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CoolProp/wrappers/MathCAD/CoolPropFluidProperties.xmcd
Ian bell b3847c7522 Initial commit for v5, but this time with the right line endings 
Signed-off-by: Ian bell <ian.h.bell@gmail.com>
2014-05-14 12:46:24 +02:00

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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This worksheet demonstrates the functions defined in the CoolProp user function (CoolProp Mathcad Wrapper.dll).<sp count="2"/>CoolProp is an open-source, cross-platform, thermophysical fluid properties database developed by Ian Bell et al. at the University of Liege, Liege, Belgium.<sp count="2"/>The following URL provides full documentation of the CoolProp code: <c val="#000">http://coolprop.sourceforge.net/EOS.html#introduction</c>
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<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Revision History</p>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">2013-10-04:<tab/>Creation and initial release of the CoolProp Mathcad Wrapper library.<sp count="2"/>S. Polak</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">2013-11-01:<tab/>Incorporated CoolProp 4.0.0 pre-release code .<sp count="2"/>S. Polak</p>
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<tab/>Replaced FluidsList call with FluidPropsParams. S. Polak<tab/>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">2013-11-21:<tab/>Corrected typos and and units.<sp count="2"/>S. Polak</p>
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<p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">List of Fluids in the CoolProp Database (and Other Database Parameters)</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Functions to parse the output of CoolProp get_global_param_string are below (hidden for clarity - double click the right-arror to expand the hidden/collapsed area)</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The function FluidPropsParams("FluidsList") will output a single string representing all the fluids available in the CoolProp database.<sp count="2"/>The single string-type input argument is trivial (at least one user-function argument is required by Mathcad), and does not affect the output.<sp count="2"/>For clarity, the string parsing functions defined above (hidden by default) split that single string into a vector of strings, providing the scrollable list of fluids as shown below:</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Click on the output vector (table) to the left to enable scrolling through the entire list</p>
</text>
</region>
<region region-id="223" left="6" top="394.5" width="320.25" height="76.5" align-x="208.5" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">strSplit</ml:id>
<ml:sequence>
<ml:apply>
<ml:id xml:space="preserve">FluidPropsParams</ml:id>
<ml:str xml:space="preserve">FluidsList</ml:str>
</ml:apply>
<ml:str xml:space="preserve">,</ml:str>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="112" cols="1">
<ml:str xml:space="preserve">Water</ml:str>
<ml:str xml:space="preserve">R134a</ml:str>
<ml:str xml:space="preserve">Helium</ml:str>
<ml:str xml:space="preserve">Oxygen</ml:str>
<ml:str xml:space="preserve">Hydrogen</ml:str>
<ml:str xml:space="preserve">ParaHydrogen</ml:str>
<ml:str xml:space="preserve">OrthoHydrogen</ml:str>
<ml:str xml:space="preserve">Argon</ml:str>
<ml:str xml:space="preserve">CarbonDioxide</ml:str>
<ml:str xml:space="preserve">Nitrogen</ml:str>
<ml:str xml:space="preserve">n-Propane</ml:str>
<ml:str xml:space="preserve">Ammonia</ml:str>
<ml:str xml:space="preserve">R1234yf</ml:str>
<ml:str xml:space="preserve">R1234ze(E)</ml:str>
<ml:str xml:space="preserve">R32</ml:str>
<ml:str xml:space="preserve">R22</ml:str>
<ml:str xml:space="preserve">SES36</ml:str>
<ml:str xml:space="preserve">Ethylene</ml:str>
<ml:str xml:space="preserve">SulfurHexafluoride</ml:str>
<ml:str xml:space="preserve">Ethanol</ml:str>
<ml:str xml:space="preserve">DimethylEther</ml:str>
<ml:str xml:space="preserve">DimethylCarbonate</ml:str>
<ml:str xml:space="preserve">R143a</ml:str>
<ml:str xml:space="preserve">R23</ml:str>
<ml:str xml:space="preserve">n-Dodecane</ml:str>
<ml:str xml:space="preserve">Propylene</ml:str>
<ml:str xml:space="preserve">Cyclopentane</ml:str>
<ml:str xml:space="preserve">R236FA</ml:str>
<ml:str xml:space="preserve">R236EA</ml:str>
<ml:str xml:space="preserve">R227EA</ml:str>
<ml:str xml:space="preserve">R365MFC</ml:str>
<ml:str xml:space="preserve">R161</ml:str>
<ml:str xml:space="preserve">HFE143m</ml:str>
<ml:str xml:space="preserve">Benzene</ml:str>
<ml:str xml:space="preserve">n-Undecane</ml:str>
<ml:str xml:space="preserve">R125</ml:str>
<ml:str xml:space="preserve">CycloPropane</ml:str>
<ml:str xml:space="preserve">Neon</ml:str>
<ml:str xml:space="preserve">R124</ml:str>
<ml:str xml:space="preserve">Propyne</ml:str>
<ml:str xml:space="preserve">Fluorine</ml:str>
<ml:str xml:space="preserve">Methanol</ml:str>
<ml:str xml:space="preserve">RC318</ml:str>
<ml:str xml:space="preserve">R21</ml:str>
<ml:str xml:space="preserve">R114</ml:str>
<ml:str xml:space="preserve">R13</ml:str>
<ml:str xml:space="preserve">R14</ml:str>
<ml:str xml:space="preserve">R12</ml:str>
<ml:str xml:space="preserve">R113</ml:str>
<ml:str xml:space="preserve">R1234ze(Z)</ml:str>
<ml:str xml:space="preserve">R245fa</ml:str>
<ml:str xml:space="preserve">R41</ml:str>
<ml:str xml:space="preserve">CarbonMonoxide</ml:str>
<ml:str xml:space="preserve">CarbonylSulfide</ml:str>
<ml:str xml:space="preserve">n-Decane</ml:str>
<ml:str xml:space="preserve">HydrogenSulfide</ml:str>
<ml:str xml:space="preserve">Isopentane</ml:str>
<ml:str xml:space="preserve">Neopentane</ml:str>
<ml:str xml:space="preserve">Isohexane</ml:str>
<ml:str xml:space="preserve">Krypton</ml:str>
<ml:str xml:space="preserve">n-Nonane</ml:str>
<ml:str xml:space="preserve">Toluene</ml:str>
<ml:str xml:space="preserve">Xenon</ml:str>
<ml:str xml:space="preserve">R116</ml:str>
<ml:str xml:space="preserve">Acetone</ml:str>
<ml:str xml:space="preserve">NitrousOxide</ml:str>
<ml:str xml:space="preserve">SulfurDioxide</ml:str>
<ml:str xml:space="preserve">R141b</ml:str>
<ml:str xml:space="preserve">R142b</ml:str>
<ml:str xml:space="preserve">R218</ml:str>
<ml:str xml:space="preserve">Methane</ml:str>
<ml:str xml:space="preserve">Ethane</ml:str>
<ml:str xml:space="preserve">n-Butane</ml:str>
<ml:str xml:space="preserve">IsoButane</ml:str>
<ml:str xml:space="preserve">n-Pentane</ml:str>
<ml:str xml:space="preserve">n-Hexane</ml:str>
<ml:str xml:space="preserve">n-Heptane</ml:str>
<ml:str xml:space="preserve">n-Octane</ml:str>
<ml:str xml:space="preserve">CycloHexane</ml:str>
<ml:str xml:space="preserve">R152A</ml:str>
<ml:str xml:space="preserve">R123</ml:str>
<ml:str xml:space="preserve">R11</ml:str>
<ml:str xml:space="preserve">MDM</ml:str>
<ml:str xml:space="preserve">MD2M</ml:str>
<ml:str xml:space="preserve">MD3M</ml:str>
<ml:str xml:space="preserve">D6</ml:str>
<ml:str xml:space="preserve">MM</ml:str>
<ml:str xml:space="preserve">MD4M</ml:str>
<ml:str xml:space="preserve">D4</ml:str>
<ml:str xml:space="preserve">D5</ml:str>
<ml:str xml:space="preserve">1-Butene</ml:str>
<ml:str xml:space="preserve">IsoButene</ml:str>
<ml:str xml:space="preserve">cis-2-Butene</ml:str>
<ml:str xml:space="preserve">trans-2-Butene</ml:str>
<ml:str xml:space="preserve">MethylPalmitate</ml:str>
<ml:str xml:space="preserve">MethylStearate</ml:str>
<ml:str xml:space="preserve">MethylOleate</ml:str>
<ml:str xml:space="preserve">MethylLinoleate</ml:str>
<ml:str xml:space="preserve">MethylLinolenate</ml:str>
<ml:str xml:space="preserve">o-Xylene</ml:str>
<ml:str xml:space="preserve">m-Xylene</ml:str>
<ml:str xml:space="preserve">p-Xylene</ml:str>
<ml:str xml:space="preserve">EthylBenzene</ml:str>
<ml:str xml:space="preserve">Deuterium</ml:str>
<ml:str xml:space="preserve">ParaDeuterium</ml:str>
<ml:str xml:space="preserve">OrthoDeuterium</ml:str>
<ml:str xml:space="preserve">Air</ml:str>
<ml:str xml:space="preserve">R404A</ml:str>
<ml:str xml:space="preserve">R410A</ml:str>
<ml:str xml:space="preserve">R407C</ml:str>
<ml:str xml:space="preserve">R507A</ml:str>
<ml:str xml:space="preserve">R407F</ml:str>
</ml:matrix>
</result>
</ml:eval>
<resultFormat>
<table item-idref="3"/>
</resultFormat>
</math>
<rendering item-idref="4"/>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidPropsParams</ml:id>
<ml:str xml:space="preserve">version</ml:str>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve">4.0.0pre</ml:str>
</result>
</ml:eval>
</math>
<rendering item-idref="5"/>
</region>
<region region-id="821" left="240" top="495" width="153" height="11.25" align-x="242.25" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Current version of the CoolProp library</p>
</text>
</region>
<region region-id="822" left="6" top="519" width="161.25" height="12.75" align-x="142.5" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidPropsParams</ml:id>
<ml:str xml:space="preserve">errstring</ml:str>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve"/>
</result>
</ml:eval>
</math>
<rendering item-idref="6"/>
</region>
<region region-id="824" left="240" top="519" width="164.25" height="11.25" align-x="249.75" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Used to retrieve the error message (if any)</p>
</text>
</region>
<region region-id="829" left="6" top="543" width="170.25" height="12.75" align-x="151.5" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidPropsParams</ml:id>
<ml:str xml:space="preserve">warnstring</ml:str>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve"/>
</result>
</ml:eval>
</math>
<rendering item-idref="7"/>
</region>
<region region-id="830" left="240" top="543" width="177.75" height="11.25" align-x="249.75" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Used to retrieve the warning message (if any)</p>
</text>
</region>
<region region-id="208" left="6" top="569.25" width="231.75" height="15.75" align-x="15.75" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Fluid Properties Not Dependent on State</p>
</text>
</region>
<region region-id="324" left="6" top="591" width="455.25" height="202.5" align-x="13.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The function FluidProp1 is used to extract fluid-specific parameters that are not dependent on the state.<sp count="2"/>The calling struction of the function is as follows:</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>
<f family="Times New Roman" charset="0" size="10">
<c val="#000">FluidProp1</c>
</f>
<f family="Times New Roman" charset="0" size="10">(Fluid &lt;string&gt;, PropertyName &lt;string&gt;)</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Where "Fluid" is one of the fluid names from the FluidList table above, and "PropertyName" is one of the property name abbreviations from the table below:</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>
<inlineAttr font-weight="normal">Tcrit<tab/>
<tab/>
</inlineAttr>
<i>
<inlineAttr font-weight="normal">Critical temperature [K]</inlineAttr>
</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>pcrit<tab/>
<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Critical pressure [kPa]</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>rhocrit<tab/>
<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Critical density [kg/m3]</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>molemass<tab/>
</inlineAttr>
<i>
<inlineAttr font-weight="normal">Molecular mass [kg/kmol]</inlineAttr>
</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>Ttriple<tab/>
<tab/>
</inlineAttr>
<i>
<inlineAttr font-weight="normal">Triple-point temperature [K]</inlineAttr>
</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>Tmin<tab/>
<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Minimum temperature [K]</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>ptriple<tab/>
<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Triple-point pressure [kPa]</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>accentric<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Accentric factor [-]</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>GWP100<tab/>
<tab/>
</inlineAttr>
<inlineAttr font-weight="normal">
<i>Global Warming Potential 100 yr</i>
</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-weight="normal">
<tab/>ODP<tab/>
<tab/>
</inlineAttr>
<i>
<inlineAttr font-weight="normal">Ozone Depletion Potential</inlineAttr>
</i>
</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 4" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example, FluidProp1</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidProp1</ml:id>
<ml:sequence>
<ml:str xml:space="preserve">Argon</ml:str>
<ml:str xml:space="preserve">rhocrit</ml:str>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>535.6</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="8"/>
</region>
<region region-id="310" left="240" top="831" width="190.5" height="11.25" align-x="255.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Extracts the critical density of Argon, in kg m^-3</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">State Dependent Fluid Properties</p>
</text>
</region>
<region region-id="343" left="6" top="891" width="456" height="22.5" align-x="18" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The function FluidProp is used to extract state-dependent fluid properties.<sp count="2"/>The calling struction of the function is as follows:</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<c val="#000">FluidProp</c>
</f>
<f family="Times New Roman" charset="0" size="10">(OutputParameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input1 Parameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input1 Value &lt;scalar&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input2 Parameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input2 Value &lt;scalar&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Fluid &lt;string&gt;)</f>
</p>
</text>
</region>
<region region-id="360" left="6" top="1005" width="457.5" height="360" align-x="18.75" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Where "Fluid" is one of the fluid names from the FluidList table above, and "OutputParameter" is one of the property name abbreviations from the table below: </p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>OutputParameter<tab/>Description [units]</b>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>Q<tab/>
<tab/>
<i>Quality [-]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>T<tab/>
<tab/>
<i>Temperature [K]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>P<tab/>
<tab/>
<i>Pressure [kPa]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>D<tab/>
<tab/>
<i>Density [kg/m3]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>C0<tab/>
<tab/>
<i>Ideal-gas specific heat at constant pressure [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>C<tab/>
<tab/>
<i>Specific heat at constant pressure [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>O<tab/>
<tab/>
<i>Specific heat at constant volume [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>U<tab/>
<tab/>
<i>Internal energy [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>H<tab/>
<tab/>
<i>Enthalpy [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>S<tab/>
<tab/>
<i>Entropy [kJ/kg/K]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>A<tab/>
<tab/>
<i>Speed of sound [m/s]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>G<tab/>
<tab/>
<i>Gibbs function [kJ/kg]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>V<tab/>
<tab/>
<i>Dynamic viscosity [Pa-s]</i>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>L<tab/>
<tab/>Thermal conductivity [kW/m/K]</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<tab/>I<tab/>
<tab/>
<i>Surface Tension [N/m]</i>
</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<tab/>w<tab/>
<tab/>
<i>Accentric Factor [-]</i>
</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">The following pairs of input parameters ("Input1 Parameter" and "Input2 Parameter") are valid:</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>
<inlineAttr font-style="normal">Input1 Parameter<tab/>Input2 Parameter</inlineAttr>
</b>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>T<tab/>
<tab/>
<tab/>P</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>T<tab/>
<tab/>
<tab/>D</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>P<tab/>
<tab/>
<tab/>D</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>T<tab/>
<tab/>
<tab/>Q</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>P<tab/>
<tab/>
<tab/>Q</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>H<tab/>
<tab/>
<tab/>P</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>S<tab/>
<tab/>
<tab/>P</inlineAttr>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<inlineAttr font-style="normal">
<tab/>S<tab/>
<tab/>
<tab/>H</inlineAttr>
</p>
</text>
</region>
<region region-id="363" left="6" top="1389" width="462" height="22.5" align-x="9" align-y="1398" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The defautl units system utilized by CoolProp is a modified SI units system, sometimes refered to as kSI.<sp count="2"/>Default units are shown in the table of varialbes above </p>
</text>
</region>
<region region-id="425" left="6" top="1431" width="93.75" height="11.25" align-x="21.75" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 4" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Examples, FluidProp</p>
</text>
</region>
<region region-id="770" left="336" top="1443" width="129.75" height="33.75" align-x="354" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Enthalpy of Helium [kJ kg^-1] at a temperature of 300 K and a Pressure of 500 kPa</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidProp</ml:id>
<ml:sequence>
<ml:str xml:space="preserve">H</ml:str>
<ml:str xml:space="preserve">T</ml:str>
<ml:real>300</ml:real>
<ml:str xml:space="preserve">P</ml:str>
<ml:real>500</ml:real>
<ml:str xml:space="preserve">Helium</ml:str>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1564.7469379430045</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="9"/>
</region>
<region region-id="773" left="336" top="1497" width="126" height="78.75" align-x="354" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Dynamic viscosity of Water [Pa*s] at a temperature of 21 C (converted to the CoolProp temperature units, K) and a Pressure of 60 psi (converetd to the CoolProp pressure units, kPa)</p>
</text>
</region>
<region region-id="752" left="6" top="1508.25" width="306.75" height="27.75" align-x="238.5" align-y="1524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">FluidProp</ml:id>
<ml:sequence>
<ml:str xml:space="preserve">V</ml:str>
<ml:str xml:space="preserve">T</ml:str>
<ml:apply>
<ml:div/>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°C</ml:id>
<ml:real>21</ml:real>
</ml:apply>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
<ml:str xml:space="preserve">P</ml:str>
<ml:apply>
<ml:div/>
<ml:apply>
<ml:mult style="auto-select"/>
<ml:real>60</ml:real>
<ml:id xml:space="preserve">psi</ml:id>
</ml:apply>
<ml:id xml:space="preserve">kPa</ml:id>
</ml:apply>
<ml:str xml:space="preserve">Water</ml:str>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0.00097745327129780462</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="10"/>
</region>
<region region-id="460" left="6" top="1583.25" width="151.5" height="15.75" align-x="15.75" align-y="1596" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Humid Air Fluid Properties</p>
</text>
</region>
<region region-id="461" left="6" top="1605" width="456" height="56.25" align-x="18" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The function HAProp is used to find fluid properties of humid air.<sp count="2"/>The physics behind the HAProps function is based on the analysis in ASHRAE RP-1845, which is available online: <c val="#000">http://rp.ashrae.biz/page/ASHRAE-D-RP-1485-20091216.pdf</c>.<sp count="2"/>It employs real gas properties for both air and water, as well as the most accurate interaction parameters and enhancement factors.<sp count="3"/>RP-1845 is based largely on the IAPWS-95 formulation for the properties of water.<sp count="2"/>The calling struction of the function is as follows:</p>
</text>
</region>
<region region-id="753" left="42" top="1689" width="147.75" height="78.75" align-x="51.75" align-y="1698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<c val="#000">HAProp</c>
</f>
<f family="Times New Roman" charset="0" size="10">(OutputParameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input1 Parameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input1 Value &lt;scalar&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input2 Parameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input2 Value &lt;scalar&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input3 Parameter &lt;string&gt;,</f>
</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="10">
<tab/>Input3 Value &lt;scalar&gt;)</f>
</p>
</text>
</region>
<region region-id="520" left="6" top="1791" width="387.75" height="168.75" align-x="7.5" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Where "OutputParameter" and all three Input Parameters are variables from the table below:</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<b>Parameter<tab/>Aliases<tab/>
<tab/>Description [units]</b>
</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<b>
<sp count="6"/>
</b>T<tab/>
<sp count="5"/>
<tab/>Tdb<tab/>
<tab/>Dry-Bulb Temperature [K]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>B<tab/>
<tab/>Twb<tab/>
<tab/>Wet-Bulb Temperature [K]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>D<tab/>
<tab/>Tdp<tab/>
<tab/>Dew-Point Temperature [K]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>P<tab/>
<tab/>
<sp/>
<tab/>
<tab/>Pressure [kPa]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>V<tab/>
<tab/>Vda<tab/>
<tab/>Mixture volume [m3/kg dry air]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>R<tab/>
<tab/>RH<tab/>
<tab/>Relative humidity in (0,1) [-]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>W<tab/>
<tab/>Omega<tab/>
<tab/>Humidity Ratio [kg water/kg dry air]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>H<tab/>
<tab/>Hda<tab/>
<tab/>Mixture enthalpy [kJ/kg dry air]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>S<tab/>
<tab/>Sda<tab/>
<tab/>Mixture entropy [kJ/kg dry air/K]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>C<tab/>
<tab/>cp<tab/>
<tab/>Mixture specific heat [kJ/kg dry air/K]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>M<tab/>
<tab/>Visc<tab/>
<tab/>Mixture viscosity [Pa-s]</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
<sp count="6"/>K<tab/>
<tab/>
<sp/>
<tab/>
<tab/>Mixture thermal conductivity [kW/m/K]</p>
</text>
</region>
<region region-id="542" left="6" top="2001" width="83.25" height="11.25" align-x="21.75" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 4" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Examples, HAProp</p>
</text>
</region>
<region region-id="549" left="318" top="2007" width="147" height="45" align-x="336" align-y="2016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Enthalpy of humid air [kJ kg^-1] at a dry-bulb temperature of 298.15 K, a Pressure of 101.325 kPa, and relative humidity of 0.5 </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:id xml:space="preserve">h</ml:id>
<ml:eval placeholderMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">HAProp</ml:id>
<ml:sequence>
<ml:str xml:space="preserve">H</ml:str>
<ml:str xml:space="preserve">T</ml:str>
<ml:real>298.15</ml:real>
<ml:str xml:space="preserve">P</ml:str>
<ml:real>101.325</ml:real>
<ml:str xml:space="preserve">R</ml:str>
<ml:real>0.5</ml:real>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>50.424928343311421</ml:real>
</result>
</ml:eval>
</ml:define>
</math>
<rendering item-idref="11"/>
</region>
<region region-id="561" left="318" top="2079" width="143.25" height="22.5" align-x="342.75" align-y="2088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature of saturated air (R=1.0) at the previous enthalphy value </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:apply>
<ml:id xml:space="preserve">HAProp</ml:id>
<ml:sequence>
<ml:str xml:space="preserve">T</ml:str>
<ml:str xml:space="preserve">P</ml:str>
<ml:real>101.325</ml:real>
<ml:str xml:space="preserve">H</ml:str>
<ml:id xml:space="preserve">h</ml:id>
<ml:str xml:space="preserve">R</ml:str>
<ml:real>1.0</ml:real>
</ml:sequence>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>290.96216888804361</ml:real>
</result>
</ml:eval>
</math>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 3" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Arrays &amp; Plotting</p>
</text>
</region>
<region region-id="573" left="6" top="2163" width="456" height="22.5" align-x="18" align-y="2172" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Like all functions in Mathcad, the CoolProp wrapper function arguments can be array variables.<sp count="2"/>If one or more function arguments are arrays, the output will also be a single or multi-dimensional array. </p>
</text>
</region>
<region region-id="839" left="6" top="2205" width="44.25" height="11.25" align-x="24" align-y="2214" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 4" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Examples</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
<ml:id xml:space="preserve" subscript="H2O">T</ml:id>
<ml:range>
<ml:sequence>
<ml:apply>
<ml:mult/>
<ml:real>280</ml:real>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
<ml:apply>
<ml:mult/>
<ml:real>290</ml:real>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
</ml:sequence>
<ml:apply>
<ml:mult/>
<ml:real>400</ml:real>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
</ml:range>
</ml:define>
</math>
<rendering item-idref="13"/>
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