Mathcad Professional 14.0 <description/> <author>mbari 1215</author> <company/> <keywords/> <revisedBy>jon</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>D7E36D06-8E0F-41AA-BC17-F0461E1FBDA9</documentID> <versionID>529CBC31-F5BB-4DAE-89B2-CB0F799135F2</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="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" 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underline="false"/> <mathStyle name="User 5" font-family="Roman" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Modern" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results 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="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="72" right="14.04" top="36" bottom="36"/> <header use-full-page-width="true"/> <footer use-full-page-width="true"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="us" 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="false" save-text-images="false" screen-dpi="120"/> <miscellaneous> <handbook handbook-region-tag-ub="545" 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="238" left="72" top="7.2" width="369.6" height="27.6" align-x="72" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <b>Heat Flow thru a cylindrical wall PV to External Sea Water.</b> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <b>09</b> <b>/06/17</b> </p> </text> </region> <region region-id="541" left="96" top="48" width="373.8" height="211.8" align-x="96" align-y="48" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="1"/> <rendering item-idref="2"/> </region> <region region-id="1" left="6" top="271.2" width="75" height="13.8" align-x="6" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <b>REQUIRED:<sp count="5"/> </b> </p> </text> </region> <region region-id="215" left="96" top="271.8" width="387.6" height="13.2" align-x="96" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Find the interior air temp. for a given convective/conductive heat flow to CH2O.<sp count="2"/> </p> </text> </region> <region region-id="3" left="6" top="313.2" width="44.4" height="13.8" align-x="6" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <b>GIVEN:<sp count="2"/> </b> </p> </text> </region> <region region-id="317" left="6" top="331.8" width="78" height="13.2" align-x="6" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">PV TUBE:<sp count="9"/> </p> </text> </region> <region region-id="318" left="162" top="331.8" width="89.4" height="13.2" align-x="162" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">6AL-4V Titanium<sp count="2"/> </p> </text> </region> <region region-id="308" left="78" top="355.8" width="66" height="13.2" align-x="78" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">ID dia. (d):<sp count="4"/> </p> </text> </region> <region region-id="309" left="342" top="357" width="53.4" height="12.6" align-x="354" 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:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:mult/> <ml:real>5.250</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="311" left="78" top="379.8" width="76.2" height="13.2" align-x="91.8" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">OD dia. (D):<sp count="5"/> </p> </text> </region> <region region-id="312" left="342" top="381" width="55.8" height="12.6" align-x="356.4" align-y="390" 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">D</ml:id> <ml:apply> <ml:mult/> <ml:real>5.875</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="320" left="78" top="403.8" width="138" height="13.2" align-x="85.2" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Case Length in.<sp count="2"/>(L):<sp count="2"/> </p> </text> </region> <region region-id="315" left="342" top="405" width="49.8" height="12.6" align-x="355.2" align-y="414" 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">L</ml:id> <ml:apply> <ml:mult/> <ml:real>15.0</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="410" left="78" top="427.8" width="138" height="13.2" align-x="93.6" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Thermal Conductivity. (k):<sp count="4"/> </p> </text> </region> <region region-id="414" left="342" top="422.4" width="58.2" height="27" align-x="354" align-y="438" 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">k</ml:id> <ml:apply> <ml:mult/> <ml:real>6.7</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">W</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="339" left="6" top="463.8" width="193.8" height="13.2" align-x="6" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">INTERIOR AIR (forced convection)<sp count="7"/> </p> </text> </region> <region region-id="494" left="30" top="487.8" width="88.2" height="13.2" align-x="35.4" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Air Velocity (v):<sp count="3"/> </p> </text> </region> <region region-id="506" left="342" top="482.4" width="57.6" height="27" align-x="354" 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 xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v</ml:id> <ml:apply> <ml:mult/> <ml:real>2.16</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="496" left="30" top="517.8" width="162" height="13.2" align-x="41.4" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Convection Coeff.<sp count="2"/>(h.i) (5-37):<sp count="4"/> </p> </text> </region> <region region-id="511" left="30" top="534.6" width="215.4" height="33" align-x="43.8" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">h</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>10.45</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">W</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">v</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">W</ml:id> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">v</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">W</ml:id> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="515" left="342" top="536.4" width="76.8" height="31.2" align-x="354.6" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">h</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">W</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>22.986938456699068</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="coulomb" power-numerator="-1"/> <unitReference unit="meter" power-numerator="-2"/> <unitReference unit="watt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="9"/> </region> <region region-id="499" left="30" top="601.8" width="109.8" height="13.2" align-x="30" align-y="612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Free Air Temp<sp count="2"/>(T.i):<sp count="3"/> </p> </text> </region> <region region-id="508" left="342" top="603" width="39" height="14.4" align-x="356.4" align-y="612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This placeholder is empty." optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">T</ml:id> <ml:apply> <ml:mult/> <ml:placeholder/> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="545" left="342" top="630.6" width="80.4" height="28.8" align-x="402.6" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math error="This variable is undefined." optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">T</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:real>9</ml:real> <ml:real>5</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:real>32</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="11"/> </region> <region region-id="542" left="30" top="673.8" width="144" height="13.2" align-x="30" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Interior Heat Transfered (Q):<sp count="2"/> </p> </text> </region> <region region-id="543" left="342" top="675" width="45.6" height="12.6" align-x="356.4" align-y="684" 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">Q</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">W</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="416" left="6" top="733.8" width="187.8" height="13.2" align-x="28.8" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">EXTERIOR WATER (free convection):</p> </text> </region> <region region-id="418" left="78" top="751.8" width="183" height="13.2" align-x="99.6" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Convection Coeff:<sp count="2"/>(h.o) (100-1200):<sp count="2"/> </p> </text> </region> <region region-id="419" left="342" top="746.4" width="69" height="31.2" align-x="358.2" 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 xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="o">h</ml:id> <ml:apply> <ml:mult/> <ml:real>300</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">W</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="458" left="78" top="781.8" width="118.2" height="13.2" align-x="86.4" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Free Water Temp (T.o):<sp count="2"/> </p> </text> </region> <region region-id="459" left="342" top="783" width="43.8" height="14.4" align-x="358.8" align-y="792" 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">T</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>7.0</ml:real> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="9" left="6" top="811.2" width="72.6" height="13.8" align-x="6" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <b>ASSUME:</b> </p> </text> </region> <region region-id="421" left="6" top="835.8" width="99.6" height="13.2" align-x="9" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. Thick Wall Tube.<sp count="2"/> </p> </text> </region> <region region-id="258" left="6" top="883.2" width="93.6" height="13.8" align-x="6" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <b>SOLUTION:</b> </p> </text> </region> <region region-id="425" left="12" top="896.4" width="44.4" height="27" align-x="39.6" align-y="912" 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="inner">r</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">d</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="520" left="78" top="903" width="67.2" height="14.4" align-x="104.4" align-y="912" 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="inner">r</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">m</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.066675</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="517" left="198" top="896.4" width="46.8" height="27" align-x="225.6" align-y="912" 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="outer">r</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">D</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="519" left="258" top="903" width="67.2" height="14.4" align-x="284.4" align-y="912" 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="outer">r</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">m</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0746125</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="432" left="6" top="937.8" width="127.8" height="13.2" align-x="6" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Inner Area of Tube (A.i):<sp count="3"/> </p> </text> </region> <region region-id="433" left="174" top="939" width="49.8" height="14.4" align-x="189.6" 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:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">A</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="434" left="294" top="934.8" width="54.6" height="18.6" align-x="308.4" 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:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="i">A</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.15961285591571178</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="439" left="6" top="967.8" width="132.6" height="13.2" align-x="6" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Outer Area of Tube (A.o):<sp count="3"/> </p> </text> </region> <region region-id="437" left="174" top="969" width="54.6" height="14.4" align-x="192" align-y="978" 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">A</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="438" left="294" top="964.8" width="61.8" height="18.6" align-x="310.8" align-y="978" 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">A</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.17861438638186794</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="422" left="6" top="997.8" width="187.8" height="13.2" align-x="6" align-y="1008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Log Mean Area of Tube Body (A.lm):<sp count="3"/> </p> </text> </region> <region region-id="423" left="6" top="1020.6" width="131.4" height="46.8" align-x="27" align-y="1038" 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="lm">A</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="outer">r</ml:id> <ml:id xml:space="preserve" subscript="inner">r</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="outer">r</ml:id> <ml:id xml:space="preserve" subscript="inner">r</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="431" left="342" top="1024.8" width="64.8" height="18.6" align-x="361.8" align-y="1038" 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="lm">A</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.16893555420595516</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="440" left="6" top="1087.8" width="178.2" height="13.2" align-x="6" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Over All Heat Tranfer Coeff.<sp count="2"/>(U.o):<sp count="2"/> </p> </text> </region> <region region-id="442" left="6" top="1107" width="78.6" height="14.4" align-x="24.6" align-y="1116" 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">Δr</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="outer">r</ml:id> <ml:id xml:space="preserve" subscript="inner">r</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="443" left="126" top="1102.8" width="88.2" height="16.8" align-x="143.4" align-y="1116" 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">Δr</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">m</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0079375</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="meter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="451" left="18" top="1136.4" width="171" height="45" align-x="36.6" align-y="1152" 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:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="i">h</ml:id> <ml:id xml:space="preserve" subscript="i">A</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Δr</ml:id> <ml:id xml:space="preserve" subscript="i">A</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve" subscript="lm">A</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="o">h</ml:id> <ml:id xml:space="preserve" subscript="o">A</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="452" left="342" top="1136.4" width="81.6" height="31.2" align-x="359.4" align-y="1152" 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> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">W</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">m</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>21.007956225331306</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="coulomb" power-numerator="-1"/> <unitReference unit="meter" power-numerator="-2"/> <unitReference unit="watt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="528" left="12" top="1213.8" width="145.2" height="13.2" align-x="12" align-y="1224" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Interior Free Air Temp (T.i):<sp count="3"/> </p> </text> </region> <region region-id="529" left="174" top="1208.4" width="70.8" height="28.8" align-x="188.4" align-y="1224" 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">T</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Q</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="o">U</ml:id> <ml:id xml:space="preserve" subscript="i">A</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="o">T</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="530" left="360" top="1215" width="58.2" height="14.4" align-x="373.2" align-y="1224" 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">T</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">C</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>21.911396970928664</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="coulomb"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="534" left="360" top="1242.6" width="91.8" height="28.8" align-x="420.6" align-y="1260" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="i">T</ml:id> <ml:id xml:space="preserve">C</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:real>9</ml:real> <ml:real>5</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:real>32</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>71.4405145476716</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="1" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="matrix" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="31"/> </region> <region region-id="535" left="30" 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