Mathcad Professional 14.0 <description/> <author>Gerhard</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy>Gerhard</revisedBy> </userData> <identityInfo> <revision>4</revision> <documentID>BE6D8B29-2061-4306-AECC-D552FADA2383</documentID> <versionID>E48CA068-1A08-4E7A-B9A1-C40E85DEBD4C</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="Überschrift 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" 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margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Untertitel" base-style="Titel"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" 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="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> 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font-style="normal" underline="false"/> <mathStyle name="Benutzer 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Benutzer 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Mathematische Text-Schriftart" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="masse" length="länge" time="zeit" current="strom" thermodynamic-temperature="temperatur" luminous-intensity="lichtstärke" amount-of-substance="stoff" 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="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" 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="8" orientation="landscape" print-single-page-width="false" page-width="1190.4" page-height="841.8"> <margins left="12" right="12" top="12" bottom="17.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="de" UI="de"/> </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="true" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC12" local-assignment="MC12"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <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="971" 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="924" left="54" top="3" width="511.8" height="18.6" align-x="74.4" 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="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="16"> <u> <inlineAttr font-weight="normal">Volumen als Funktion der Füllhöhe bei zusammengesetzten Körperformen:</inlineAttr> </u> </f> </p> </text> </region> <region region-id="969" left="510" top="33" width="211.8" height="10.8" align-x="527.4" align-y="42" 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">Beispiel : Kugelvolumen bei beliebigem Füllstand</p> </text> </region> <region region-id="971" left="750" top="30.6" width="242.4" height="442.2" align-x="781.8" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">Anmerkungen :</f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">1. Berechnung ist die untere Halbkugel als </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">"</f> <f size="12"> <b>Kugelsegment</b> </f> <f size="12">" mit Hilfe der steigenden </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">"Bereichsvariablen" </f> <f size="12"> <b>h</b> </f> <f size="12"> <b> <sub>u </sub> </b> </f> <f size="12">von Füllhöhe </f> <f size="12"> <b>0</b> </f> <f size="12"> bis </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Füllhöhe </f> <b> <f size="12">r</f> </b> <f size="12">. Ergebnisse in Tabelle </f> <b> <f size="12">V</f> </b> <f size="12"> <sub> <b>u</b> </sub> </f> <f size="12"> <b>(h</b> </f> <f size="12"> <b> <sub>u</sub> </b> </f> <f size="12"> <b>)</b> </f> <f size="12">.</f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">2. Berechnung ist die obere Halbkugel als </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12">"</f> <f size="12"> <b>Kugelschicht</b> </f> <f size="12">" vom Mittelpunkt aufwärts. </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Das Volumen </f> <f size="12">der Kugelschicht ergibt sich </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">durch Subtraktion von oberer Halbkugel ab-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">züglich verbleibendes "Kugelsegment". </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Das jeweilige Gesamtvolumen ergibt sich </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">durch Addition des unteren Halbkugelvolu-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">mens. Mit Hilfe der fallenden </f> <f size="12">"Bereichsvari-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">ablen" </f> <b> <f size="12">h</f> </b> <f size="12"> <b> <sub>o</sub> </b> </f> <f size="12"> von Füllhöhe </f> <b> <f size="12">r</f> </b> <f size="12"> bis Füllhöhe </f> <b> <f size="12">0 </f> </b> <f size="12">ent-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">stehen die Ergebnisse in der Tabelle </f> <b> <f size="12">V</f> </b> <b> <f size="12"> <sub>o</sub> </f> </b> <b> <f size="12">(h</f> </b> <f size="12"> <b> <sub>o</sub> </b> </f> <b> <f size="12">)</f> </b> <f size="12">.</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Nun wird auf dem Arbeitsblatt eine leere Ta-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">belle eingefügt (</f> <f size="12"> <b>V</b> </f> <f size="12"> <b> <sub>r50</sub> </b> </f> <f size="12">). </f> <f size="12">Die Inhalte der beiden </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Tabellen [</f> <f size="12"> <b>Vu(hu) / Vo(ho)</b> </f> <f size="12">] werden hinter-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">einander in eine Excel-Tabellenspalte kopiert </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">(Endwert von 1. Tabelle ist gleichzeitig An-</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">fangswert von 2. Tabelle). </f> <f size="12">Alle gefüllte Zellen </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">dieser Spalte werden nun kopiert und mit </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">dem Befehl "</f> <b> <f size="12">Tabelle einfügen</f> </b> <f size="12">" in die leere </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Tabelle </f> <f size="12">des Mathcad-Arbeitsblattes eingefügt.</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">Im Diagramm wird für die X-Achse der Index </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">(h</f> <f size="12"> <sub>F</sub> </f> <f size="12">) durch die Tastenkombination ( AltGr+[ ) </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="12">erzeugt.</f> </p> </text> </region> <region region-id="926" left="60" top="37.8" width="58.2" height="14.4" align-x="88.2" align-y="48" 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">Kugelradius</ml:id> </math> <rendering item-idref="2"/> </region> <region region-id="927" left="132" top="37.8" width="49.8" height="14.4" align-x="145.2" align-y="48" 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