN KILOPASCAL

     tpl:hasRole :C58dd12f1-ecd5-11e4-b80c-0800200c9a66 ; # p1

     tpl:hasDefined :Cf228c943-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cf228c944-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a variable p2 AND NORMAL OUTLET PRESSURE IN KILOPASCAL"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597861-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :Cbafbfe62-ecda-11e4-b80c-0800200c9a66 ; # NORMAL OUTLET PRESSURE IN KILOPASCAL

     tpl:hasRole :C58dd12f2-ecd5-11e4-b80c-0800200c9a66 ; # p2

     tpl:hasDefined :Cf228c944-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cf228c945-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a variable ρ AND DENSITY IN KILOGRAM PER METRE CUBED"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597862-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :Cbafbfe63-ecda-11e4-b80c-0800200c9a66 ; # DENSITY IN KILOGRAM PER METRE CUBED

     tpl:hasRole :C58dd12f3-ecd5-11e4-b80c-0800200c9a66 ; # ρ

     tpl:hasDefined :Cf228c945-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cf228c946-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a variable v2 AND AVERAGE VELOCITY IN METRE PER SECOND"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597863-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :Cbafbfe64-ecda-11e4-b80c-0800200c9a66 ; # AVERAGE VELOCITY IN METRE PER SECOND

     tpl:hasRole :C58dd12f4-ecd5-11e4-b80c-0800200c9a66 ; # v2

     tpl:hasDefined :Cf228c946-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cf228c947-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a constant (9.81) AND ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597864-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :Cbafbfe65-ecda-11e4-b80c-0800200c9a66 ; # ACCELLERATION OF GRAVITY IN METRE PER SECOND SQUARED

     tpl:hasRole :C58dd12f5-ecd5-11e4-b80c-0800200c9a66 ; # g

     tpl:hasDefined :Cf228c947-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cf228c948-ecc1-11e4-b80c-0800200c9a66 rdf:type dm:RoleAndDomain, owl:Class ;

     rdfs:subclassOf rdl:RDS460952191 ; # ISO 15926-4 ROLE AND DOMAIN INSTANCE

     skos:definition "an ISO 15926-4 ROLE AND DOMAIN INSTANCE that is a variable h AND HEAD IN METRE"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Tc7597865-ee63-11e4-b80c-0800200c9a66 rdf:type tpl:DefinitionOfRoleAndDomain, owl:Thing ;

     tpl:hasDomain :C58dd12f6-ecd5-11e4-b80c-0800200c9a66 ; # HEAD IN METRE

     tpl:hasRole :C58dd12f6-ecd5-11e4-b80c-0800200c9a66 ; # h

     tpl:hasDefined :Cf228c948-ecc1-11e4-b80c-0800200c9a66 ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of 6 Roles

:C58dd12f0-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf rdl:RDS327144371 ; # ISO 15926-4 ROLE INSTANCE

     rdfs:label "VARIABLE IN EQUATION" ;

     skos:definition "an ISO 15926-4 ROLE INSTANCE that is a variable playing a role in an equation"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cd435eff0-ed87-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf rdl:RDS327144371 ; # ISO 15926-4 ROLE INSTANCE

     rdfs:label "CONSTANT IN EQUATION" ;

     skos:definition "an ISO 15926-4 ROLE INSTANCE that is a constant playing a role in an equation"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f1-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :C58dd12f0-ecd5-11e4-b80c-0800200c9a66 ; # VARIABLE IN EQUATION

     rdfs:label "p1" ;

     dc:description "a VARIABLE IN EQUATION that is a symbol for inlet pressure"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f2-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :C58dd12f0-ecd5-11e4-b80c-0800200c9a66 ; # VARIABLE IN EQUATION

     rdfs:label "p2" ;

     dc:description "a VARIABLE IN EQUATION that is a symbol for outlet pressure"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f3-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :C58dd12f0-ecd5-11e4-b80c-0800200c9a66 ; # VARIABLE IN EQUATION

     rdfs:label "ρ" ;

     dc:description "a VARIABLE IN EQUATION that is a symbol for density"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f4-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :C58dd12f0-ecd5-11e4-b80c-0800200c9a66 ; # VARIABLE IN EQUATION

     rdfs:label "v2" ;

     dc:description "a VARIABLE IN EQUATION that is a symbol for outlet fluid velocity"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f5-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :Cd435eff0-ed87-11e4-b80c-0800200c9a66 ; # CONSTANT IN EQUATION

     rdfs:label "g" ;

     dc:description "a CONSTANT IN EQUATION that is a symbol for accelleration of gravity"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:C58dd12f6-ecd5-11e4-b80c-0800200c9a66 rdf:type dm:Role, owl:Class ;

     rdfs:subclassOf :C58dd12f0-ecd5-11e4-b80c-0800200c9a66 ; # VARIABLE IN EQUATION

     rdfs:label "h" ;

     dc:description "a VARIABLE IN EQUATION that is a symbol for pump head"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Definition of 5 (Indirect)Properties with predefined Scale

:Cbafbfe61-ecda-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfIndirectProperty, owl:Class ;

     rdfs:subclassOf rdl:RDS7343782 ; # NORMAL INLET PRESSURE

     skos:definition "a NORMAL INLET PRESSURE of which the value is mapped to the Scale KILOPASCAL"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cbafbfe62-ecda-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfIndirectProperty, owl:Class ;

     rdfs:subclassOf rdl:RDS14261705 ; # NORMAL OUTLET PRESSURE

     skos:definition "a NORMAL OUTLET PRESSURE of which the value is mapped to the Scale KILOPASCAL"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cbafbfe63-ecda-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfIndirectProperty, owl:Class ;

     rdfs:subclassOf rdl:RDS358874 ; # DENSITY

     skos:definition "a DENSITY of which the value is mapped to the Scale KILOGRAM PER METRE CUBED"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cbafbfe64-ecda-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfIndirectProperty, owl:Class ;

     rdfs:subclassOf rdl:RDS13107740 ; # AVERAGE VELOCITY

     skos:definition "an AVERAGE VELOCITY of which the value is mapped to the Scale METRE PER SECOND"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Cbafbfe65-ecda-11e4-b80c-0800200c9a66 rdf:type dm:ClassOfIndirectProperty, owl:Class ;

     rdfs:subclassOf rdl:RDS362609 ; # HEAD

     skos:definition "a HEAD of which the value is mapped to the Scale METRE"@en ;

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# NOTE - In order to make these six definitions computer-interpretable we would need to use templates. That has been left out here.


Code for the variables

@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://rds.posccaesar.org/2008/02/OWL/ISO-15926-2_2003#> .

@prefix edm: <http://data.posccaesar.org/edm/> .

@prefix meta: <http://data.posccaesar.org/meta/> .

@prefix tpl: <http://data.posccaesar.org/tpl/> .

@prefix rdl: <http://data.posccaesar.org/rdl/> .

@prefix xyzrdl: <http://www.rdl.xyz-corp.com/> . # local RDL extension

 

#    ////////////////////////////////////////////////////////////////

#    //

#    // THIS ONTOLOGY REPRESENTS AN EQUATION WITH DETAILED VARIABLES

#    //

#    ////////////////////////////////////////////////////////////////

 

#    ///////////////////

#    //

#    // DECLARED OBJECTS

#    //

#    ///////////////////

 

# Declaration and tagging of Unit Operation UO137

:UO137 rdf:type dm:ClassOfActivity ;

     rdfs:subclassOf xyzrdl:Cb21a5d30-ecdc-11e4-b80c-0800200c9a66 ; # UO_CENTRIFUGAL_PUMP

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Td2ab7d71-ecd9-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedIdentificationOfIndividual ;

     tpl:hasIdentifier :UO137 ;

     tpl:valIdentifier "UO137" ;

     tpl:hasIdentificationType rdl:RDSNEW002 ; # IDENTIFICATION WITH PROCESS DESIGN TAG

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration and tagging of Pump P137

:P137 rdf:type dm:ClassOfInanimatePhysicalObject ;

     rdfs:subclassOf rdl:RDS416834 ; # CENTRIFUGAL PUMP

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Td2ab7d72-ecd9-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedIdentificationOfIndividual ;

     tpl:hasIdentifier :P137 ;

     tpl:valIdentifier "P137" ;

     tpl:hasIdentificationType rdl:RDSNEW002 ; # IDENTIFICATION WITH PROCESS DESIGN TAG

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration and tagging of Stream STRM137in

:STRM137in rdf:type edm:ClassOfStream ;

     rdfs:subclassOf rdl:RDS436813371 ; # ISO 15926-4 STREAM

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Td2ab7d73-ecd9-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedIdentificationOfIndividual ;

     tpl:hasIdentifier :STRM137in ;

     tpl:valIdentifier "STRM137in" ;

     tpl:hasIdentificationType rdl:RDSNEW002 ; # IDENTIFICATION WITH PROCESS DESIGN TAG

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Declaration and tagging of Stream STRM137out

:STRM137out rdf:type edm:ClassOfStream ;

     rdfs:subclassOf rdl:RDS436813371 ; # ISO 15926-4 STREAM

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

:Td2ab7d74-ecd9-11e4-b80c-0800200c9a66 rdf:type tpl:ClassifiedIdentificationOfIndividual ;

     tpl:hasIdentifier :STRM137out ;

     tpl:valIdentifier "STRM137out" ;

     tpl:hasIdentificationType rdl:RDSNEW002 ; # IDENTIFICATION WITH PROCESS DESIGN TAG

     meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

     meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

 

#    //////////////////////////////////////////////////////////////

#    //

#    // INSTANTIATING THE TEMPLATE FunctionalMappingOf5ExpressReals

#    //

#    //////////////////////////////////////////////////////////////

 

:Taf9ce340-ef0f-11e4-b80c-0800200c9a66 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 xyzrdl:Cf228c940-ecc1-11e4-b80c-0800200c9a66 ;

    meta:lifecycleActivity 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 datatypes cannot have a URI.

 

#    ///////////////////////////

#    //

#    // TEMPLATES FOR VARIABLES

#    //

#    ///////////////////////////

 

# Template for inlet pressure p1

:Ta6c90530-ed86-11e4-b80c-0800200c9a66 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:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for density ρ

:Ta6c90531-ed86-11e4-b80c-0800200c9a66 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:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for outlet pressure p2

:Ta6c90532-ed86-11e4-b80c-0800200c9a66 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:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for outlet fluid velocity v2

:Ta6c90533-ed86-11e4-b80c-0800200c9a66 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:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .

# Template for head h

:Ta6c90534-ed86-11e4-b80c-0800200c9a66 rdf:type tpl:ClassOfIndividualHasIndirectPropertyWithValue ;

    tpl:hasPossessorType :P137 ;

    tpl:hasIndirectPropertyType rdl:RDS362609 ; # HEAD

    tpl:valPropertyValue "32.12"^^xsd:decimal ;

    tpl:hasScale rdl:RDS1332674 ; # METRE

    meta:lifecycleActivity rdl:RDS9648872 ; # PROCESS DESIGN

    meta:valEffectiveDate "2015-04-26T11:41:35Z"^^xsd:dateTime .