<description/> <author>Gene Massion</author> <company/> <keywords/> <revisedBy>delete</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>F1059CC3-69A6-4A38-9288-45D4D0B50E2E</documentID> <versionID>F93D30F4-ECEB-4A1B-8BF0-36B99B211EEB</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="120"/> <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="3" width="418.8" height="43.2" 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" width="38.4" height="12.6" align-x="19.2" 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="57" width="57" height="10.8" 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" width="40.2" height="12.6" align-x="138.6" 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="57" width="67.8" height="10.8" 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="81" width="61.2" height="21.6" 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="81" width="64.2" height="21.6" 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="93" width="64.2" height="10.8" 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="93" width="63.6" height="10.8" 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="123" width="48" height="10.8" 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" width="69.6" height="14.4" align-x="110.4" 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>.063</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="153" left="162" top="123" width="73.8" height="14.4" align-x="210.6" 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>.913</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="160" left="258" top="123" width="76.2" height="14.4" align-x="309" 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>.873</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="178" left="348" top="123" width="74.4" height="14.4" align-x="397.2" 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>.063</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="144" left="6" top="141" width="40.8" height="10.8" 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" width="67.2" height="14.4" align-x="108" 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>.062</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="154" left="162" top="141" width="71.4" height="14.4" align-x="208.2" 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>.911</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="166" left="258" top="141" width="73.8" height="14.4" align-x="306.6" 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>.871</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="179" left="348" top="141" width="72" height="14.4" align-x="394.8" 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>.061</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="145" left="6" top="159" width="43.8" height="10.8" 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" width="67.8" height="14.4" align-x="108.6" 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>.064</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="170" left="162" top="159" width="72" height="14.4" align-x="208.8" 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>.915</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="173" left="258" top="159" width="74.4" height="14.4" align-x="307.2" 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>.875</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="180" left="348" top="159" width="72.6" height="14.4" align-x="395.4" 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>.065</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="182" left="6" top="195" width="105.6" height="10.8" align-x="6" align-y="204" 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="207" width="57.6" height="14.4" align-x="18" align-y="216" 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="207" width="45.6" height="12.6" align-x="88.8" align-y="216" 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>0.063</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="207" width="64.8" height="14.4" align-x="176.4" align-y="216" 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="207" width="48" height="12.6" align-x="271.2" align-y="216" 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>0.063</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="449" left="6" top="225" width="62.4" height="14.4" align-x="18.6" align-y="234" 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="225" width="46.2" height="12.6" align-x="89.4" align-y="234" 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>0.913</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="225" width="65.4" height="14.4" align-x="175.2" align-y="234" 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="225" width="46.8" height="12.6" align-x="270" align-y="234" 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>0.873</ml:real> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="355" left="6" top="243" width="202.2" height="10.8" align-x="6" align-y="252" 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="261" width="64.8" height="10.8" align-x="18" align-y="270" 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="261" width="45" height="14.4" align-x="97.8" align-y="270" 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="261" width="30.6" height="14.4" align-x="150.6" align-y="270" 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</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="261" width="70.2" height="10.8" align-x="210" align-y="270" 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="261" width="46.8" height="14.4" align-x="304.2" align-y="270" 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="261" width="50.4" height="14.4" align-x="357" align-y="270" 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="26"/> </region> <region region-id="593" left="18" top="276.6" width="58.8" height="28.8" align-x="59.4" align-y="294" 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="276.6" width="65.4" height="28.8" align-x="165.6" align-y="294" 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="273.6" width="153.6" height="36.6" align-x="305.4" align-y="294" 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="309" width="63.6" height="12.6" align-x="58.2" align-y="318" 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>0</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="309" width="73.2" height="12.6" align-x="164.4" align-y="318" 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>-4.3811610076670355</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="309" width="75.6" height="12.6" align-x="304.2" align-y="318" 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>8.6113789778206549</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="333" width="22.2" height="12.6" align-x="22.2" align-y="342" 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="343.8" width="220.2" height="38.4" align-x="18.6" align-y="366" 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="343.8" width="223.8" height="38.4" align-x="243" align-y="366" 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="390.6" width="174.6" height="29.4" align-x="198.6" align-y="408" 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>117.23375142548633738</ml:real> <ml:real>88.006526557794330953</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="36"/> </region> <region region-id="305" left="6" top="447" width="199.8" height="10.8" align-x="6" align-y="456" 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="471" width="55.8" height="14.4" align-x="30" align-y="480" 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="471" width="45.6" height="12.6" align-x="100.8" align-y="480" 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>0.064</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="471" width="62.4" height="14.4" align-x="188.4" align-y="480" 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="471" width="48" height="12.6" align-x="283.2" align-y="480" 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>0.061</ml:real> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="490" left="18" top="489" width="60" height="14.4" align-x="30.6" align-y="498" 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="489" width="46.2" height="12.6" align-x="101.4" align-y="498" 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>0.911</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="489" width="63.6" height="14.4" align-x="187.2" align-y="498" 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="489" width="46.8" height="12.6" align-x="282" align-y="498" 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="44"/> </region> <region region-id="494" left="18" top="507" width="202.2" height="10.8" align-x="18" align-y="516" 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="525" width="64.8" height="10.8" align-x="30" align-y="534" 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="525" width="45" height="14.4" align-x="109.8" align-y="534" 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="525" width="52.8" height="14.4" align-x="162.6" align-y="534" 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>-0.0030000000000000027</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="525" width="70.2" height="10.8" align-x="222" align-y="534" 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="525" width="46.8" height="14.4" align-x="316.2" align-y="534" 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="525" width="55.2" height="14.4" align-x="369" align-y="534" 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>-0.036000000000000032</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="540.6" width="58.8" height="28.8" align-x="71.4" align-y="558" 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="540.6" width="65.4" height="28.8" align-x="177.6" align-y="558" 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="537.6" width="153.6" height="36.6" align-x="317.4" align-y="558" 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="573" width="69" height="12.6" align-x="70.2" 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: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>-4.6875000000000044</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="573" width="73.2" height="12.6" align-x="176.4" 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: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>-3.9517014270032962</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="573" width="75.6" height="12.6" align-x="316.2" 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: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>7.7402597402597406</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="603" width="22.2" height="12.6" align-x="22.2" align-y="612" 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="607.8" width="220.2" height="38.4" align-x="18.6" align-y="630" 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="607.8" width="223.8" height="38.4" align-x="243" align-y="630" 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="648.6" width="174.6" height="29.4" align-x="210.6" align-y="666" 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>73.87048978898635156</ml:real> <ml:real>78.779086006442701901</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="58"/> </region> <region region-id="541" left="6" top="711" width="203.4" height="10.8" align-x="6" align-y="720" 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="735" width="55.2" height="14.4" align-x="30" align-y="744" 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="735" width="45.6" height="12.6" align-x="100.8" align-y="744" 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>0.062</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="735" width="63" height="14.4" align-x="188.4" align-y="744" 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="735" width="48" height="12.6" align-x="283.2" align-y="744" 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>0.065</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="546" left="18" top="753" width="60.6" height="14.4" align-x="30.6" align-y="762" 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="753" width="46.2" height="12.6" align-x="101.4" align-y="762" 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>0.915</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="753" width="63" height="14.4" align-x="187.2" align-y="762" 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="753" width="46.8" height="12.6" align-x="282" align-y="762" 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>0.871</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="550" left="18" top="771" width="202.2" height="10.8" align-x="18" align-y="780" 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="789" width="64.8" height="10.8" align-x="30" align-y="798" 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="789" width="45" height="14.4" align-x="109.8" 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" 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="789" width="47.4" height="14.4" align-x="162.6" 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: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>0.0030000000000000027</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="789" width="70.2" height="10.8" align-x="222" align-y="798" 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" 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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="120"/> <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="3" width="418.8" height="43.2" 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" width="38.4" height="12.6" align-x="19.2" 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="57" width="57" height="10.8" 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" width="40.2" height="12.6" align-x="138.6" 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="57" width="67.8" height="10.8" 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="81" width="61.2" height="21.6" 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="81" width="64.2" height="21.6" 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="93" width="64.2" height="10.8" 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="93" width="63.6" height="10.8" 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="123" width="48" height="10.8" 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" width="69.6" height="14.4" align-x="110.4" 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>.063</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="153" left="162" top="123" width="73.8" height="14.4" align-x="210.6" 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>.913</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="160" left="258" top="123" width="76.2" height="14.4" align-x="309" 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>.873</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="178" left="348" top="123" width="74.4" height="14.4" align-x="397.2" 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="71.4" height="14.4" align-x="208.2" 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>.911</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="166" left="258" top="141" width="73.8" height="14.4" align-x="306.6" 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>.871</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="179" left="348" top="141" width="72" height="14.4" align-x="394.8" align-y="150" show-border="false" 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subscript="max">sealID</ml:id> <ml:real>.064</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="170" left="162" top="159" width="72" height="14.4" align-x="208.8" 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>.915</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="173" left="258" top="159" width="74.4" height="14.4" align-x="307.2" 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>.875</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="180" left="348" top="159" width="72.6" height="14.4" align-x="395.4" 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>.065</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="182" left="6" top="195" width="105.6" height="10.8" align-x="6" align-y="204" 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="207" width="57.6" height="14.4" align-x="18" align-y="216" 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="207" width="45.6" height="12.6" align-x="88.8" align-y="216" 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>0.063</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="207" width="64.8" height="14.4" align-x="176.4" align-y="216" 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="207" width="48" height="12.6" align-x="271.2" align-y="216" 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>0.063</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="449" left="6" top="225" width="62.4" height="14.4" align-x="18.6" align-y="234" 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="225" width="46.2" height="12.6" align-x="89.4" align-y="234" 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>0.913</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="225" width="65.4" height="14.4" align-x="175.2" align-y="234" 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="225" width="46.8" height="12.6" align-x="270" align-y="234" 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>0.873</ml:real> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="355" left="6" top="243" width="202.2" height="10.8" align-x="6" align-y="252" 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="261" width="64.8" height="10.8" align-x="18" align-y="270" 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="261" width="45" height="14.4" align-x="97.8" align-y="270" 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="261" width="30.6" height="14.4" align-x="150.6" align-y="270" 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</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="261" width="70.2" height="10.8" align-x="210" align-y="270" 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="261" width="46.8" height="14.4" align-x="304.2" align-y="270" 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="261" width="50.4" height="14.4" align-x="357" align-y="270" 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="26"/> </region> <region region-id="593" left="18" top="276.6" width="58.8" height="28.8" align-x="59.4" align-y="294" 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="276.6" width="65.4" height="28.8" align-x="165.6" align-y="294" 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="273.6" width="153.6" height="36.6" align-x="305.4" align-y="294" 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="309" width="63.6" height="12.6" align-x="58.2" align-y="318" 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>0</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="309" width="73.2" height="12.6" align-x="164.4" align-y="318" 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>-4.3811610076670355</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="309" width="75.6" height="12.6" align-x="304.2" align-y="318" 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>8.6113789778206549</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="333" width="22.2" height="12.6" align-x="22.2" align-y="342" 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="343.8" width="220.2" height="38.4" align-x="18.6" align-y="366" 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="343.8" width="223.8" height="38.4" align-x="243" align-y="366" 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="390.6" width="174.6" height="29.4" align-x="198.6" align-y="408" 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>117.23375142548633738</ml:real> <ml:real>88.006526557794330953</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="36"/> </region> <region region-id="305" left="6" top="447" width="199.8" height="10.8" align-x="6" align-y="456" 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="471" width="55.8" height="14.4" align-x="30" align-y="480" 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="471" width="45.6" height="12.6" align-x="100.8" align-y="480" 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>0.064</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="471" width="62.4" height="14.4" align-x="188.4" align-y="480" 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="471" width="48" height="12.6" align-x="283.2" align-y="480" 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>0.061</ml:real> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="490" left="18" top="489" width="60" height="14.4" align-x="30.6" align-y="498" 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="489" width="46.2" height="12.6" align-x="101.4" align-y="498" 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>0.911</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="489" width="63.6" height="14.4" align-x="187.2" align-y="498" 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="489" width="46.8" height="12.6" align-x="282" align-y="498" 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="44"/> </region> <region region-id="494" left="18" top="507" width="202.2" height="10.8" align-x="18" align-y="516" 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="525" width="64.8" height="10.8" align-x="30" align-y="534" 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="525" width="45" height="14.4" align-x="109.8" align-y="534" 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="525" width="52.8" height="14.4" align-x="162.6" align-y="534" 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>-0.0030000000000000027</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="525" width="70.2" height="10.8" align-x="222" align-y="534" 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="525" width="46.8" height="14.4" align-x="316.2" align-y="534" 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="525" width="55.2" height="14.4" align-x="369" align-y="534" 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>-0.036000000000000032</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="540.6" width="58.8" height="28.8" align-x="71.4" align-y="558" 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="540.6" width="65.4" height="28.8" align-x="177.6" align-y="558" 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="537.6" width="153.6" height="36.6" align-x="317.4" align-y="558" 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="573" width="69" height="12.6" align-x="70.2" 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: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>-4.6875000000000044</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="573" width="73.2" height="12.6" align-x="176.4" 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: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>-3.9517014270032962</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="573" width="75.6" height="12.6" align-x="316.2" 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: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>7.7402597402597406</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="603" width="22.2" height="12.6" align-x="22.2" align-y="612" 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="607.8" width="220.2" height="38.4" align-x="18.6" align-y="630" 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="607.8" width="223.8" height="38.4" align-x="243" align-y="630" 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="648.6" width="174.6" height="29.4" align-x="210.6" align-y="666" 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>73.87048978898635156</ml:real> <ml:real>78.779086006442701901</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="58"/> </region> <region region-id="541" left="6" top="711" width="203.4" height="10.8" align-x="6" align-y="720" 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="735" width="55.2" height="14.4" align-x="30" align-y="744" 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="735" width="45.6" height="12.6" align-x="100.8" align-y="744" 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>0.062</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="735" width="63" height="14.4" align-x="188.4" align-y="744" 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="735" width="48" height="12.6" align-x="283.2" align-y="744" 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>0.065</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="546" left="18" top="753" width="60.6" height="14.4" align-x="30.6" align-y="762" 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="753" width="46.2" height="12.6" align-x="101.4" align-y="762" 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>0.915</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="753" width="63" height="14.4" align-x="187.2" align-y="762" 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="753" width="46.8" height="12.6" align-x="282" align-y="762" 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>0.871</ml:real> </result> </ml:eval> </math> <rendering item-idref="66"/> </region> <region region-id="550" left="18" top="771" width="202.2" height="10.8" align-x="18" align-y="780" 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="789" width="64.8" height="10.8" align-x="30" align-y="798" 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="789" width="45" height="14.4" align-x="109.8" 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" 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="789" width="47.4" height="14.4" align-x="162.6" 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: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>0.0030000000000000027</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="789" width="70.2" height="10.8" align-x="222" align-y="798" 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="789" width="46.8" height="14.4" align-x="316.2" 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" 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="789" width="55.2" height="14.4" align-x="369" 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: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>-0.044000000000000039</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="810.6" width="58.8" height="28.8" align-x="71.4" align-y="828" 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="810.6" width="65.4" height="28.8" align-x="177.6" align-y="828" 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="807.6" width="153.6" height="36.6" align-x="317.4" align-y="828" 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="843" width="63.6" height="12.6" align-x="70.2" align-y="852" 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>4.8387096774193585</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="843" width="73.2" height="12.6" align-x="176.4" align-y="852" 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>-4.8087431693989107</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="843" width="75.6" height="12.6" align-x="316.2" align-y="852" 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>9.4752580152415469</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="867" width="22.2" height="12.6" align-x="16.2" 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: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="883.8" width="220.2" height="38.4" align-x="18.6" align-y="906" 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="883.8" width="223.8" height="38.4" align-x="243" align-y="906" 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> 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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="930.6" width="174.6" height="29.4" align-x="210.6" align-y="948" 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>161.52722357096563333</ml:real> <ml:real>97.167965086520923907</ml:real> </ml:matrix> </ml:symResult> 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