<description/> <author>Gene Massion</author> <company/> <keywords/> <revisedBy>Gene Massion</revisedBy> </userData> <identityInfo> <revision>3</revision> <documentID>02BA871C-0B02-4AD4-BBFB-1D1FA1BF33C3</documentID> <versionID>7C39F620-736A-4C58-837C-A2CB9639F199</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr 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<currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="144"/> <miscellaneous> <handbook handbook-region-tag-ub="603" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="63" left="6" top="2.5" width="419" height="46" align-x="6" align-y="12" 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"> This spread sheet caclulates the radial pressures at the inner and outer surfaces of a Morrision type seal given a change in inner radius and outer radius dimensions.<sp count="2"/>It uses the formula for a axisymmetric cylinder subjected to internal and external pressure given in Strength of Materials, Part II, 3rd edition;Timoshenko;page 210 equation 178. </text> </region> <region region-id="85" left="6" top="57.5" width="38.5" height="12" align-x="19" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">υ</ml:id> <ml:real>.499</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="86" left="54" top="56.5" width="57" height="11.5" align-x="54" align-y="66" 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"> Poisson ratio </text> </region> <region region-id="136" left="126" top="57.5" width="41" height="12" align-x="139" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:real>1000</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="137" left="174" top="56.5" width="68" height="11.5" align-x="174" align-y="66" 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"> Elastic modulus </text> </region> <region region-id="416" left="72" top="80.5" width="61" height="34.5" align-x="72" align-y="90" 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"> Seal Inner Diameter </text> </region> <region region-id="412" left="156" top="80.5" width="64" height="34.5" align-x="156" align-y="90" 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"> Seal Outer Diameter </text> </region> <region region-id="413" left="264" top="92.5" width="64" height="11.5" align-x="264" align-y="102" 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"> Bore Diameter </text> </region> <region region-id="414" left="348" top="92.5" width="63.5" height="11.5" align-x="348" align-y="102" 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"> Wire Diameter </text> </region> <region region-id="139" left="6" top="122.5" width="48" height="11.5" align-x="6" align-y="132" 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"> nominal val </text> </region> <region region-id="135" left="66" top="123.5" width="71.5" height="14" align-x="112" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">sealID</ml:id> <ml:real>.057</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="153" left="162" top="123.5" width="75.5" height="14" align-x="212" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">sealOD</ml:id> <ml:real>.917</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="160" left="258" top="123.5" width="78" height="14" align-x="310.5" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">boreDia</ml:id> <ml:real>.875</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="178" left="348" top="123.5" width="79" height="14" align-x="401.5" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">wireDia</ml:id> <ml:real>.058</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="144" left="6" top="140.5" width="40.5" height="11.5" align-x="6" align-y="150" 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"> min value </text> </region> <region region-id="146" left="66" top="141.5" width="69" height="14" align-x="109.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="min">sealID</ml:id> <ml:real>.055</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="154" left="162" top="141.5" width="73" height="14" align-x="209.5" align-y="150" 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<rendering item-idref="11"/> </region> <region region-id="170" left="162" top="159.5" width="75" height="14" align-x="211.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">sealOD</ml:id> <ml:real>.920</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="173" left="258" top="159.5" width="77.5" height="14" align-x="310" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">boreDia</ml:id> <ml:real>.877</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="180" left="348" top="159.5" width="78.5" height="14" align-x="401" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">wireDia</ml:id> <ml:real>.060</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="182" left="6" top="182.5" width="105.5" height="11.5" align-x="6" align-y="192" 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"> NOMINAL CONDITION: </text> </region> <region region-id="183" left="6" top="195.5" width="59" height="14" align-x="18" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="nom">sealID</ml:id> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="190" left="78" top="195.5" width="46.5" height="12" align-x="89" align-y="204" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.057</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" 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xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.058</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="449" left="6" top="213.5" width="63" height="14" align-x="18" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="nom">sealOD</ml:id> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="450" left="78" top="213.5" width="46.5" height="12" align-x="89" align-y="222" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.917</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="20"/> </region> <region region-id="452" left="162" top="213.5" width="67" height="14" align-x="175.5" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="nom">boreDia</ml:id> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="454" left="258" top="213.5" width="48" height="12" align-x="270.5" align-y="222" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.875</ml:real> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="355" left="6" top="230.5" width="202" height="11.5" align-x="6" align-y="240" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="372" left="18" top="248.5" width="65" height="11.5" align-x="18" align-y="258" 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"> ID deformation </text> </region> <region region-id="373" left="84" top="249.5" width="44" height="14" align-x="97" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="457" left="138" top="249.5" width="47.5" height="14" align-x="150" align-y="258" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0010000000000000009</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="24"/> </region> <region region-id="461" left="210" top="248.5" width="70" height="11.5" align-x="210" align-y="258" 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"> OD deformation </text> </region> <region region-id="462" left="288" top="249.5" width="45.5" height="14" align-x="303.5" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="464" left="342" top="249.5" width="55.5" height="14" align-x="356.5" align-y="258" 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:id xml:space="preserve" subscript="o">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.042000000000000037</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="26"/> </region> <region region-id="593" left="18" top="264.5" width="60" height="28" align-x="61" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="594" left="120" top="264.5" width="66.5" height="28" align-x="167" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ODstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="595" left="252" top="262" width="159" height="35" align-x="308.5" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">areaSqueeze</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="596" left="18" top="297.5" width="66" height="12" align-x="60" align-y="306" 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:id xml:space="preserve">IDstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.7543859649122824</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="30"/> </region> <region region-id="597" left="120" top="297.5" width="75.5" height="12" align-x="166" align-y="306" 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:id xml:space="preserve">ODstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.5801526717557293</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="31"/> </region> <region region-id="598" left="252" top="297.5" width="79.5" height="12" align-x="307.5" align-y="306" 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:id xml:space="preserve">areaSqueeze</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.9989733059548467</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="32"/> </region> <region region-id="603" left="12" top="321.5" width="24.5" height="12" align-x="23.5" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="33"/> </region> <region region-id="599" left="6" top="332" width="228" height="37" align-x="18" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="600" left="228" top="332" width="230.5" height="37" align-x="242.5" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="601" left="144" top="379.5" width="179.5" height="28.5" align-x="198.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:sequence> </ml:apply> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:real>134.33297452641958752</ml:real> <ml:real>92.074544662056639607</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="36"/> </region> <region region-id="305" left="6" top="416.5" width="200" height="11.5" align-x="6" align-y="426" 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"> MINIMUM RADIAL PRESSURE CONDITION: </text> </region> <region region-id="486" left="18" top="441.5" width="58.5" height="14" align-x="30" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="max">sealID</ml:id> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="487" left="90" top="441.5" width="46.5" height="12" align-x="101" align-y="450" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.059</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="38"/> </region> <region region-id="488" left="174" top="441.5" width="66.5" height="14" align-x="188.5" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve" subscript="min">wireDia</ml:id> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="489" left="270" top="441.5" width="49" height="12" align-x="283.5" align-y="450" 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:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.056</ml:real> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="490" left="18" top="459.5" width="60.5" height="14" align-x="30" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="min">sealOD</ml:id> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="491" left="90" top="459.5" width="46.5" height="12" align-x="101" align-y="468" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.917</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="42"/> </region> <region region-id="492" left="174" top="459.5" width="66.5" height="14" align-x="187.5" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="max">boreDia</ml:id> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="493" left="270" top="459.5" width="48" height="12" align-x="282.5" align-y="468" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.877</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="494" left="18" top="476.5" width="202" height="11.5" align-x="18" align-y="486" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="495" left="30" top="494.5" width="65" height="11.5" align-x="30" 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="true"> ID deformation </text> </region> <region region-id="496" left="96" top="495.5" width="44" height="14" align-x="109" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="497" left="150" top="495.5" width="53" height="14" align-x="162" align-y="504" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.0029999999999999957</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="46"/> </region> <region region-id="498" left="222" top="494.5" width="70" height="11.5" align-x="222" 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="true"> OD deformation </text> </region> <region region-id="499" left="300" top="495.5" width="45.5" height="14" align-x="315.5" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="500" left="354" top="495.5" width="50.5" height="14" align-x="368.5" align-y="504" 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:id xml:space="preserve" subscript="o">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.040000000000000036</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="48"/> </region> <region region-id="584" left="30" top="510.5" width="60" height="28" align-x="73" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="585" left="132" top="510.5" width="66.5" height="28" align-x="179" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ODstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="586" left="264" top="508" width="159" height="35" align-x="320.5" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">areaSqueeze</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="587" left="30" top="543.5" width="71.5" height="12" align-x="72" 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:id xml:space="preserve">IDstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-5.0847457627118571</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="52"/> </region> <region region-id="588" left="132" top="543.5" width="75.5" height="12" align-x="178" 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:id xml:space="preserve">ODstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.3620501635768845</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="53"/> </region> <region region-id="589" left="264" top="543.5" width="79.5" height="12" align-x="319.5" 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:id xml:space="preserve">areaSqueeze</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.5281009973633175</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="54"/> </region> <region region-id="571" left="12" top="573.5" width="24.5" height="12" align-x="23.5" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="55"/> </region> <region region-id="590" left="6" top="578" width="228" height="37" align-x="18" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <region region-id="591" left="228" top="578" width="230.5" height="37" align-x="242.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="57"/> </region> <region region-id="592" left="156" top="619.5" width="179.5" height="28.5" align-x="210.5" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:sequence> </ml:apply> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:real>82.165680515602565025</ml:real> <ml:real>86.986865299691846368</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="58"/> </region> <region region-id="541" left="6" top="680.5" width="203.5" height="11.5" align-x="6" align-y="690" 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"> MAXIMUM RADIAL PRESSURE CONDITION: </text> </region> <region region-id="542" left="18" top="705.5" width="56.5" height="14" align-x="30" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="min">sealID</ml:id> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="543" left="90" top="705.5" width="46.5" height="12" align-x="101" align-y="714" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.055</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="60"/> </region> <region region-id="544" left="174" top="705.5" width="68.5" height="14" align-x="188.5" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve" subscript="max">wireDia</ml:id> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="545" left="270" top="705.5" width="44" height="12" align-x="283.5" align-y="714" 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:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.06</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="546" left="18" top="723.5" width="62.5" height="14" align-x="30" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="max">sealOD</ml:id> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="547" left="90" top="723.5" width="41.5" height="12" align-x="101" align-y="732" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.92</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="64"/> </region> <region region-id="548" left="174" top="723.5" width="64.5" height="14" align-x="187.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="min">boreDia</ml:id> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="549" left="270" top="723.5" width="48" height="12" align-x="282.5" align-y="732" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.875</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="550" left="18" top="740.5" width="202" height="11.5" align-x="18" align-y="750" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="551" left="30" top="758.5" width="65" height="11.5" align-x="30" align-y="768" 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"> ID deformation </text> </region> <region region-id="552" left="96" top="759.5" width="44" height="14" align-x="109" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="553" left="150" top="759.5" width="47.5" height="14" align-x="162" align-y="768" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0049999999999999975</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="68"/> </region> <region region-id="554" left="222" top="758.5" width="70" height="11.5" align-x="222" align-y="768" 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"> OD deformation </text> 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</calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="144"/> <miscellaneous> <handbook handbook-region-tag-ub="603" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="63" left="6" top="2.5" width="419" height="46" align-x="6" align-y="12" 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"> This spread sheet caclulates the radial pressures at the inner and outer surfaces of a Morrision type seal given a change in inner radius and outer radius dimensions.<sp count="2"/>It uses the formula for a axisymmetric cylinder subjected to internal and external pressure given in Strength of Materials, Part II, 3rd edition;Timoshenko;page 210 equation 178. </text> </region> <region region-id="85" left="6" top="57.5" width="38.5" height="12" align-x="19" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">υ</ml:id> <ml:real>.499</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="86" left="54" top="56.5" width="57" height="11.5" align-x="54" align-y="66" 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"> Poisson ratio </text> </region> <region region-id="136" left="126" top="57.5" width="41" height="12" align-x="139" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E</ml:id> <ml:real>1000</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="137" left="174" top="56.5" width="68" height="11.5" align-x="174" align-y="66" 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"> Elastic modulus </text> </region> <region region-id="416" left="72" top="80.5" width="61" height="34.5" align-x="72" align-y="90" 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"> Seal Inner Diameter </text> </region> <region region-id="412" left="156" top="80.5" width="64" height="34.5" align-x="156" align-y="90" 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"> Seal Outer Diameter </text> </region> <region region-id="413" left="264" top="92.5" width="64" height="11.5" align-x="264" align-y="102" 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"> Bore Diameter </text> </region> <region region-id="414" left="348" top="92.5" width="63.5" height="11.5" align-x="348" align-y="102" 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"> Wire Diameter </text> </region> <region region-id="139" left="6" top="122.5" width="48" height="11.5" align-x="6" align-y="132" 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"> nominal val </text> </region> <region region-id="135" left="66" top="123.5" width="71.5" height="14" align-x="112" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">sealID</ml:id> <ml:real>.057</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="153" left="162" top="123.5" width="75.5" height="14" align-x="212" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">sealOD</ml:id> <ml:real>.917</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="160" left="258" top="123.5" width="78" height="14" align-x="310.5" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="nom">boreDia</ml:id> <ml:real>.875</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="178" left="348" top="123.5" width="79" height="14" align-x="401.5" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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width="73" height="14" align-x="209.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="min">sealOD</ml:id> <ml:real>.917</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="166" left="258" top="141.5" width="75.5" height="14" align-x="308" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="min">boreDia</ml:id> <ml:real>.875</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="179" left="348" top="141.5" width="76.5" height="14" align-x="399" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="min">wireDia</ml:id> <ml:real>.056</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="145" left="6" top="158.5" width="43.5" height="11.5" align-x="6" align-y="168" 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"> max value </text> </region> <region region-id="169" left="66" top="159.5" width="71" height="14" align-x="111.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">sealID</ml:id> <ml:real>.059</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="170" left="162" top="159.5" width="75" height="14" align-x="211.5" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">sealOD</ml:id> <ml:real>.920</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="173" left="258" top="159.5" width="77.5" height="14" align-x="310" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">boreDia</ml:id> <ml:real>.877</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="180" left="348" top="159.5" width="78.5" height="14" align-x="401" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="max">wireDia</ml:id> <ml:real>.060</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="182" left="6" top="182.5" width="105.5" height="11.5" align-x="6" align-y="192" 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"> NOMINAL CONDITION: </text> </region> <region region-id="183" left="6" top="195.5" width="59" height="14" align-x="18" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="nom">sealID</ml:id> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="190" left="78" top="195.5" width="46.5" height="12" align-x="89" align-y="204" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.057</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="16"/> </region> <region region-id="451" left="162" top="195.5" width="69" height="14" align-x="176.5" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve" subscript="nom">wireDia</ml:id> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="453" left="258" top="195.5" width="49" height="12" align-x="271.5" align-y="204" 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:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.058</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="449" left="6" top="213.5" width="63" height="14" align-x="18" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="nom">sealOD</ml:id> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="450" left="78" top="213.5" width="46.5" height="12" align-x="89" align-y="222" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.917</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="20"/> </region> <region region-id="452" left="162" top="213.5" width="67" height="14" align-x="175.5" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="nom">boreDia</ml:id> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="454" left="258" top="213.5" width="48" height="12" align-x="270.5" align-y="222" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.875</ml:real> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="355" left="6" top="230.5" width="202" height="11.5" align-x="6" align-y="240" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="372" left="18" top="248.5" width="65" height="11.5" align-x="18" align-y="258" 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"> ID deformation </text> </region> <region region-id="373" left="84" top="249.5" width="44" height="14" align-x="97" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="457" left="138" top="249.5" width="47.5" height="14" align-x="150" align-y="258" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0010000000000000009</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="24"/> </region> <region region-id="461" left="210" top="248.5" width="70" height="11.5" align-x="210" align-y="258" 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"> OD deformation </text> </region> <region region-id="462" left="288" top="249.5" width="45.5" height="14" align-x="303.5" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="464" left="342" top="249.5" width="55.5" height="14" align-x="356.5" align-y="258" 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:id xml:space="preserve" subscript="o">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.042000000000000037</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="26"/> </region> <region region-id="593" left="18" top="264.5" width="60" height="28" align-x="61" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="594" left="120" top="264.5" width="66.5" height="28" align-x="167" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ODstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="595" left="252" top="262" width="159" height="35" align-x="308.5" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">areaSqueeze</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="596" left="18" top="297.5" width="66" height="12" align-x="60" align-y="306" 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:id xml:space="preserve">IDstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.7543859649122824</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="30"/> </region> <region region-id="597" left="120" top="297.5" width="75.5" height="12" align-x="166" align-y="306" 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:id xml:space="preserve">ODstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.5801526717557293</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="31"/> </region> <region region-id="598" left="252" top="297.5" width="79.5" height="12" align-x="307.5" align-y="306" 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:id xml:space="preserve">areaSqueeze</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.9989733059548467</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="32"/> </region> <region region-id="603" left="12" top="321.5" width="24.5" height="12" align-x="23.5" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="33"/> </region> <region region-id="599" left="6" top="332" width="228" height="37" align-x="18" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="600" left="228" top="332" width="230.5" height="37" align-x="242.5" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="601" left="144" top="379.5" width="179.5" height="28.5" align-x="198.5" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:sequence> </ml:apply> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:real>134.33297452641958752</ml:real> <ml:real>92.074544662056639607</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="36"/> </region> <region region-id="305" left="6" top="416.5" width="200" height="11.5" align-x="6" align-y="426" 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"> MINIMUM RADIAL PRESSURE CONDITION: </text> </region> <region region-id="486" left="18" top="441.5" width="58.5" height="14" align-x="30" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="max">sealID</ml:id> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="487" left="90" top="441.5" width="46.5" height="12" align-x="101" align-y="450" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.059</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="38"/> </region> <region region-id="488" left="174" top="441.5" width="66.5" height="14" align-x="188.5" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve" subscript="min">wireDia</ml:id> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="489" left="270" top="441.5" width="49" height="12" align-x="283.5" align-y="450" 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:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.056</ml:real> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="490" left="18" top="459.5" width="60.5" height="14" align-x="30" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="min">sealOD</ml:id> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="491" left="90" top="459.5" width="46.5" height="12" align-x="101" align-y="468" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.917</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="42"/> </region> <region region-id="492" left="174" top="459.5" width="66.5" height="14" align-x="187.5" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="max">boreDia</ml:id> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="493" left="270" top="459.5" width="48" height="12" align-x="282.5" align-y="468" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.877</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="494" left="18" top="476.5" width="202" height="11.5" align-x="18" align-y="486" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="495" left="30" top="494.5" width="65" height="11.5" align-x="30" 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="true"> ID deformation </text> </region> <region region-id="496" left="96" top="495.5" width="44" height="14" align-x="109" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="497" left="150" top="495.5" width="53" height="14" align-x="162" align-y="504" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.0029999999999999957</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="46"/> </region> <region region-id="498" left="222" top="494.5" width="70" height="11.5" align-x="222" 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="true"> OD deformation </text> </region> <region region-id="499" left="300" top="495.5" width="45.5" height="14" align-x="315.5" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="500" left="354" top="495.5" width="50.5" height="14" align-x="368.5" align-y="504" 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:id xml:space="preserve" subscript="o">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.040000000000000036</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="48"/> </region> <region region-id="584" left="30" top="510.5" width="60" height="28" align-x="73" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="585" left="132" top="510.5" width="66.5" height="28" align-x="179" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ODstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="586" left="264" top="508" width="159" height="35" align-x="320.5" 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:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">areaSqueeze</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="587" left="30" top="543.5" width="71.5" height="12" align-x="72" 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:id xml:space="preserve">IDstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-5.0847457627118571</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="52"/> </region> <region region-id="588" left="132" top="543.5" width="75.5" height="12" align-x="178" 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:id xml:space="preserve">ODstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.3620501635768845</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="53"/> </region> <region region-id="589" left="264" top="543.5" width="79.5" height="12" align-x="319.5" 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:id xml:space="preserve">areaSqueeze</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.5281009973633175</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="54"/> </region> <region region-id="571" left="12" top="573.5" width="24.5" height="12" align-x="23.5" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="55"/> </region> <region region-id="590" left="6" top="578" width="228" height="37" align-x="18" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <region region-id="591" left="228" top="578" width="230.5" height="37" align-x="242.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="57"/> </region> <region region-id="592" left="156" top="619.5" width="179.5" height="28.5" align-x="210.5" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:Find auto-method="true" method="conjugate" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:sequence> </ml:apply> <ml:symResult> <ml:matrix rows="2" cols="1"> <ml:real>82.165680515602565025</ml:real> <ml:real>86.986865299691846368</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="58"/> </region> <region region-id="541" left="6" top="680.5" width="203.5" height="11.5" align-x="6" align-y="690" 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"> MAXIMUM RADIAL PRESSURE CONDITION: </text> </region> <region region-id="542" left="18" top="705.5" width="56.5" height="14" align-x="30" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve" subscript="min">sealID</ml:id> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="543" left="90" top="705.5" width="46.5" height="12" align-x="101" align-y="714" 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:id xml:space="preserve">a</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.055</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="60"/> </region> <region region-id="544" left="174" top="705.5" width="68.5" height="14" align-x="188.5" align-y="714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve" subscript="max">wireDia</ml:id> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="545" left="270" top="705.5" width="44" height="12" align-x="283.5" align-y="714" 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:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.06</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="546" left="18" top="723.5" width="62.5" height="14" align-x="30" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve" subscript="max">sealOD</ml:id> </ml:define> </math> <rendering item-idref="63"/> </region> <region region-id="547" left="90" top="723.5" width="41.5" height="12" align-x="101" align-y="732" 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:id xml:space="preserve">b</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.92</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="64"/> </region> <region region-id="548" left="174" top="723.5" width="64.5" height="14" align-x="187.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve" subscript="min">boreDia</ml:id> </ml:define> </math> <rendering item-idref="65"/> </region> <region region-id="549" left="270" top="723.5" width="48" height="12" align-x="282.5" align-y="732" 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:id xml:space="preserve">B</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.875</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="550" left="18" top="740.5" width="202" height="11.5" align-x="18" align-y="750" 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"> Seal deformation (-deformation is toward CL): </text> </region> <region region-id="551" left="30" top="758.5" width="65" height="11.5" align-x="30" align-y="768" 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"> ID deformation </text> </region> <region region-id="552" left="96" top="759.5" width="44" height="14" align-x="109" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="553" left="150" top="759.5" width="47.5" height="14" align-x="162" align-y="768" 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:id xml:space="preserve" subscript="i">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.0049999999999999975</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="68"/> </region> <region region-id="554" left="222" top="758.5" width="70" height="11.5" align-x="222" align-y="768" 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"> OD deformation </text> </region> <region region-id="555" left="300" top="759.5" width="45.5" height="14" align-x="315.5" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="556" left="354" top="759.5" width="55.5" height="14" align-x="368.5" align-y="768" 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:id xml:space="preserve" subscript="o">u</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.04500000000000004</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="70"/> </region> <region region-id="557" left="30" top="780.5" width="60" height="28" align-x="73" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">IDstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="558" left="132" top="780.5" width="66.5" height="28" align-x="179" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ODstretch</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="559" left="264" top="778" width="159" height="35" align-x="320.5" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">areaSqueeze</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="560" left="30" top="813.5" width="66" height="12" align-x="72" align-y="822" 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:id xml:space="preserve">IDstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>9.0909090909090864</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="74"/> </region> <region region-id="561" left="132" top="813.5" width="75.5" height="12" align-x="178" align-y="822" 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:id xml:space="preserve">ODstretch</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-4.8913043478260914</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="75"/> </region> <region region-id="562" left="264" top="813.5" width="84.5" height="12" align-x="319.5" align-y="822" 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:id xml:space="preserve">areaSqueeze</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>9.64576848969913</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="0" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="5"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="76"/> </region> <region region-id="568" left="6" top="837.5" width="24.5" height="12" align-x="17.5" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="77"/> </region> <region region-id="576" left="6" top="854" width="228" height="37" align-x="18" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="i">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="78"/> </region> <region region-id="577" left="228" top="854" width="230.5" height="37" align-x="242.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:id xml:space="preserve" subscript="o">u</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="i">p</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">υ</ml:id> </ml:apply> <ml:id xml:space="preserve">E</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="i">p</ml:id> <ml:id xml:space="preserve" subscript="o">p</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">b</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="79"/> </region> <region region-id="566" left="156" top="901.5" 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