<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="2022" minor="2"/>
<View-Properties presentation="true" autoexpanding_sections="true" UserProfileName="Maple Default Profile" NumericFormat-ApplyInteger="true" NumericFormat-ApplyRational="true" NumericFormat-ApplyExponent="false" editable="true">
</View-Properties>
<Styles>
<Font name="Heading 1" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[120,0,14]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkError" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Atomic Variable" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[175,0,175]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkWarning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="true" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="24" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Caption Reference" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Units" background="[255,255,255]" bold="true" executable="false" family="Arial" foreground="[128,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Segoe UI" foreground="[0,0,255]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Caption Text" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkError" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkWarning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
</Styles>
<Section-Style section-display-top="true" section-display-bottom="true" section-display-first-page="false" section-display-control="true" section-thickness="1.0" section-color="[128,128,128]" section-opacity="100" section-margin="0"/>
<Print-Borders/>
<MapleFlow-Canvas canvas-background-color="[255,255,255]" canvas-grid-color="[192,192,192]" canvas-grid-h-space="20" canvas-grid-v-space="20" canvas-opacity="1.0" canvas-show-h-grid="false" canvas-show-v-grid="false"><MapleFlow-Math origin="78.0,3119.0" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="1" bounds="40.0,3106.0,76.0,30.0">
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origin="340.5,82.5" fixed-width="false" fixed-height="false" bounds="20.0,80.0,635.0,3.0"><Image height="3" width="635" zoomable="true" labelreference="L615" drawcaption="false" captionalignment="0" captionposition="1">TUZOV3RLVWI8b2I8Uj1NRExDZE5OWnVbPT5bQFplUXVDUTw8ajpIUWNYTltub0hhXWNdPnZmO2djO2tSeXI/bHlqUDpgSnJcXG5mSEFXYmpuOz1SP0tjTDtOOjxqUGBOXFxATmRcXG9dcFhlQXZAPmBGTlprTnR3eWhoV3hiYVxcQnFsSF9vOmFec1g9UFJheT9PUkhxXW9QbEFuXVVGWj9mZVY+bXJdOkZjP29jPm9vPD9mPDw6Ojo6OjI6XCJce1x9<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQk9VTkRTX1lHRictJS1CT1VORFNfV0lEVEhHRictJS5CT1VORFNfSEVJR0hUR0YnLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></MapleFlow-Image><MapleFlow-Text origin="344.0,158.0" fixed-width="false" fixed-height="false" bounds="20.0,88.0,648.0,140.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Segoe UI" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">In this document, the 3-K method calculation of fittings' loss coefficient is introduced. There are
various types of calculation for pressure drop of fittings, e.g. Elbow, Tees. The 3-K method is
developed by Darby as the most accurate for all Reynolds numbers and fitting sizes. However,
in terms of Mass flow rate calculation, the solution can not be obtained directly with the set of
equations. 

So, as the first step, the steps of how to manipulate the set of equation is explanied. after that,
the validation of the manipulation is performed with an example case.</Font></Text-field></MapleFlow-Text><MapleFlow-Image origin="339.5,954.0" fixed-width="false" fixed-height="false" bounds="20.0,960.0,635.0,2.0"><Image height="2" width="635" zoomable="true" labelreference="L793" drawcaption="false" captionalignment="0" captionposition="1">TUZOV3RLVWI8b2I8Uj1NRExDZE5OWnVbPD5bQFpabmpUdlBGWm1PZEFPQldnbXNSdEI7SVVKVVRKRnBJWFt2SWY/WkM+aEJHZW1LQUxGV2o6UHNPdGpHakxgTlxcQE5kXFxvXXB4XFxBdj48Sko8S1o9VW91eVdodEFYVFZES05wb2RhcTo+YEpxeUFCUnNmaHdZbz1yOmtoYTtFZj46TVRLV0RLV2dKO2VaOjo6OjE6XCJce1x9<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQk9VTkRTX1lHRictJS1CT1VORFNfV0lEVEhHRictJS5CT1VORFNfSEVJR0hUR0YnLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></MapleFlow-Image><MapleFlow-Text origin="143.5,928.5" fixed-width="false" fixed-height="false" bounds="20.0,923.0,241.0,29.0"><Text-field style="Heading 1" layout="Heading 1">1. Equation manipulation</Text-field></MapleFlow-Text><MapleFlow-Text origin="257.0,298.0" fixed-width="false" fixed-height="false" bounds="20.0,968.0,634.0,16.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">The pressure drop of fittings with 3-K method is calculated with the following set of equations.</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="344.0,799.0" fixed-width="false" fixed-height="false" bounds="40.0,748.0,594.0,100.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">References:
 - Ron Darby, Chemical Engineering Fluid Mechanics 2nd edition, Marcel Dekker, 2001
 - Ron Darby, Correlate pressure drop through pipe fittings, Chemical Engineering, 
                       -New York- Mcgraw Hill Incorporated then Chemical Week Publishing Llc-,
                       vol 106, 1999.</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="339.0,1191.0" fixed-width="false" fixed-height="false" bounds="20.0,1168.0,638.0,40.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Thus, in order to obtain the equation for Mass flow rate calculation, need to solve a polynomial.
The polynomial can be obtained with the following steps.</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="209.5,1422.0" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="12" bounds="40.0,1281.0,335.0,72.0">
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</Group></MapleFlow-Math><MapleFlow-Text origin="139.0,1473.0" fixed-width="false" fixed-height="false" bounds="20.0,1368.0,226.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Eq2 can be manipulated wth Eq5</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="268.5,1531.0" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="13" bounds="40.0,1388.0,445.0,72.0">
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Text origin="109.5,1582.0" fixed-width="false" fixed-height="false" bounds="20.0,1468.0,159.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Substitue Eq8 into Eq6</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="336.5,1645.0" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="14" bounds="40.0,1491.0,577.0,102.0">
<Group view="presentation" inline-output="true" labelreference="L1101" drawlabel="true" applyint="true" applyrational="true" applyexponent="false"><MapleFlow-Row family="Arial" size="12" bold="false" italic="false" underline="false" subscript="false" superscript="false" foreground="[0,0,0]" background="[255,255,255]" opaque="true" executable="false" readonly="false" composed="false" converted="false" imselected="false" placeholder="false" selection-placeholder="false" mathcolor="[0,0,0]" mathbackground="[255,255,255]" fontfamily="Arial" mathvariant="normal" mathsize="12">
<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Text origin="122.5,1710.0" fixed-width="false" fixed-height="false" bounds="20.0,1608.0,167.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Reorganize Eq9 as Eq10</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="314.5,1775.5" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="15" bounds="100.0,1648.0,401.0,67.0">
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiUtRiM2KS1JJm1mcmFjR0YkNigtRiM2Ky1JJW1zdWJHRiQ2Ji1GLDYmUSJLRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JlEiMUYnRj9GQkZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1JI21vR0YkNi5RJyZzZG90O0YnRkJGRS8lJmZlbmNlR0ZBLyUqc2VwYXJhdG9yR0ZBLyUpc3RyZXRjaHlHRkEvJSpzeW1tZXRyaWNHRkEvJShsYXJnZW9wR0ZBLyUubW92YWJsZWxpbWl0c0dGQS8lJ2FjY2VudEdGQS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRl9vLUYsNiZRIkFGJ0Y/RkJGRUZRLUYsNiZRJSZtdTtGJ0Y/RkJGRS8lK2V4ZWN1dGFibGVHRkEvJSlyZWFkb25seUdRJXRydWVGJy9GQ1EqMkR+T3V0cHV0RidGRS1GIzYpLUYsNiZRJm1mbG93RidGP0ZCRkVGUS1GOjYmLUYsNiZRIkRGJ0Y/RkJGRS1GLDYmUSJoRidGP0ZCRkVGS0ZORmhvRmpvRl1wRkUvJS5saW5ldGhpY2tuZXNzR0ZKLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBxLyUpYmV2ZWxsZWRHRkEtRlI2LlEnJnBsdXM7RidGQkZFRlVGV0ZZRmVuRmduRmluRltvL0Zeb1EsMC4yMjIyMjIyZW1GJy9GYW9GaXEtRiM2KS1GOjYmRjwtRiw2JlEiaUYnRj9GQkZFRktGTkZRLUYwNiUtRiM2KS1JI21uR0YkNiVGSkZCRkVGZXEtRjU2KC1GOjYmRjwtRiw2JlEiZEYnRj9GQkZFRktGTi1JJW1zdXBHRiQ2JS1GOjYmRmZwLUYsNiZRJWhfaW5GJ0Y/RkJGRUZLRk4tRmdyNiZRJjAuMzAwRidGQkZFL0ZPUSMuM0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdGTUZccUZecUZhcUZjcUZob0Zqb0ZdcEZFRkJGRUZob0Zqb0ZdcEZFRmhvRmpvRl1wRkVGQkZFRlEtRmFzNiVGYXAtRmdyNiVRIjJGJ0ZCRkVGXXQtRlI2LlEiPUYnRkJGRUZVRldGWUZlbkZnbkZpbkZbby9GXm9RLDAuMjc3Nzc3OGVtRicvRmFvRmh0RmF0RlEtRiw2JlEnJiM5NjE7RidGP0ZCRkVGUS1GYXM2JUZiby1GIzYlRmF0RkJGRUZddEZRLUYsNiZRI2RwRidGP0ZCRkUvJSdmYW1pbHlHUSZBcmlhbEYnRmhvRkU=">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</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Math origin="298.0,1768.5" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="16" bounds="40.0,1728.0,492.0,67.0">
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Text origin="179.0,1315.0" fixed-width="false" fixed-height="false" bounds="20.0,1848.0,300.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Substitute terms in Eq10 with the followings</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="143.5,1376.5" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="17" bounds="40.0,1888.0,175.0,67.0">
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JJ1NpbXBsZUc2JC9JK21vZHVsZW5hbWVHNiJJJlVuaXRzRzYkSShfc3lzbGliR0YoJSpwcm90ZWN0ZWRHRixJIipHRiw2JC1GIzYkJCIrKysrK10hIzUtX0YkSSIrR0YsNiQtX0YkSSItRzYkRixGKzYjSSJZR0YoLV9GJEklc3FydEdGOzYjLUY1NiQtRiM2JC1GIzYkIiIlSSJYR0YoSSJaR0YoLV9GJEkiXkdGLDYkRj0iIiMtX0YkSSIvR0Y7NiNGSQ==</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Text origin="277.0,1703.0" fixed-width="false" fixed-height="false" bounds="20.0,2228.0,510.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Because the mass flow rate </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmbWZsb3dGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUnZmFtaWx5R1EmQXJpYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmbWZsb3dGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUnZmFtaWx5R1EmQXJpYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg==</Equation><Font style="Text"> needs to be positive value, the solution is</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="202.0,1752.5" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="22" bounds="40.0,2275.0,320.0,45.0">
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<Input><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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</Group></MapleFlow-Math><MapleFlow-Text origin="335.5,2405.0" fixed-width="false" fixed-height="false" bounds="20.0,2388.0,617.0,40.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">The final equation will be obtained by substituting X, Y, Z, and considering the flow direction
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</Group></MapleFlow-Math><MapleFlow-Text origin="28.0,2791.0" fixed-width="false" fixed-height="false" bounds="21.0,2788.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">In this section, the obtained equation is validated with an example case. The following is the
condition of this example calculation.</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="48.0,2911.0" fixed-width="false" fixed-height="false" bounds="41.0,2908.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Hydraulic diameter</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="76.5,2998.0" fixed-width="false" fixed-height="false" bounds="40.0,2988.0,73.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Flow area</Font></Text-field></MapleFlow-Text><MapleFlow-Image origin="343.5,3680.5" fixed-width="false" fixed-height="false" bounds="20.0,3720.0,635.0,1.0"><Image height="1" width="635" zoomable="true" labelreference="L617" drawcaption="false" captionalignment="0" captionposition="1">TUZOV3RLVWI8b2I8Uj1NRExDZE5OWnVbOz5bQFpgUFxcYkc9RlptT2RBT0JXZ21zUnRCO0lVSlVUSkZwSVhbdklmP1pDPmhCR2VtS0FERldqOlBLTmROOj9aOm5dQ19iO19kQldjZ1lyO0g7W0M9O0hiY3l5QXdvd1hGY0JhT1lRbnFNV1ttQWk7Rlp0SWlvWUU+WkNnYkhfYmhQYlpPSjo6OjoyOlwiXHtcfQ==<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQk9VTkRTX1lHRictJS1CT1VORFNfV0lEVEhHRictJS5CT1VORFNfSEVJR0hUR0YnLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></MapleFlow-Image><MapleFlow-Text origin="209.5,3665.5" fixed-width="false" fixed-height="false" bounds="20.0,3683.0,369.0,29.0"><Text-field style="Heading 1" layout="Heading 1">2-1. Pressure drop from Mass flow rate</Text-field></MapleFlow-Text><MapleFlow-Text origin="315.0,3697.0" fixed-width="false" fixed-height="false" bounds="20.0,3728.0,574.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">The pressure drop can be calculated directly from the set of equtions for 3-K method.</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="98.0,3757.0" fixed-width="false" fixed-height="false" bounds="20.0,3788.0,148.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Mas flow rate setting</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="74.5,3821.0" fixed-width="false" fixed-height="false" bounds="20.0,3848.0,95.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Flow velocity</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="28.0,3871.0" fixed-width="false" fixed-height="false" bounds="21.0,3908.0,126.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Reynolds number</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="80.5,3933.0" fixed-width="false" fixed-height="false" bounds="20.0,3968.0,111.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Loss coefficient</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="74.5,3996.0" fixed-width="false" fixed-height="false" bounds="20.0,4028.0,101.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Pressure drop</Font></Text-field></MapleFlow-Text><MapleFlow-Image origin="338.5,4098.5" fixed-width="false" fixed-height="false" bounds="21.0,4138.0,635.0,1.0"><Image height="1" width="635" zoomable="true" labelreference="L617" drawcaption="false" captionalignment="0" captionposition="1">TUZOV3RLVWI8b2I8Uj1NRExDZE5OWnVbOz5bQFpgUFxcYkc9RlptT2RBT0JXZ21zUnRCO0lVSlVUSkZwSVhbdklmP1pDPmhCR2VtS0FERldqOlBLTmROOj9aOm5dQ19iO19kQldjZ1lyO0g7W0M9O0hiY3l5QXdvd1hGY0JhT1lRbnFNV1ttQWk7Rlp0SWlvWUU+WkNnYkhfYmhQYlpPSjo6OjozOlwiXHtcfQ==<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQk9VTkRTX1lHRictJS1CT1VORFNfV0lEVEhHRictJS5CT1VORFNfSEVJR0hUR0YnLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></MapleFlow-Image><MapleFlow-Text origin="205.5,4075.5" fixed-width="false" fixed-height="false" bounds="21.0,4103.0,369.0,29.0"><Text-field style="Heading 1" layout="Heading 1">2-2. Mass flow rate from Pressure drop</Text-field></MapleFlow-Text><MapleFlow-Text origin="48.0,3231.0" fixed-width="false" fixed-height="false" bounds="41.0,3228.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Density</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="48.0,3391.0" fixed-width="false" fixed-height="false" bounds="41.0,3388.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Viscosity</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="28.0,4151.0" fixed-width="false" fixed-height="false" bounds="21.0,4148.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">In order to validate the obtained equation in section 1, calculate mass flow rate with the result
that is calculated in 2-1.</Font></Text-field></MapleFlow-Text><MapleFlow-Text origin="71.5,4221.0" fixed-width="false" fixed-height="false" bounds="20.0,4208.0,101.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Pressure drop</Font></Text-field></MapleFlow-Text><MapleFlow-Math origin="285.5,4215.0" symbolic="false" hidden-parts="0" background-color="-1" error-status="OK" evaluationID="35" bounds="180.0,4199.0,205.0,34.0">
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</Group></MapleFlow-Math><MapleFlow-Text origin="28.0,4391.0" fixed-width="false" fixed-height="false" bounds="21.0,4388.0,200.0,20.0"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="12" readonly="false" background="[255,255,255]" placeholder="false" family="Arial" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"><Font style="Text">Therefore, we can confirm the manipulation of the set of equations is appropriate. </Font></Text-field></MapleFlow-Text><MapleFlow-Image origin="340.0,492.5" fixed-width="false" fixed-height="false" bounds="100.0,300.0,450.0,391.0"><Image height="391" width="450" zoomable="true" labelreference="L1230" drawcaption="false" captionalignment="0" 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